Finite Group Databasebeta

← C5×Dic11×#3861 #44568484

Subgroups — C5×Dic11×#3861 #44568484

Order 32340.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×C11×#3861C211yesmaximal, characteristic
2C5×C72×Dic11C311yesmaximal, characteristic, complemented, Hall
3C5×C11×#3861C411yescharacteristic, complemented, Hall
4Dic11×#3861C511yesmaximal, characteristic, direct product factor, Hall
5C2×C5×C72×C11C2×C311yescharacteristic
6C5×ΓL(1,𝔽8)×Dic11—78nomaximal
7C2×C11×#3861C2×C511yescharacteristic
8C4×C5×#3861—111nomaximal, Hall
9C5×C72×C11C3×C411yescharacteristic, complemented, Hall
10C2×C5×C11×ΓL(1,𝔽8)—78no—
11C72×Dic11C3×C511yescharacteristic, complemented, Hall
12C11×#3861C4×C511yescharacteristic, complemented, Hall
13C5×C7×Dic11ΓL(1,𝔽8)18yescomplemented
14C2×C5×#3861D1111yescharacteristic
15C5×C11×ΓL(1,𝔽8)—78no—
16C2×C72×C11C2×C3×C511yescharacteristic
17C4×C5×C72—111noHall
18ΓL(1,𝔽8)×Dic11—78no—
19C2×C5×C7×C11C2×ΓL(1,𝔽8)18yes—
20C5×#3861Dic1111yescharacteristic, direct product factor, Hall
21C3×C5×Dic11—491noHall
22C4×#3861—111noHall
23C72×C11C3×C4×C511yescharacteristic, complemented, Hall
24C2×C5×C72C3×D1111yescharacteristic
25C2×C11×ΓL(1,𝔽8)—78no—
26C4×C5×ΓL(1,𝔽8)—778no—
27C5×C7×C11C4×ΓL(1,𝔽8)18yescomplemented
28C2×C3×C5×C11—491no—
29C7×Dic11C5×ΓL(1,𝔽8)18yescomplemented
30C2×#3861C5×D1111yescharacteristic
31C5×C72C3×Dic1111yescharacteristic, complemented, Hall
32C11×ΓL(1,𝔽8)—78no—
33C5×Dic11#386111yescharacteristic, direct product factor, Hall
34C2×C5×ΓL(1,𝔽8)—78no—
35C4×C72—111noHall
36C3×C5×C11—491noHall
37C2×C7×C11C2×C5×ΓL(1,𝔽8)18yes—
38#3861C5×Dic1111yescharacteristic, direct product factor, Hall
39C4×C5×C7—118no—
40C3×Dic11—491noHall
41C2×C5×C11C2×#386111yescharacteristic
42C5×ΓL(1,𝔽8)—78no—
43C2×C72C3×C5×D1111yescharacteristic
44C4×ΓL(1,𝔽8)—778no—
45C7×C11C4×C5×ΓL(1,𝔽8)18yescomplemented
46C2×C5×C7ΓL(1,𝔽8)×D1118yes—
47C2×C3×C11—491no—
48C3×C4×C5—5391noHall
49C5×C11C4×#386111yescharacteristic, complemented, Hall
50C72C3×C5×Dic1111yescharacteristic, complemented, Sylow
51Dic11C5×#386111yescharacteristic, direct product factor, Hall
52C2×ΓL(1,𝔽8)—78no—
53C5×C7ΓL(1,𝔽8)×Dic1118yescomplemented
54C3×C11—491noHall
55C2×C3×C5—491no—
56C4×C7—118no—
57C2×C11C2×C5×#386111yescharacteristic
58ΓL(1,𝔽8)—78no—
59C4×C5—111noHall
60C3×C5—491noHall
61C2×C7C5×ΓL(1,𝔽8)×D1118yes—
62C3×C4—5391noHall
63C11C4×C5×#386111yescharacteristic, complemented, Sylow
64C2×C5D11×#386111yescharacteristic
65C7C5×ΓL(1,𝔽8)×Dic1118yescomplemented
66C2×C3—491no—
67C5Dic11×#386111yescharacteristic, direct product factor, Sylow
68C4—111noSylow
69C3—491noSylow
70C2C5×D11×#386111yescharacteristic
subgroupG/H
center, hypercenterC2×C5D11×#3861
commutator, hypocenterC72×C11C3×C4×C5
FrattiniC2C5×D11×#3861
Fitting, socleC2×C5×C72×C11C2×C3
prime radicalC2×C5×C11×#3861C2
cosocleC2×C72×C11C2×C3×C5
LCSG ▷ C72×C11
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
2. C5×C72×Dic11C3semidirect
3. C5×C11×#3861C4semidirect
4. Dic11×#3861C5direct (N × H)
9. C5×C72×C11C3×C4semidirect
11. C72×Dic11C3×C5semidirect
12. C11×#3861C4×C5semidirect
13. C5×C7×Dic11ΓL(1,𝔽8)semidirect
20. C5×#3861Dic11direct (N × H)
23. C72×C11C3×C4×C5semidirect
27. C5×C7×C11C4×ΓL(1,𝔽8)semidirect
29. C7×Dic11C5×ΓL(1,𝔽8)semidirect
31. C5×C72C3×Dic11semidirect
33. C5×Dic11#3861direct (N × H)
38. #3861C5×Dic11direct (N × H)
45. C7×C11C4×C5×ΓL(1,𝔽8)semidirect
49. C5×C11C4×#3861semidirect
50. C72C3×C5×Dic11semidirect
51. Dic11C5×#3861direct (N × H)
53. C5×C7ΓL(1,𝔽8)×Dic11semidirect
63. C11C4×C5×#3861semidirect
65. C7C5×ΓL(1,𝔽8)×Dic11semidirect
67. C5Dic11×#3861direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×C11×#38612
C5×C72×Dic113
Dic11×#38615
C5×ΓL(1,𝔽8)×Dic117
C4×C5×#386111