Finite Group Databasebeta

← C13×C3⋊(C3⋊(C5⋊D5)) #19154399

Subgroups — C13×C3⋊(C3⋊(C5⋊D5)) #19154399

Order 5850.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C52×C13C211yesmaximal, characteristic, complemented, Hall
2C13×C3⋊(C5⋊D5)—34nomaximal
3C13×C3⋊D15—56nomaximal
4C3×C52×C13D314yescomplemented
5C13×C5⋊D5—91noHall
6C32×C5×C13D516yescomplemented
7C3⋊(C3⋊(C5⋊D5))C1311yesmaximal, characteristic, direct product factor, Hall
8C13×D15—1524no—
9C52×C13C3⋊D311yescharacteristic, complemented, Hall
10C13×C3⋊D3—251noHall
11C32×C52C2×C1311yescharacteristic, complemented, Hall
12C3×C5×C13D15124yescomplemented
13C3⋊(C5⋊D5)—34no—
14D5×C13—456no—
15C32×C13C5⋊D511yescharacteristic, complemented, Hall
16C3⋊D15—56no—
17D3×C13—754no—
18C3×C52D3×C1314yescomplemented
19C5×C13C3⋊D1516yescomplemented
20C5⋊D5—91noHall
21C32×C5D5×C1316yescomplemented
22C3×C13C3⋊(C5⋊D5)14yescomplemented
23D15—1524no—
24C2×C13—2251noHall
25C52C13×C3⋊D311yescharacteristic, complemented, Sylow
26C3⋊D3—251noHall
27C3×C5C13×D15124yescomplemented
28C13C3⋊(C3⋊(C5⋊D5))11yescharacteristic, direct product factor, Sylow
29D5—456no—
30C32C13×C5⋊D511yescharacteristic, complemented, Sylow
31D3—754no—
32C5C13×C3⋊D1516yescomplemented
33C3C13×C3⋊(C5⋊D5)14yescomplemented
34C2—2251noSylow
subgroupG/H
center, hypercenterC13C3⋊(C3⋊(C5⋊D5))
commutator, hypocenterC32×C52C2×C13
FrattiniC1G
Fitting, socleC32×C52×C13C2
LCSG ▷ C32×C52
UCSC1 ◁ C13

Complements

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

NH ≅ G/Ntype
1. C32×C52×C13C2semidirect
4. C3×C52×C13D3semidirect
6. C32×C5×C13D5semidirect
7. C3⋊(C3⋊(C5⋊D5))C13direct (N × H)
9. C52×C13C3⋊D3semidirect
11. C32×C52C2×C13semidirect
12. C3×C5×C13D15semidirect
15. C32×C13C5⋊D5semidirect
18. C3×C52D3×C13semidirect
19. C5×C13C3⋊D15semidirect
21. C32×C5D5×C13semidirect
22. C3×C13C3⋊(C5⋊D5)semidirect
25. C52C13×C3⋊D3semidirect
27. C3×C5C13×D15semidirect
28. C13C3⋊(C3⋊(C5⋊D5))direct (N × H)
30. C32C13×C5⋊D5semidirect
32. C5C13×C3⋊D15semidirect
33. C3C13×C3⋊(C5⋊D5)semidirect