Finite Group Databasebeta

← C3⋊(C5⋊(C5⋊(D31⋊C3))) #28358489

Subgroups — C3⋊(C5⋊(C5⋊(D31⋊C3))) #28358489

Order 13950.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C52×C31⋊C3C211yesmaximal, characteristic, complemented, Hall
2C3⋊(C5⋊D155)C311yesmaximal, characteristic, complemented
3C5⋊(C5⋊(D31⋊C3))—31nomaximal
4C3⋊(C5⋊(D31⋊C3))—56nomaximal
5C52×C31⋊C3—21no—
6C52×C31⋊C3D311yescharacteristic, complemented
7C3×C52×C31C2×C311yescharacteristic, complemented
8C5⋊D155—31noHall
9C3×C5×C31⋊C3D516yescomplemented
10D465—56no—
11C5⋊(D31⋊C3)—156no—
12C52×C31C3×D311yescharacteristic, complemented, Hall
13C3⋊(D31⋊C3)—251noHall
14C3×C5×C31C3×D516yescomplemented
15C5×C31⋊C3—26no—
16C5×C31⋊C3D1516yescomplemented
17C3×C3⋊(C5⋊D5)—311nomaximal, Hall
18D155—156no—
19C3×C31⋊C3C5⋊D511yescharacteristic, complemented, Hall
20C32×C52—311noHall
21D93—251no—
22D31⋊C3—751no—
23C5×C31C3×D1516yescomplemented
24C3⋊(C5⋊D5)—311no—
25C3×C5⋊D5—931no—
26C3×C31C3×C5⋊D511yescharacteristic, complemented
27C31⋊C3—21no—
28C31⋊C3C3⋊(C5⋊D5)11yescharacteristic, complemented
29C3×D15—1556no—
30C3×C52—311no—
31C3×C52—621no—
32C3×C52D31⋊C311yescharacteristic, complemented
33D31—751noHall
34C5⋊D5—931noHall
35C32×C5—316no—
36C31C3×C3⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
37D15—1556no—
38C3×D5—4656no—
39C52C3⋊(D31⋊C3)11yescharacteristic, complemented, Sylow
40C3×D3—7751noHall
41C3×C5—316no—
42C3×C5—626no—
43C3×C5C5⋊(D31⋊C3)16yescomplemented
44D5—4656no—
45C32—311noSylow
46C2×C3—23251no—
47D3—7751no—
48C5C3⋊(C5⋊(D31⋊C3))16yescomplemented
49C3—311no—
50C3—621no—
51C3C5⋊(C5⋊(D31⋊C3))11yescharacteristic, complemented
52C2—23251noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C31C2×C3
LCSG ▷ C3×C52×C31
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C52×C31⋊C3C2semidirect
2. C3⋊(C5⋊D155)C3semidirect
6. C52×C31⋊C3D3semidirect
7. C3×C52×C31C2×C3semidirect
9. C3×C5×C31⋊C3D5semidirect
12. C52×C31C3×D3semidirect
14. C3×C5×C31C3×D5semidirect
16. C5×C31⋊C3D15semidirect
19. C3×C31⋊C3C5⋊D5semidirect
23. C5×C31C3×D15semidirect
26. C3×C31C3×C5⋊D5semidirect
28. C31⋊C3C3⋊(C5⋊D5)semidirect
32. C3×C52D31⋊C3semidirect
36. C31C3×C3⋊(C5⋊D5)semidirect
39. C52C3⋊(D31⋊C3)semidirect
43. C3×C5C5⋊(D31⋊C3)semidirect
48. C5C3⋊(C5⋊(D31⋊C3))semidirect
51. C3C5⋊(C5⋊(D31⋊C3))semidirect

Maximal subgroups

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

subgroupindex
C3×C52×C31⋊C32
C3⋊(C5⋊D155)3
C5⋊(C5⋊(D31⋊C3))3
C3⋊(C5⋊(D31⋊C3))5
C3×C3⋊(C5⋊D5)31