Finite Group Databasebeta

← C3⋊(C3⋊(C5⋊(D31⋊C5))) #28358469

Subgroups — C3⋊(C3⋊(C5⋊(D31⋊C5))) #28358469

Order 13950.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×ΓL(1,𝔽32)C211yesmaximal, characteristic, complemented, Hall
2C3⋊(C5⋊(D31⋊C5))—34nomaximal
3C3⋊D465C511yesmaximal, characteristic, complemented
4C3⋊(C3⋊(D31⋊C5))—51nomaximal
5C3×C5×ΓL(1,𝔽32)D314yescomplemented
6C5⋊(D31⋊C5)—91noHall
7C32×C5×C31C2×C511yescharacteristic, complemented
8C32×ΓL(1,𝔽32)—22no—
9C32×ΓL(1,𝔽32)D511yescharacteristic, complemented
10D465—34no—
11C3⋊(D31⋊C5)—154no—
12C5×ΓL(1,𝔽32)C3⋊D311yescharacteristic, complemented, Hall
13C3⋊D93—51noHall
14C3×C5×C31C5×D314yescomplemented
15C3×ΓL(1,𝔽32)—28no—
16C3×ΓL(1,𝔽32)D1514yescomplemented
17C5×C3⋊D15—311nomaximal, Hall
18D155—91no—
19D31⋊C5—451no—
20C32×C31C5×D511yescharacteristic, complemented, Hall
21C32×C52—311noHall
22D93—154no—
23C5×C31C5×C3⋊D311yescharacteristic, complemented
24ΓL(1,𝔽32)—22no—
25ΓL(1,𝔽32)C3⋊D1511yescharacteristic, complemented
26C5×D15—934no—
27C3×C31C5×D1514yescomplemented
28C3⋊D15—311no—
29C5×C3⋊D3—1551no—
30C3×C52—314no—
31D31—451noHall
32C5×D5—2791noHall
33C32×C5—311no—
34C32×C5—622no—
35C32×C5D31⋊C511yescharacteristic, complemented
36C31C5×C3⋊D1511yescharacteristic, complemented, Sylow
37D15—934no—
38C5×D3—4654no—
39C52—311noSylow
40C3⋊D3—1551noHall
41C3×C5—314no—
42C3×C5—628no—
43C3×C5C3⋊(D31⋊C5)14yescomplemented
44C2×C5—13951no—
45D5—2791no—
46C32C5⋊(D31⋊C5)11yescharacteristic, complemented, Sylow
47D3—4654no—
48C5—311no—
49C5—622no—
50C5C3⋊(C3⋊(D31⋊C5))11yescharacteristic, complemented
51C3C3⋊(C5⋊(D31⋊C5))14yescomplemented
52C2—13951noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C31C2×C5
LCSG ▷ C32×C5×C31
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×C5×ΓL(1,𝔽32)C2semidirect
3. C3⋊D465C5semidirect
5. C3×C5×ΓL(1,𝔽32)D3semidirect
7. C32×C5×C31C2×C5semidirect
9. C32×ΓL(1,𝔽32)D5semidirect
12. C5×ΓL(1,𝔽32)C3⋊D3semidirect
14. C3×C5×C31C5×D3semidirect
16. C3×ΓL(1,𝔽32)D15semidirect
20. C32×C31C5×D5semidirect
23. C5×C31C5×C3⋊D3semidirect
25. ΓL(1,𝔽32)C3⋊D15semidirect
27. C3×C31C5×D15semidirect
35. C32×C5D31⋊C5semidirect
36. C31C5×C3⋊D15semidirect
43. C3×C5C3⋊(D31⋊C5)semidirect
46. C32C5⋊(D31⋊C5)semidirect
50. C5C3⋊(C3⋊(D31⋊C5))semidirect
51. C3C3⋊(C5⋊(D31⋊C5))semidirect

Maximal subgroups

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

subgroupindex
C32×C5×ΓL(1,𝔽32)2
C3⋊(C5⋊(D31⋊C5))3
C3⋊D4655
C3⋊(C3⋊(D31⋊C5))5
C5×C3⋊D1531