Finite Group Databasebeta

← C3⋊(C5⋊D5)×C23⋊C11 #49182113

Subgroups — C3⋊(C5⋊D5)×C23⋊C11 #49182113

Order 37950.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C52×C23⋊C11C211yesmaximal, characteristic, complemented, Hall
2C5⋊D5×C23⋊C11—31nomaximal, Hall
3D15×C23⋊C11—56nomaximal
4C52×C23⋊C11D311yescharacteristic, complemented, Hall
5C3×C5×C23⋊C11D516yescomplemented
6C23×C3⋊(C5⋊D5)C1111yesmaximal, characteristic, complemented, Hall
7D5×C23⋊C11—156no—
8C3×C52×C23C2×C1111yescharacteristic, complemented, Hall
9C11×C3⋊(C5⋊D5)—231nomaximal, Hall
10D3×C23⋊C11—251noHall
11C5×C23⋊C11D1516yescomplemented
12C23×C5⋊D5—31noHall
13C3×C52×C11—231noHall
14C3×C23⋊C11C5⋊D511yescharacteristic, complemented, Hall
15C23×D15—56no—
16C52×C23D3×C1111yescharacteristic, complemented, Hall
17C11×C5⋊D5—691noHall
18C2×C23⋊C11—751noHall
19C3×C5×C23D5×C1116yescomplemented
20C11×D15—1156no—
21C52×C11—231noHall
22C23⋊C11C3⋊(C5⋊D5)11yescharacteristic, direct product factor, Hall
23D5×C23—156no—
24C3×C5×C11—236no—
25C3⋊(C5⋊D5)C23⋊C1111yescharacteristic, direct product factor, Hall
26D3×C23—251noHall
27C5×C23C11×D1516yescomplemented
28D5×C11—3456no—
29C3×C52C2×C23⋊C1111yescharacteristic, complemented, Hall
30C3×C23C11×C5⋊D511yescharacteristic, complemented, Hall
31D3×C11—5751noHall
32C5×C11—236no—
33C5⋊D5—31noHall
34C2×C23—751noHall
35C3×C11—231noHall
36D15—56no—
37C52D3×C23⋊C1111yescharacteristic, complemented, Sylow
38C23C11×C3⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
39C2×C11—17251noHall
40C3×C5D5×C23⋊C1116yescomplemented
41C11—231noSylow
42D5—156no—
43D3—251noHall
44C5D15×C23⋊C1116yescomplemented
45C3C5⋊D5×C23⋊C1111yescharacteristic, complemented, Sylow
46C2—751noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C23C2×C11
LCSG ▷ C3×C52×C23
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C52×C23⋊C11C2semidirect
4. C52×C23⋊C11D3semidirect
5. C3×C5×C23⋊C11D5semidirect
6. C23×C3⋊(C5⋊D5)C11semidirect
8. C3×C52×C23C2×C11semidirect
11. C5×C23⋊C11D15semidirect
14. C3×C23⋊C11C5⋊D5semidirect
16. C52×C23D3×C11semidirect
19. C3×C5×C23D5×C11semidirect
22. C23⋊C11C3⋊(C5⋊D5)direct (N × H)
25. C3⋊(C5⋊D5)C23⋊C11direct (N × H)
27. C5×C23C11×D15semidirect
29. C3×C52C2×C23⋊C11semidirect
30. C3×C23C11×C5⋊D5semidirect
37. C52D3×C23⋊C11semidirect
38. C23C11×C3⋊(C5⋊D5)semidirect
40. C3×C5D5×C23⋊C11semidirect
44. C5D15×C23⋊C11semidirect
45. C3C5⋊D5×C23⋊C11semidirect

Maximal subgroups

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

subgroupindex
C3×C52×C23⋊C112
C5⋊D5×C23⋊C113
D15×C23⋊C115
C23×C3⋊(C5⋊D5)11
C11×C3⋊(C5⋊D5)23