Finite Group Databasebeta

← C2×C3×C52⋊#3861 #36348055

Subgroups — C2×C3×C52⋊#3861 #36348055

Order 22050.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C52⋊#3861C211yesmaximal, characteristic, direct product factor, Hall
2C2×C52⋊#3861C313yesmaximal, direct product factor
3C2×C3×C52×C72C311yesmaximal, characteristic, complemented
4C52⋊#3861C2×C313yesdirect product factor
5C3×C52×C72C2×C311yescharacteristic, complemented
6C2×C3×C7⋊(C52⋊C3)—78nomaximal
7C2×C52×C72C3211yescharacteristic, complemented, Hall
8C3×C7⋊(C52⋊C3)—78no—
9C2×C3×C5×C72—32no—
10C52×C72C2×C3211yescharacteristic, complemented, Hall
11C2×C3×C52×C7ΓL(1,𝔽8)18yescomplemented
12C2×C7⋊(C52⋊C3)—724no—
13C2×C3×#3861—251nomaximal, Hall
14C3×C5×C72—32no—
15C3×C52×C7C2×ΓL(1,𝔽8)18yescomplemented
16C7⋊(C52⋊C3)—724no—
17C2×C5×C72—32no—
18C2×C3×C52⋊C3—491noHall
19C3×#3861—251noHall
20C2×C52×C7C3×ΓL(1,𝔽8)18yescomplemented
21C2×C3×C72C52⋊C311yescharacteristic, complemented
22C2×#3861—253no—
23C5×C72—32no—
24C3×C52⋊C3—491noHall
25C2×C3×C5×C7—316no—
26C52×C7C2×C3×ΓL(1,𝔽8)18yescomplemented
27C2×C3×C52#386111yescharacteristic, complemented
28C2×C52⋊C3—493no—
29C3×C72C2×C52⋊C311yescharacteristic, complemented
30#3861—253no—
31C2×C3×ΓL(1,𝔽8)—1758no—
32C3×C5×C7—316no—
33C2×C72C3×C52⋊C311yescharacteristic, complemented, Hall
34C3×C52C2×#386111yescharacteristic, complemented
35C52⋊C3—493no—
36C2×C5×C7—316no—
37C3×ΓL(1,𝔽8)—1758no—
38C2×C52C3×#386111yescharacteristic, complemented, Hall
39C72C2×C3×C52⋊C311yescharacteristic, complemented, Sylow
40C2×C3×C7C7⋊(C52⋊C3)18yescomplemented
41C2×ΓL(1,𝔽8)—17524no—
42C5×C7—316no—
43C2×C3×C5—32no—
44C52C2×C3×#386111yescharacteristic, complemented, Sylow
45C3×C7C2×C7⋊(C52⋊C3)18yescomplemented
46ΓL(1,𝔽8)—17524no—
47C2×C32—12251noHall
48C3×C5—32no—
49C2×C7C3×C7⋊(C52⋊C3)18yescomplemented
50C2×C5—32no—
51C32—12251noSylow
52C7C2×C3×C7⋊(C52⋊C3)18yescomplemented
53C2×C3—12253no—
54C2×C3C52⋊#386111yescharacteristic, direct product factor
55C5—32no—
56C3—12253no—
57C3C2×C52⋊#386111yescharacteristic, direct product factor
58C2C3×C52⋊#386111yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2×C3C52⋊#3861
commutator, cosocle, hypocenterC52×C72C2×C32
FrattiniC1G
Fitting, socleC2×C3×C52×C72C3
LCSG ▷ C52×C72
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C3×C52⋊#3861C2direct (N × H)
2. C2×C52⋊#3861C3direct (N × H)
3. C2×C3×C52×C72C3semidirect
4. C52⋊#3861C2×C3direct (N × H)
5. C3×C52×C72C2×C3semidirect
7. C2×C52×C72C32semidirect
10. C52×C72C2×C32semidirect
11. C2×C3×C52×C7ΓL(1,𝔽8)semidirect
15. C3×C52×C7C2×ΓL(1,𝔽8)semidirect
20. C2×C52×C7C3×ΓL(1,𝔽8)semidirect
21. C2×C3×C72C52⋊C3semidirect
26. C52×C7C2×C3×ΓL(1,𝔽8)semidirect
27. C2×C3×C52#3861semidirect
29. C3×C72C2×C52⋊C3semidirect
33. C2×C72C3×C52⋊C3semidirect
34. C3×C52C2×#3861semidirect
38. C2×C52C3×#3861semidirect
39. C72C2×C3×C52⋊C3semidirect
40. C2×C3×C7C7⋊(C52⋊C3)semidirect
44. C52C2×C3×#3861semidirect
45. C3×C7C2×C7⋊(C52⋊C3)semidirect
49. C2×C7C3×C7⋊(C52⋊C3)semidirect
52. C7C2×C3×C7⋊(C52⋊C3)semidirect
54. C2×C3C52⋊#3861direct (N × H)
57. C3C2×C52⋊#3861direct (N × H)
58. C2C3×C52⋊#3861direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C52⋊#38612
C2×C52⋊#38613
C2×C3×C52×C723
C2×C3×C7⋊(C52⋊C3)7
C2×C3×#386125