Finite Group Databasebeta

← C2×C3×C13×C23⋊C11 #34089395

Subgroups — C2×C3×C13×C23⋊C11 #34089395

Order 19734.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C13×C23⋊C11C211yesmaximal, characteristic, direct product factor, Hall
2C2×C13×C23⋊C11C311yesmaximal, characteristic, direct product factor, Hall
3C13×C23⋊C11C2×C311yescharacteristic, direct product factor, Hall
4C2×C3×C13×C23C1111yesmaximal, characteristic, complemented, Hall
5C2×C3×C23⋊C11C1311yesmaximal, characteristic, direct product factor, Hall
6C3×C13×C23C2×C1111yescharacteristic, complemented, Hall
7C2×C3×C11×C13—231nomaximal, Hall
8C3×C23⋊C11C2×C1311yescharacteristic, direct product factor, Hall
9C2×C13×C23C3×C1111yescharacteristic, complemented, Hall
10C2×C23⋊C11C3×C1311yescharacteristic, direct product factor, Hall
11C3×C11×C13—231noHall
12C13×C23C2×C3×C1111yescharacteristic, complemented, Hall
13C2×C11×C13—231noHall
14C23⋊C11C2×C3×C1311yescharacteristic, direct product factor, Hall
15C11×C13—231noHall
16C2×C3×C23C11×C1311yescharacteristic, complemented, Hall
17C2×C3×C13C23⋊C1111yescharacteristic, direct product factor, Hall
18C3×C23C2×C11×C1311yescharacteristic, complemented, Hall
19C2×C3×C11—231noHall
20C2×C23C3×C11×C1311yescharacteristic, complemented, Hall
21C3×C13C2×C23⋊C1111yescharacteristic, direct product factor, Hall
22C3×C11—231noHall
23C2×C13C3×C23⋊C1111yescharacteristic, direct product factor, Hall
24C23C2×C3×C11×C1311yescharacteristic, complemented, Sylow
25C2×C11—231noHall
26C13C2×C3×C23⋊C1111yescharacteristic, direct product factor, Sylow
27C11—231noSylow
28C2×C3C13×C23⋊C1111yescharacteristic, direct product factor, Hall
29C3C2×C13×C23⋊C1111yescharacteristic, direct product factor, Sylow
30C2C3×C13×C23⋊C1111yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2×C3×C13C23⋊C11
commutator, cosocle, hypocenterC23C2×C3×C11×C13
FrattiniC1G
Fitting, socleC2×C3×C13×C23C11
LCSG ▷ C23
UCSC1 ◁ C2×C3×C13

Complements

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

NH ≅ G/Ntype
1. C3×C13×C23⋊C11C2direct (N × H)
2. C2×C13×C23⋊C11C3direct (N × H)
3. C13×C23⋊C11C2×C3direct (N × H)
4. C2×C3×C13×C23C11semidirect
5. C2×C3×C23⋊C11C13direct (N × H)
6. C3×C13×C23C2×C11semidirect
8. C3×C23⋊C11C2×C13direct (N × H)
9. C2×C13×C23C3×C11semidirect
10. C2×C23⋊C11C3×C13direct (N × H)
12. C13×C23C2×C3×C11semidirect
14. C23⋊C11C2×C3×C13direct (N × H)
16. C2×C3×C23C11×C13semidirect
17. C2×C3×C13C23⋊C11direct (N × H)
18. C3×C23C2×C11×C13semidirect
20. C2×C23C3×C11×C13semidirect
21. C3×C13C2×C23⋊C11direct (N × H)
23. C2×C13C3×C23⋊C11direct (N × H)
24. C23C2×C3×C11×C13semidirect
26. C13C2×C3×C23⋊C11direct (N × H)
28. C2×C3C13×C23⋊C11direct (N × H)
29. C3C2×C13×C23⋊C11direct (N × H)
30. C2C3×C13×C23⋊C11direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C13×C23⋊C112
C2×C13×C23⋊C113
C2×C3×C13×C2311
C2×C3×C23⋊C1113
C2×C3×C11×C1323