Finite Group Databasebeta

← C11×C5⋊#64424 #30633549

Subgroups — C11×C5⋊#64424 #30633549

Order 16170.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C11×#3861C211yesmaximal, characteristic, complemented, Hall
2C11×C5⋊(C7⋊D7)C311yesmaximal, characteristic, complemented, Hall
3C11×#64424—51nomaximal, Hall
4C5×C72×C11C2×C311yescharacteristic, complemented, Hall
5C11×C5⋊AGL(1,𝔽7)—78nomaximal
6C11×#3861D511yescharacteristic, complemented, Hall
7C5⋊#64424C1111yesmaximal, characteristic, direct product factor, Hall
8C5×C11×ΓL(1,𝔽8)—78no—
9C11×C7⋊D7—51noHall
10C11×D35—78no—
11C5×#3861C2×C1111yescharacteristic, complemented, Hall
12C72×C11C3×D511yescharacteristic, complemented, Hall
13C5⋊(C7⋊D7)C3×C1111yescharacteristic, complemented, Hall
14C11×AGL(1,𝔽7)—358no—
15C5×C7×C11AGL(1,𝔽7)18yescomplemented
16C3×D5×C11—491noHall
17#64424—51noHall
18C5×C72C2×C3×C1111yescharacteristic, complemented, Hall
19C11×ΓL(1,𝔽8)—78no—
20C5⋊AGL(1,𝔽7)—78no—
21C3×C5×C11—491noHall
22C11×D7—358no—
23#3861D5×C1111yescharacteristic, complemented, Hall
24D5×C11—491noHall
25C5×ΓL(1,𝔽8)—78no—
26C7⋊D7—51noHall
27C7×C11C5⋊AGL(1,𝔽7)18yescomplemented
28D35—78no—
29C2×C3×C11—2451noHall
30C5×C11#6442411yescharacteristic, complemented, Hall
31C72C3×D5×C1111yescharacteristic, complemented, Sylow
32AGL(1,𝔽7)—358no—
33C5×C7C11×AGL(1,𝔽7)18yescomplemented
34C3×C11—491noHall
35C3×D5—491noHall
36C2×C11—2451noHall
37ΓL(1,𝔽8)—78no—
38C3×C5—491noHall
39D7—358no—
40C11C5⋊#6442411yescharacteristic, direct product factor, Sylow
41D5—491noHall
42C7C11×C5⋊AGL(1,𝔽7)18yescomplemented
43C2×C3—2451noHall
44C5C11×#6442411yescharacteristic, complemented, Sylow
45C3—491noSylow
46C2—2451noSylow
subgroupG/H
center, hypercenterC11C5⋊#64424
commutator, cosocle, hypocenterC5×C72C2×C3×C11
FrattiniC1G
Fitting, socleC5×C72×C11C2×C3
LCSG ▷ C5×C72
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C5×C11×#3861C2semidirect
2. C11×C5⋊(C7⋊D7)C3semidirect
4. C5×C72×C11C2×C3semidirect
6. C11×#3861D5semidirect
7. C5⋊#64424C11direct (N × H)
11. C5×#3861C2×C11semidirect
12. C72×C11C3×D5semidirect
13. C5⋊(C7⋊D7)C3×C11semidirect
15. C5×C7×C11AGL(1,𝔽7)semidirect
18. C5×C72C2×C3×C11semidirect
23. #3861D5×C11semidirect
27. C7×C11C5⋊AGL(1,𝔽7)semidirect
30. C5×C11#64424semidirect
31. C72C3×D5×C11semidirect
33. C5×C7C11×AGL(1,𝔽7)semidirect
40. C11C5⋊#64424direct (N × H)
42. C7C11×C5⋊AGL(1,𝔽7)semidirect
44. C5C11×#64424semidirect

Maximal subgroups

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

subgroupindex
C5×C11×#38612
C11×C5⋊(C7⋊D7)3
C11×#644245
C11×C5⋊AGL(1,𝔽7)7
C5⋊#6442411