Finite Group Databasebeta

← C2×C11⋊C5×#3861 #30633513

Subgroups — C2×C11⋊C5×#3861 #30633513

Order 16170.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11⋊C5×#3861C211yesmaximal, characteristic, direct product factor, Hall
2C2×C72×C11⋊C5C311yesmaximal, characteristic, complemented, Hall
3C2×C11×#3861C511yesmaximal, characteristic, complemented, Hall
4C72×C11⋊C5C2×C311yescharacteristic, complemented, Hall
5C2×ΓL(1,𝔽8)×C11⋊C5—78nomaximal
6C11×#3861C2×C511yescharacteristic, complemented, Hall
7C2×C5×#3861—111nomaximal, Hall
8ΓL(1,𝔽8)×C11⋊C5—78no—
9C2×C72×C11C3×C511yescharacteristic, complemented, Hall
10C2×C7×C11⋊C5ΓL(1,𝔽8)18yescomplemented
11C5×#3861—111noHall
12C72×C11C2×C3×C511yescharacteristic, complemented, Hall
13C2×C5×C72—111noHall
14C2×C11×ΓL(1,𝔽8)—78no—
15C7×C11⋊C5C2×ΓL(1,𝔽8)18yescomplemented
16C2×C3×C11⋊C5—491noHall
17C2×#3861C11⋊C511yescharacteristic, direct product factor, Hall
18C5×C72—111noHall
19C11×ΓL(1,𝔽8)—78no—
20C2×C5×ΓL(1,𝔽8)—778no—
21C3×C11⋊C5—491noHall
22C2×C7×C11C5×ΓL(1,𝔽8)18yescomplemented
23#3861C2×C11⋊C511yescharacteristic, direct product factor, Hall
24C2×C11⋊C5#386111yescharacteristic, direct product factor, Hall
25C5×ΓL(1,𝔽8)—778no—
26C2×C72C3×C11⋊C511yescharacteristic, complemented, Hall
27C7×C11C2×C5×ΓL(1,𝔽8)18yescomplemented
28C2×C5×C7—118no—
29C2×C3×C11—491noHall
30C11⋊C5C2×#386111yescharacteristic, direct product factor, Hall
31C72C2×C3×C11⋊C511yescharacteristic, complemented, Sylow
32C2×ΓL(1,𝔽8)—78no—
33C5×C7—118no—
34C3×C11—491noHall
35C2×C3×C5—5391noHall
36C2×C11C5×#386111yescharacteristic, complemented, Hall
37ΓL(1,𝔽8)—78no—
38C3×C5—5391noHall
39C2×C7ΓL(1,𝔽8)×C11⋊C518yescomplemented
40C11C2×C5×#386111yescharacteristic, complemented, Sylow
41C2×C5—111noHall
42C7C2×ΓL(1,𝔽8)×C11⋊C518yescomplemented
43C2×C3—491noHall
44C5—111noSylow
45C3—491noSylow
46C2C11⋊C5×#386111yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2C11⋊C5×#3861
commutator, cosocle, hypocenterC72×C11C2×C3×C5
FrattiniC1G
Fitting, socleC2×C72×C11C3×C5
LCSG ▷ C72×C11
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C11⋊C5×#3861C2direct (N × H)
2. C2×C72×C11⋊C5C3semidirect
3. C2×C11×#3861C5semidirect
4. C72×C11⋊C5C2×C3semidirect
6. C11×#3861C2×C5semidirect
9. C2×C72×C11C3×C5semidirect
10. C2×C7×C11⋊C5ΓL(1,𝔽8)semidirect
12. C72×C11C2×C3×C5semidirect
15. C7×C11⋊C5C2×ΓL(1,𝔽8)semidirect
17. C2×#3861C11⋊C5direct (N × H)
22. C2×C7×C11C5×ΓL(1,𝔽8)semidirect
23. #3861C2×C11⋊C5direct (N × H)
24. C2×C11⋊C5#3861direct (N × H)
26. C2×C72C3×C11⋊C5semidirect
27. C7×C11C2×C5×ΓL(1,𝔽8)semidirect
30. C11⋊C5C2×#3861direct (N × H)
31. C72C2×C3×C11⋊C5semidirect
36. C2×C11C5×#3861semidirect
39. C2×C7ΓL(1,𝔽8)×C11⋊C5semidirect
40. C11C2×C5×#3861semidirect
42. C7C2×ΓL(1,𝔽8)×C11⋊C5semidirect
46. C2C11⋊C5×#3861direct (N × H)

Maximal subgroups

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

subgroupindex
C11⋊C5×#38612
C2×C72×C11⋊C53
C2×C11×#38615
C2×ΓL(1,𝔽8)×C11⋊C57
C2×C5×#386111