Finite Group Databasebeta

← C13×H(7,𝔽2) #13112652

Subgroups — C13×H(7,𝔽2) #13112652

Order 1664.

5992 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#585C2128yesmaximal, complemented
2C2×C13×H(5,𝔽2)C2135yesmaximal, complemented
3C13×2−1+4C22156yescomplemented
4C13×H(5,𝔽2)C221280yescomplemented
5C2×C13×#41C221210yescomplemented
6C22×D4×C13C221105yescomplemented
7C24×C13C23130yescomplemented
8C13×#41C231560yescomplemented
9C2×Q8×C13C23170yescomplemented
10C2×D4×C13C231630yescomplemented
11C22×C4×C13C231105yescomplemented
12H(7,𝔽2)C1311yesmaximal, characteristic, direct product factor, Sylow
13C23×C13—830no—
14C23×C13C241105yes—
15Q8×C13C24156yes—
16D4×C13C241280yes—
17C2×C4×C13C241210yes—
18#585C2×C13128yescomplemented
19C2×H(5,𝔽2)C2×C13135yescomplemented
20C22×C13—4105no—
21C22×C13C25135yes—
22C4×C13C25128yes—
232−1+4C22×C13156yescomplemented
24H(5,𝔽2)C22×C131280yescomplemented
25C2×#41C22×C131210yescomplemented
26C22×D4C22×C131105yescomplemented
27C2×C13—235no—
28C2×C13C2611yescharacteristic
29C24C23×C13130yescomplemented
30#41C23×C131560yescomplemented
31C2×Q8C23×C13170yescomplemented
32C2×D4C23×C131630yescomplemented
33C22×C4C23×C131105yescomplemented
34C13H(7,𝔽2)11yescharacteristic, direct product factor, Sylow
35C23—830no—
36C23C24×C131105yes—
37Q8C24×C13156yes—
38D4C24×C131280yes—
39C2×C4C24×C131210yes—
40C22—4105no—
41C22C25×C13135yes—
42C4C25×C13128yes—
43C2—235no—
44C2C26×C1311yescharacteristic
subgroupG/H
center, socleC2×C13C26
commutator, Frattini, cosocleC2C26×C13
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#585C2semidirect
2. C2×C13×H(5,𝔽2)C2semidirect
3. C13×2−1+4C22semidirect
4. C13×H(5,𝔽2)C22semidirect
5. C2×C13×#41C22semidirect
6. C22×D4×C13C22semidirect
7. C24×C13C23semidirect
8. C13×#41C23semidirect
9. C2×Q8×C13C23semidirect
10. C2×D4×C13C23semidirect
11. C22×C4×C13C23semidirect
12. H(7,𝔽2)C13direct (N × H)
18. #585C2×C13semidirect
19. C2×H(5,𝔽2)C2×C13semidirect
23. 2−1+4C22×C13semidirect
24. H(5,𝔽2)C22×C13semidirect
25. C2×#41C22×C13semidirect
26. C22×D4C22×C13semidirect
29. C24C23×C13semidirect
30. #41C23×C13semidirect
31. C2×Q8C23×C13semidirect
32. C2×D4C23×C13semidirect
33. C22×C4C23×C13semidirect
34. C13H(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×#5852
C2×C13×H(5,𝔽2)2
H(7,𝔽2)13