Subgroup Information for GL2_5
Created in GAP4 by M. Schaps
- H
= C1=
SM_1 of order 1. Class: 1 Length: 1 Order: 1
G = (C5XC5):H =
SM_2 of order 25 =
C5XC5
k(B) = 25, l(B) = 1
- H
= C2=
SM_1 of order 2. Class: 2 Length: 1 Order: 2
G = (C5XC5):H =
SM_4 of order 50 =
(C5XC5):C2
k(B) = 14, l(B) = 2
- H
= C2=
SM_1 of order 2. Class: 3 Length: 30 Order: 2
G = (C5XC5):H =
SM_3 of order 50 =
D10XC5
k(B) = 20, l(B) = 2
- H
= C3=
SM_1 of order 3. Class: 4 Length: 10 Order: 3
G = (C5XC5):H =
SM_2 of order 75 =
(C5XC5):C3
k(B) = 11, l(B) = 3
- H
= C4=
SM_1 of order 4. Class: 5 Length: 1 Order: 4
G = (C5XC5):H =
SM_11 of order 100 =
(C5XC5):C4
k(B) = 10, l(B) = 4
Non-trivial central extensions by C2:
C8 =
SM_1
of order 8
, k(B2) = 10, l(B2) = 4;
SM_20
of order 200
- H
= C2XC2=
SM_2 of order 4. Class: 6 Length: 15 Order: 4
G = (C5XC5):H =
SM_13 of order 100 =
D10XD10
k(B) = 16, l(B) = 4
Maximal subgroups: H1 =C2
H2 =C2
H3 =C2
Non-trivial central extensions by C2:
C4XC2 =
SM_2
of order 8
, k(B2) = 16, l(B2) = 4;
SM_23
of order 200
D8 =
SM_3
of order 8
, k(B2) = 13, l(B2) = 1;
SM_25
of order 200
Q8 =
SM_4
of order 8
, k(B2) = 13, l(B2) = 1;
SM_26
of order 200
- H
= C4=
SM_1 of order 4. Class: 7 Length: 15 Order: 4
G = (C5XC5):H =
SM_12 of order 100 =
(C5XC5):C4
k(B) = 10, l(B) = 4
Non-trivial central extensions by C2:
C8 =
SM_1
of order 8
, k(B2) = 10, l(B2) = 4;
SM_21
of order 200
- H
= C4=
SM_1 of order 4. Class: 8 Length: 30 Order: 4
G = (C5XC5):H =
SM_9 of order 100 =
GQ20XC5
k(B) = 25, l(B) = 4
Non-trivial central extensions by C2:
C8 =
SM_1
of order 8
, k(B2) = 25, l(B2) = 4;
SM_18
of order 200
- H
= C4=
SM_1 of order 4. Class: 9 Length: 30 Order: 4
G = (C5XC5):H =
SM_10 of order 100 =
(C5XC5):C4
k(B) = 13, l(B) = 4
Non-trivial central extensions by C2:
C8 =
SM_1
of order 8
, k(B2) = 13, l(B2) = 4;
SM_19
of order 200
- H
= C6=
SM_2 of order 6. Class: 11 Length: 10 Order: 6
G = (C5XC5):H =
SM_6 of order 150
k(B) = 10, l(B) = 6
Maximal subgroups: H1 =C3
H2 =C2
- H
= S3=
SM_1 of order 6. Class: 12 Length: 20 Order: 6
G = (C5XC5):H =
SM_5 of order 150
k(B) = 13, l(B) = 3
Maximal subgroups: H1 =C3
H2 =C2
H3 =C2
H4 =C2
- H
= Q8=
SM_4 of order 8. Class: 13 Length: 5 Order: 8
G = (C5XC5):H =
SM_44 of order 200
k(B) = 8, l(B) = 5
Maximal subgroups: H1 =C4
H2 =C4
H3 =C4
Non-trivial central extensions by C2:
(C4:C4) =
SM_4
of order 16
, k(B2) = 8, l(B2) = 5;
SM_134
of order 400
- H
= C8=
SM_1 of order 8. Class: 14 Length: 10 Order: 8
G = (C5XC5):H =
SM_40 of order 200
k(B) = 11, l(B) = 8
Non-trivial central extensions by C2:
C16 =
SM_1
of order 16
, k(B2) = 11, l(B2) = 8;
SM_116
of order 400
- H
= C4XC2=
SM_2 of order 8. Class: 15 Length: 15 Order: 8
G = (C5XC5):H =
SM_42 of order 200
k(B) = 14, l(B) = 8
Maximal subgroups: H1 =C4
H2 =C2XC2
H3 =C4
Non-trivial central extensions by C2:
C4XC4 =
SM_2
of order 16
, k(B2) = 14, l(B2) = 8;
SM_124
of order 400
(C2XC2):C4 =
SM_3
of order 16
, k(B2) = 8, l(B2) = 2;
SM_125
of order 400
(C4:C4) =
SM_4
of order 16
, k(B2) = 8, l(B2) = 2;
SM_126
of order 400
C2XC8 =
SM_5
of order 16
, k(B2) = 14, l(B2) = 8;
SM_127
of order 400
C8:C2 =
SM_6
of order 16
, k(B2) = 8, l(B2) = 2;
SM_128
of order 400
- H
= D8=
SM_3 of order 8. Class: 16 Length: 15 Order: 8
G = (C5XC5):H =
SM_43 of order 200
k(B) = 14, l(B) = 5
Maximal subgroups: H1 =C4
H2 =C2XC2
H3 =C2XC2
Non-trivial central extensions by C2:
(C2XC2):C4 =
SM_3
of order 16
, k(B2) = 14, l(B2) = 5;
SM_129
of order 400
(C4:C4) =
SM_4
of order 16
, k(B2) = 14, l(B2) = 5;
SM_130
of order 400
D16 =
SM_7
of order 16
, k(B2) = 11, l(B2) = 2;
SM_131
of order 400
C8:C2 =
SM_8
of order 16
, k(B2) = 11, l(B2) = 2;
SM_132
of order 400
GQ16 =
SM_9
of order 16
, k(B2) = 11, l(B2) = 2;
SM_133
of order 400
- H
= C4XC2=
SM_2 of order 8. Class: 17 Length: 30 Order: 8
G = (C5XC5):H =
SM_41 of order 200
k(B) = 20, l(B) = 8
Maximal subgroups: H1 =C4
H2 =C4
H3 =C2XC2
Non-trivial central extensions by C2:
C4XC4 =
SM_2
of order 16
, k(B2) = 20, l(B2) = 8;
SM_117
of order 400
(C2XC2):C4 =
SM_3
of order 16
, k(B2) = 14, l(B2) = 2;
SM_118
of order 400
(C4:C4) =
SM_4
of order 16
, k(B2) = 14, l(B2) = 2;
SM_119
of order 400
C2XC8 =
SM_5
of order 16
, k(B2) = 20, l(B2) = 8;
SM_121
of order 400
C8:C2 =
SM_6
of order 16
, k(B2) = 14, l(B2) = 2;
SM_123
of order 400
- H
= GQ12=
SM_1 of order 12. Class: 21 Length: 10 Order: 12
G = (C5XC5):H =
SM_23 of order 300
k(B) = 8, l(B) = 6
Maximal subgroups: H1 =C6
H2 =C4
H3 =C4
H4 =C4
Non-trivial central extensions by C2:
C3:C8 =
SM_1
of order 24
, k(B2) = 8, l(B2) = 6;
SM_55
of order 600
- H
= C12=
SM_2 of order 12. Class: 22 Length: 10 Order: 12
G = (C5XC5):H =
SM_24 of order 300
k(B) = 14, l(B) = 12
Maximal subgroups: H1 =C6
H2 =C4
Non-trivial central extensions by C2:
C24 =
SM_2
of order 24
, k(B2) = 14, l(B2) = 12;
SM_56
of order 600
- H
= D12=
SM_4 of order 12. Class: 23 Length: 10 Order: 12
G = (C5XC5):H =
SM_25 of order 300
k(B) = 14, l(B) = 6
Maximal subgroups: H1 =S3
H2 =S3
H3 =C6
H4 =C2XC2
H5 =C2XC2
H6 =C2XC2
Non-trivial central extensions by C2:
C3:Q8 =
SM_4
of order 24
, k(B2) = 11, l(B2) = 3;
SM_57
of order 600
S3XC4 =
SM_5
of order 24
, k(B2) = 14, l(B2) = 6;
SM_58
of order 600
D24 =
SM_6
of order 24
, k(B2) = 11, l(B2) = 3;
SM_59
of order 600
GQ12XC2 =
SM_7
of order 24
, k(B2) = 14, l(B2) = 6;
SM_60
of order 600
D8PS3 =
SM_8
of order 24
, k(B2) = 11, l(B2) = 3;
SM_61
of order 600
- H
= D8YC4=
SM_13 of order 16. Class: 24 Length: 5 Order: 16
G = (C5XC5):H =
SM_207 of order 400
k(B) = 16, l(B) = 10
Maximal subgroups: H1 =D8
H2 =D8
H3 =D8
H4 =C4XC2
H5 =C4XC2
H6 =C4XC2
H7 =Q8
Non-trivial central extensions by C2:
(C4XC2):C4 =
SM_24
of order 32
, k(B2) = 16, l(B2) = 10;
SM_965
of order 800
D8XC4 =
SM_25
of order 32
, k(B2) = 16, l(B2) = 10;
SM_966
of order 800
Q8XC4 =
SM_26
of order 32
, k(B2) = 16, l(B2) = 10;
SM_967
of order 800
D8PD8 =
SM_28
of order 32
, k(B2) = 10, l(B2) = 4;
SM_968
of order 800
((C2XC2):C4)PQ8 =
SM_29
of order 32
, k(B2) = 10, l(B2) = 4;
SM_969
of order 800
(C4XC2XC2):C2 =
SM_30
of order 32
, k(B2) = 10, l(B2) = 4;
SM_970
of order 800
(C4XC4):C2 =
SM_31
of order 32
, k(B2) = 10, l(B2) = 4;
SM_971
of order 800
(C4XC4).C2 =
SM_32
of order 32
, k(B2) = 10, l(B2) = 4;
SM_972
of order 800
(C4XC4):C2 =
SM_33
of order 32
, k(B2) = 10, l(B2) = 4;
SM_973
of order 800
- H
= C4XC4=
SM_2 of order 16. Class: 25 Length: 15 Order: 16
G = (C5XC5):H =
SM_205 of order 400
k(B) = 25, l(B) = 16
Maximal subgroups: H1 =C4XC2
H2 =C4XC2
H3 =C4XC2
Non-trivial central extensions by C2:
(C2XC4):C4 =
SM_2
of order 32
, k(B2) = 13, l(B2) = 4;
SM_957
of order 800
C4XC8 =
SM_3
of order 32
, k(B2) = 25, l(B2) = 16;
SM_959
of order 800
C8:C4 =
SM_4
of order 32
, k(B2) = 13, l(B2) = 4;
SM_961
of order 800
- H
= C8:C2=
SM_6 of order 16. Class: 26 Length: 15 Order: 16
G = (C5XC5):H =
SM_206 of order 400
k(B) = 13, l(B) = 10
Maximal subgroups: H1 =C4XC2
H2 =C8
H3 =C8
Non-trivial central extensions by C2:
C8:C4 =
SM_4
of order 32
, k(B2) = 13, l(B2) = 10;
SM_962
of order 800
(C2XC2):C8 =
SM_5
of order 32
, k(B2) = 13, l(B2) = 10;
SM_963
of order 800
C4:C8 =
SM_12
of order 32
, k(B2) = 13, l(B2) = 10;
SM_964
of order 800
- H
= Q8:C3=
SM_3 of order 24. Class: 34 Length: 5 Order: 24
G = (C5XC5):H =
SM_150 of order 600
k(B) = 8, l(B) = 7
Maximal subgroups: H1 =Q8
H2 =C6
H3 =C6
H4 =C6
H5 =C6
Non-trivial central extensions by C2:
- H
= C3:C8=
SM_1 of order 24. Class: 35 Length: 10 Order: 24
G = (C5XC5):H =
SM_148 of order 600
k(B) = 13, l(B) = 12
Maximal subgroups: H1 =C12
H2 =C8
H3 =C8
H4 =C8
Non-trivial central extensions by C2:
C3:C16 =
SM_1
of order 48
, k(B2) = 13, l(B2) = 12;
SM_485
of order 1200
- H
= C24=
SM_2 of order 24. Class: 36 Length: 10 Order: 24
G = (C5XC5):H =
SM_149 of order 600
k(B) = 25, l(B) = 24
Maximal subgroups: H1 =C12
H2 =C8
Non-trivial central extensions by C2:
C48 =
SM_2
of order 48
, k(B2) = 25, l(B2) = 24;
SM_486
of order 1200
- H
= S3XC4=
SM_5 of order 24. Class: 37 Length: 10 Order: 24
G = (C5XC5):H =
SM_151 of order 600
k(B) = 16, l(B) = 12
Maximal subgroups: H1 =D12
H2 =C12
H3 =GQ12
H4 =C4XC2
H5 =C4XC2
H6 =C4XC2
Non-trivial central extensions by C2:
S3XC8 =
SM_4
of order 48
, k(B2) = 16, l(B2) = 12;
SM_487
of order 1200
C3S(C8SC2) =
SM_5
of order 48
, k(B2) = 10, l(B2) = 6;
SM_488
of order 1200
GQ12XC4 =
SM_11
of order 48
, k(B2) = 16, l(B2) = 12;
SM_489
of order 1200
C3:(C4:C4) =
SM_12
of order 48
, k(B2) = 10, l(B2) = 6;
SM_490
of order 1200
C3:((C4XC2):C2)) =
SM_14
of order 48
, k(B2) = 10, l(B2) = 6;
SM_491
of order 1200
- H
= (C4XC4):C2=
SM_11 of order 32. Class: 38 Length: 15 Order: 32
G = (C5XC5):H =
SM_1191 of order 800
k(B) = 20, l(B) = 14
Maximal subgroups: H1 =C8:C2
H2 =C4XC4
H3 =D8YC4
Non-trivial central extensions by C2:
(C8XC4):C2 =
SM_6
of order 64
, k(B2) = 20, l(B2) = 14;
SM_9789
of order 1600
(C8XC4).C2 =
SM_7
of order 64
, k(B2) = 20, l(B2) = 14;
SM_9790
of order 1600
(D8XC2):C4 =
SM_8
of order 64
, k(B2) = 11, l(B2) = 5;
SM_9791
of order 1600
(Q8XC2):C4 =
SM_9
of order 64
, k(B2) = 11, l(B2) = 5;
SM_9792
of order 1600
(D8XC2).C4 =
SM_10
of order 64
, k(B2) = 11, l(B2) = 5;
SM_9793
of order 1600
(C4:C4).C4 =
SM_11
of order 64
, k(B2) = 11, l(B2) = 5;
SM_9794
of order 1600
(C4XC4):C4 =
SM_20
of order 64
, k(B2) = 20, l(B2) = 14;
SM_9795
of order 1600
- H
= (Q8YC4):C3=
SM_33 of order 48. Class: 42 Length: 5 Order: 48
G = (C5XC5):H =
SM_947 of order 1200
k(B) = 16, l(B) = 14
Maximal subgroups: H1 =Q8:C3
H2 =D8YC4
H3 =C12
H4 =C12
H5 =C12
H6 =C12
Non-trivial central extensions by C2:
(Q8:C3)XC4 =
SM_69
of order 96
, k(B2) = 16, l(B2) = 14
- H
= C3S(C8SC2)=
SM_5 of order 48. Class: 43 Length: 10 Order: 48
G = (C5XC5):H =
SM_946 of order 1200
k(B) = 20, l(B) = 18
Maximal subgroups: H1 =S3XC4
H2 =C24
H3 =C3:C8
H4 =C8:C2
H5 =C8:C2
H6 =C8:C2
Non-trivial central extensions by C2:
C3:(C4:C8) =
SM_21
of order 96
, k(B2) = 20, l(B2) = 18
C3:(C8:C4) =
SM_22
of order 96
, k(B2) = 20, l(B2) = 18
C3:((C2XC2):C8) =
SM_27
of order 96
, k(B2) = 20, l(B2) = 18
- H
= ((C2XC2XC4):C3).C2=
SM_67 of order 96. Class: 45 Length: 5 Order: 96
G = (C5XC5):H of order 2400
k(B) = 20, l(B) = 16
Maximal subgroups: H1 =(Q8YC4):C3
H2 =(C4XC4):C2
H3 =(C4XC4):C2
H4 =(C4XC4):C2
H5 =C3:C8
H6 =C3:C8
H7 =C3:C8
H8 =C3:C8
Non-trivial central extensions by C2:
SM_183
of order 192
, k(B2) = 20, l(B2) = 16
All computations performed in GAP4
[GAP 99] the GAP Group, Version 4.2, Aachen,St.Andrews ,1999.
http://www-gap.dcs.st-and.ac.uk/~gap
Last Updated June 16, '02 using BlockHtml.gap, created by M. Schaps