Finite Group Databasebeta

← C3×C5×C5⋊(C11⋊D11) #31827716

Subgroups — C3×C5×C5⋊(C11⋊D11) #31827716

Order 18150.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C52×C112C211yesmaximal, characteristic, complemented, Hall
2C5×C5⋊(C11⋊D11)C311yesmaximal, characteristic, direct product factor, Hall
3C3×C5⋊(C11⋊D11)C511yesmaximal, characteristic, direct product factor
4C3×C5×C11⋊D11—51nomaximal
5C52×C112C2×C311yescharacteristic, complemented, Hall
6C3×C5×C112—22no—
7C3×C5×C112D511yescharacteristic, complemented
8C3×C5×C112C2×C511yescharacteristic, complemented
9C3×C5×D55—1112nomaximal
10C5⋊(C11⋊D11)C3×C511yescharacteristic, direct product factor
11C5×C11⋊D11—51no—
12C3×C52×C11D11112yescomplemented
13C3×C11⋊D11—51noHall
14C5×C112—22no—
15C5×C112C3×D511yescharacteristic, complemented
16C5×C112C2×C3×C511yescharacteristic, complemented
17C5×D55—1112no—
18C3×C112C5×D511yescharacteristic, complemented, Hall
19C3×D55—1112no—
20C3×C5×D11—5512no—
21C52×C11C3×D11112yescomplemented
22C11⋊D11—51noHall
23C3×C5×C11—224no—
24C3×C5×C11C5×D11112yescomplemented
25C3×C5×C11D55112yescomplemented
26C3×C5×D5—1211noHall
27C112C3×C5×D511yescharacteristic, complemented, Sylow
28D55—1112no—
29C5×D11—5512no—
30C3×C52C11⋊D1111yescharacteristic, complemented, Hall
31C3×D11—5512no—
32C5×C11—224no—
33C5×C11C3×C5×D11112yescomplemented
34C5×C11C3×D55112yescomplemented
35C5×D5—1211noHall
36C3×C11C5×D55112yescomplemented
37C2×C3×C5—6051no—
38C3×D5—1211no—
39C52C3×C11⋊D1111yescharacteristic, complemented, Sylow
40D11—5512no—
41C3×C5—22no—
42C3×C5C5×C11⋊D1111yescharacteristic, complemented
43C3×C5C5⋊(C11⋊D11)11yescharacteristic, direct product factor
44C11C3×C5×D55112yescomplemented
45C2×C5—6051no—
46D5—1211no—
47C2×C3—6051noHall
48C5—22no—
49C5C3×C5×C11⋊D1111yescharacteristic, complemented
50C5C3×C5⋊(C11⋊D11)11yescharacteristic, direct product factor
51C3C5×C5⋊(C11⋊D11)11yescharacteristic, direct product factor, Sylow
52C2—6051noSylow
subgroupG/H
center, hypercenterC3×C5C5⋊(C11⋊D11)
commutator, cosocle, hypocenterC5×C112C2×C3×C5
FrattiniC1G
Fitting, socleC3×C52×C112C2
LCSG ▷ C5×C112
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C3×C52×C112C2semidirect
2. C5×C5⋊(C11⋊D11)C3direct (N × H)
3. C3×C5⋊(C11⋊D11)C5direct (N × H)
5. C52×C112C2×C3semidirect
7. C3×C5×C112D5semidirect
8. C3×C5×C112C2×C5semidirect
10. C5⋊(C11⋊D11)C3×C5direct (N × H)
12. C3×C52×C11D11semidirect
15. C5×C112C3×D5semidirect
16. C5×C112C2×C3×C5semidirect
18. C3×C112C5×D5semidirect
21. C52×C11C3×D11semidirect
24. C3×C5×C11C5×D11semidirect
25. C3×C5×C11D55semidirect
27. C112C3×C5×D5semidirect
30. C3×C52C11⋊D11semidirect
33. C5×C11C3×C5×D11semidirect
34. C5×C11C3×D55semidirect
36. C3×C11C5×D55semidirect
39. C52C3×C11⋊D11semidirect
42. C3×C5C5×C11⋊D11semidirect
43. C3×C5C5⋊(C11⋊D11)direct (N × H)
44. C11C3×C5×D55semidirect
49. C5C3×C5×C11⋊D11semidirect
50. C5C3×C5⋊(C11⋊D11)direct (N × H)
51. C3C5×C5⋊(C11⋊D11)direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C52×C1122
C5×C5⋊(C11⋊D11)3
C3×C5⋊(C11⋊D11)5
C3×C5×C11⋊D115
C3×C5×D5511