Finite Group Databasebeta

← C2×C13×H(7,𝔽2) #15749440

Subgroups — C2×C13×H(7,𝔽2) #15749440

Order 3328.

60570 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×H(7,𝔽2)C2164yesmaximal, direct product factor
2C2×C13×#585C2128yesmaximal, complemented
3C22×C13×H(5,𝔽2)C2135yesmaximal, complemented
4C13×#585C221896yescomplemented
5C2×C13×2−1+4C22156yescomplemented
6C2×C13×H(5,𝔽2)C221280yescomplemented
7C2×C13×H(5,𝔽2)C2211120yescomplemented
8C22×C13×#41C221210yescomplemented
9C23×D4×C13C221105yescomplemented
10C25×C13C23130yescomplemented
11C13×2−1+4C231896yescomplemented
12C13×H(5,𝔽2)C2314480yescomplemented
13C2×C13×#41C231560yescomplemented
14C2×C13×#41C2313360yescomplemented
15C22×Q8×C13C23170yescomplemented
16C22×D4×C13C231630yescomplemented
17C22×D4×C13C2311680yescomplemented
18C23×C4×C13C231105yescomplemented
19C2×H(7,𝔽2)C1311yesmaximal, characteristic, direct product factor, Sylow
20C24×C13—860no—
21C24×C13C241105yes—
22C24×C13C241240yescomplemented
23C13×#41C2414480yescomplemented
24C2×Q8×C13C24156yes—
25C2×Q8×C13C241560yescomplemented
26C2×D4×C13C241280yes—
27C2×D4×C13C2415040yescomplemented
28C22×C4×C13C241210yes—
29C22×C4×C13C241840yescomplemented
30H(7,𝔽2)C2×C13164yesdirect product factor
31C2×#585C2×C13128yescomplemented
32C22×H(5,𝔽2)C2×C13135yescomplemented
33C23×C13—4210no—
34C23×C13—8240no—
35C23×C13C25135yes—
36C23×C13C251420yes—
37Q8×C13C251224yes—
38D4×C13C2511120yes—
39C2×C4×C13C251840yes—
40C2×C4×C13C25128yes—
41#585C22×C131896yescomplemented
42C2×2−1+4C22×C13156yescomplemented
43C2×H(5,𝔽2)C22×C131280yescomplemented
44C2×H(5,𝔽2)C22×C1311120yescomplemented
45C22×#41C22×C131210yescomplemented
46C23×D4C22×C131105yescomplemented
47C22×C13—270no—
48C22×C13—4420no—
49C22×C13C26170yes—
50C22×C13C2611yescharacteristic
51C4×C13C26156yes—
52C25C23×C13130yescomplemented
532−1+4C23×C131896yescomplemented
54H(5,𝔽2)C23×C1314480yescomplemented
55C2×#41C23×C131560yescomplemented
56C2×#41C23×C1313360yescomplemented
57C22×Q8C23×C13170yescomplemented
58C22×D4C23×C131630yescomplemented
59C22×D4C23×C1311680yescomplemented
60C23×C4C23×C131105yescomplemented
61C2×C13—270no—
62C2×C13H(7,𝔽2)12yesdirect product factor
63C2×C13C2711yescharacteristic
64C24—860no—
65C24C24×C131105yes—
66C24C24×C131240yescomplemented
67#41C24×C1314480yescomplemented
68C2×Q8C24×C13156yes—
69C2×Q8C24×C131560yescomplemented
70C2×D4C24×C131280yes—
71C2×D4C24×C1315040yescomplemented
72C22×C4C24×C131210yes—
73C22×C4C24×C131840yescomplemented
74C13C2×H(7,𝔽2)11yescharacteristic, direct product factor, Sylow
75C23—4210no—
76C23—8240no—
77C23C25×C13135yes—
78C23C25×C131420yes—
79Q8C25×C131224yes—
80D4C25×C1311120yes—
81C2×C4C25×C13128yes—
82C2×C4C25×C131840yes—
83C22—270no—
84C22—4420no—
85C22C26×C13170yes—
86C22C26×C1311yescharacteristic
87C4C26×C13156yes—
88C2—270no—
89C2C13×H(7,𝔽2)12yesdirect product factor
90C2C27×C1311yescharacteristic
subgroupG/H
center, socleC22×C13C26
commutator, Frattini, cosocleC2C27×C13
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C13×H(7,𝔽2)C2direct (N × H)
2. C2×C13×#585C2semidirect
3. C22×C13×H(5,𝔽2)C2semidirect
4. C13×#585C22semidirect
5. C2×C13×2−1+4C22semidirect
6. C2×C13×H(5,𝔽2)C22semidirect
7. C2×C13×H(5,𝔽2)C22semidirect
8. C22×C13×#41C22semidirect
9. C23×D4×C13C22semidirect
10. C25×C13C23semidirect
11. C13×2−1+4C23semidirect
12. C13×H(5,𝔽2)C23semidirect
13. C2×C13×#41C23semidirect
14. C2×C13×#41C23semidirect
15. C22×Q8×C13C23semidirect
16. C22×D4×C13C23semidirect
17. C22×D4×C13C23semidirect
18. C23×C4×C13C23semidirect
19. C2×H(7,𝔽2)C13direct (N × H)
22. C24×C13C24semidirect
23. C13×#41C24semidirect
25. C2×Q8×C13C24semidirect
27. C2×D4×C13C24semidirect
29. C22×C4×C13C24semidirect
30. H(7,𝔽2)C2×C13direct (N × H)
31. C2×#585C2×C13semidirect
32. C22×H(5,𝔽2)C2×C13semidirect
41. #585C22×C13semidirect
42. C2×2−1+4C22×C13semidirect
43. C2×H(5,𝔽2)C22×C13semidirect
44. C2×H(5,𝔽2)C22×C13semidirect
45. C22×#41C22×C13semidirect
46. C23×D4C22×C13semidirect
52. C25C23×C13semidirect
53. 2−1+4C23×C13semidirect
54. H(5,𝔽2)C23×C13semidirect
55. C2×#41C23×C13semidirect
56. C2×#41C23×C13semidirect
57. C22×Q8C23×C13semidirect
58. C22×D4C23×C13semidirect
59. C22×D4C23×C13semidirect
60. C23×C4C23×C13semidirect
62. C2×C13H(7,𝔽2)direct (N × H)
66. C24C24×C13semidirect
67. #41C24×C13semidirect
69. C2×Q8C24×C13semidirect
71. C2×D4C24×C13semidirect
73. C22×C4C24×C13semidirect
74. C13C2×H(7,𝔽2)direct (N × H)
89. C2C13×H(7,𝔽2)direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C13×H(7,𝔽2)2
C2×C13×#5852
C22×C13×H(5,𝔽2)2
C2×H(7,𝔽2)13