Finite Group Databasebeta

← C3⋊(C3⋊(C13⋊(D31⋊C5))) #49136606

Subgroups — C3⋊(C3⋊(C13⋊(D31⋊C5))) #49136606

Order 36270.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C13×ΓL(1,𝔽32)C211yesmaximal, characteristic, complemented, Hall
2C3⋊(C13⋊(D31⋊C5))—34nomaximal
3C3⋊D1209C511yesmaximal, characteristic, complemented, Hall
4C3×C13×ΓL(1,𝔽32)D314yescomplemented
5C13⋊(D31⋊C5)—91noHall
6C32×C13×C31C2×C511yescharacteristic, complemented, Hall
7C3⋊(C3⋊(D31⋊C5))—131nomaximal, Hall
8D1209—34no—
9C13×ΓL(1,𝔽32)C3⋊D311yescharacteristic, complemented, Hall
10C32×ΓL(1,𝔽32)D1311yescharacteristic, complemented, Hall
11C3×C13×C31C5×D314yescomplemented
12C5×C3⋊D39—311nomaximal, Hall
13C3⋊(D31⋊C5)—394no—
14D403—91noHall
15C32×C5×C13—311noHall
16C3⋊D93—131noHall
17C3×ΓL(1,𝔽32)D3914yescomplemented
18C13×C31C5×C3⋊D311yescharacteristic, complemented, Hall
19C5×D39—934no—
20D31⋊C5—1171noHall
21C32×C31C5×D1311yescharacteristic, complemented, Hall
22C3⋊D39—311noHall
23C3×C5×C13—314no—
24D93—394no—
25ΓL(1,𝔽32)C3⋊D3911yescharacteristic, complemented, Hall
26C5×D13—2791noHall
27C32×C13D31⋊C511yescharacteristic, complemented, Hall
28C3×C31C5×D3914yescomplemented
29C5×C3⋊D3—4031noHall
30D39—934no—
31C5×C13—311noHall
32D31—1171noHall
33C32×C5—311noHall
34C3×C13C3⋊(D31⋊C5)14yescomplemented
35C31C5×C3⋊D3911yescharacteristic, complemented, Sylow
36C5×D3—12094no—
37D13—2791noHall
38C3⋊D3—4031noHall
39C3×C5—314no—
40C13C3⋊(C3⋊(D31⋊C5))11yescharacteristic, complemented, Sylow
41C2×C5—36271noHall
42C32C13⋊(D31⋊C5)11yescharacteristic, complemented, Sylow
43D3—12094no—
44C5—311noSylow
45C3C3⋊(C13⋊(D31⋊C5))14yescomplemented
46C2—36271noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C13×C31C2×C5
LCSG ▷ C32×C13×C31
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×C13×ΓL(1,𝔽32)C2semidirect
3. C3⋊D1209C5semidirect
4. C3×C13×ΓL(1,𝔽32)D3semidirect
6. C32×C13×C31C2×C5semidirect
9. C13×ΓL(1,𝔽32)C3⋊D3semidirect
10. C32×ΓL(1,𝔽32)D13semidirect
11. C3×C13×C31C5×D3semidirect
17. C3×ΓL(1,𝔽32)D39semidirect
18. C13×C31C5×C3⋊D3semidirect
21. C32×C31C5×D13semidirect
25. ΓL(1,𝔽32)C3⋊D39semidirect
27. C32×C13D31⋊C5semidirect
28. C3×C31C5×D39semidirect
34. C3×C13C3⋊(D31⋊C5)semidirect
35. C31C5×C3⋊D39semidirect
40. C13C3⋊(C3⋊(D31⋊C5))semidirect
42. C32C13⋊(D31⋊C5)semidirect
45. C3C3⋊(C13⋊(D31⋊C5))semidirect

Maximal subgroups

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

subgroupindex
C32×C13×ΓL(1,𝔽32)2
C3⋊(C13⋊(D31⋊C5))3
C3⋊D12095
C3⋊(C3⋊(D31⋊C5))13
C5×C3⋊D3931