Finite Group Databasebeta

← C2×C11⋊C5×D31 #20291908

Subgroups — C2×C11⋊C5×D31 #20291908

Order 6820.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11⋊C5×D31C212yesmaximal, direct product factor
2C2×C31×C11⋊C5C211yesmaximal, characteristic, complemented
3C31×C11⋊C5C2211yescharacteristic, complemented, Hall
4C2×C11×D31C511yesmaximal, characteristic, complemented, Hall
5C2×C11×C31C2×C511yescharacteristic, complemented
6C11×D31C2×C512yescomplemented
7C2×C5×D31—111nomaximal, Hall
8C11×C31C22×C511yescharacteristic, complemented, Hall
9C2×C5×C31—111no—
10C5×D31—112no—
11C22×C11⋊C5—311nomaximal, Hall
12C5×C31—111noHall
13C2×D31C11⋊C511yescharacteristic, direct product factor, Hall
14C2×C11⋊C5—312no—
15C2×C11⋊C5D3111yescharacteristic, direct product factor
16C2×C31C2×C11⋊C511yescharacteristic, complemented
17D31C2×C11⋊C512yesdirect product factor
18C11⋊C5C2×D3111yescharacteristic, direct product factor, Hall
19C22×C11—311noHall
20C31C22×C11⋊C511yescharacteristic, complemented, Sylow
21C2×C11—312no—
22C2×C11C5×D3111yescharacteristic, complemented
23C22×C5—3411noHall
24C11C2×C5×D3111yescharacteristic, complemented, Sylow
25C2×C5—111no—
26C2×C5—3412no—
27C5—111noSylow
28C22—311noSylow
29C2—312no—
30C2C11⋊C5×D3111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C11⋊C5×D31
commutator, hypocenterC11×C31C22×C5
FrattiniC1G
Fitting, socleC2×C11×C31C2×C5
LCSG ▷ C11×C31
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C11⋊C5×D31C2direct (N × H)
2. C2×C31×C11⋊C5C2semidirect
3. C31×C11⋊C5C22semidirect
4. C2×C11×D31C5semidirect
5. C2×C11×C31C2×C5semidirect
6. C11×D31C2×C5semidirect
8. C11×C31C22×C5semidirect
13. C2×D31C11⋊C5direct (N × H)
15. C2×C11⋊C5D31direct (N × H)
16. C2×C31C2×C11⋊C5semidirect
17. D31C2×C11⋊C5direct (N × H)
18. C11⋊C5C2×D31direct (N × H)
20. C31C22×C11⋊C5semidirect
22. C2×C11C5×D31semidirect
24. C11C2×C5×D31semidirect
30. C2C11⋊C5×D31direct (N × H)