Finite Group Databasebeta

← C13×C3⋊(C3⋊(D31⋊C5)) #49136604

Subgroups — C13×C3⋊(C3⋊(D31⋊C5)) #49136604

Order 36270.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C13×ΓL(1,𝔽32)C211yesmaximal, characteristic, complemented, Hall
2C13×C3⋊(D31⋊C5)—34nomaximal
3C13×C3⋊D93C511yesmaximal, characteristic, complemented, Hall
4C3×C13×ΓL(1,𝔽32)D314yescomplemented
5C13×D31⋊C5—91noHall
6C32×C13×C31C2×C511yescharacteristic, complemented, Hall
7C3⋊(C3⋊(D31⋊C5))C1311yesmaximal, characteristic, direct product factor, Hall
8C13×D93—34no—
9C13×ΓL(1,𝔽32)C3⋊D311yescharacteristic, complemented, Hall
10C32×ΓL(1,𝔽32)C2×C1311yescharacteristic, complemented, Hall
11C3×C13×C31C5×D314yescomplemented
12C5×C13×C3⋊D3—311nomaximal, Hall
13C3⋊(D31⋊C5)—34no—
14C13×D31—91noHall
15C32×C5×C13—311noHall
16C3⋊D93C5×C1311yescharacteristic, complemented, Hall
17C3×ΓL(1,𝔽32)D3×C1314yescomplemented
18C13×C31C5×C3⋊D311yescharacteristic, complemented, Hall
19C5×D3×C13—934no—
20D31⋊C5—91noHall
21C32×C31C2×C5×C1311yescharacteristic, complemented, Hall
22C13×C3⋊D3—311noHall
23C3×C5×C13—314no—
24D93—34no—
25ΓL(1,𝔽32)C13×C3⋊D311yescharacteristic, complemented, Hall
26C2×C5×C13—2791noHall
27C32×C13D31⋊C511yescharacteristic, complemented, Hall
28C3×C31C5×D3×C1314yescomplemented
29C5×C3⋊D3—311noHall
30D3×C13—934no—
31C5×C13—311noHall
32D31—91noHall
33C32×C5—311noHall
34C3×C13C3⋊(D31⋊C5)14yescomplemented
35C31C5×C13×C3⋊D311yescharacteristic, complemented, Sylow
36C5×D3—934no—
37C2×C13—2791noHall
38C3⋊D3—311noHall
39C3×C5—314no—
40C13C3⋊(C3⋊(D31⋊C5))11yescharacteristic, direct product factor, Sylow
41C2×C5—2791noHall
42C32C13×D31⋊C511yescharacteristic, complemented, Sylow
43D3—934no—
44C5—311noSylow
45C3C13×C3⋊(D31⋊C5)14yescomplemented
46C2—2791noSylow
subgroupG/H
center, hypercenterC13C3⋊(C3⋊(D31⋊C5))
commutator, cosocle, hypocenterC32×C31C2×C5×C13
FrattiniC1G
Fitting, socleC32×C13×C31C2×C5
LCSG ▷ C32×C31
UCSC1 ◁ C13

Complements

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

NH ≅ G/Ntype
1. C32×C13×ΓL(1,𝔽32)C2semidirect
3. C13×C3⋊D93C5semidirect
4. C3×C13×ΓL(1,𝔽32)D3semidirect
6. C32×C13×C31C2×C5semidirect
7. C3⋊(C3⋊(D31⋊C5))C13direct (N × H)
9. C13×ΓL(1,𝔽32)C3⋊D3semidirect
10. C32×ΓL(1,𝔽32)C2×C13semidirect
11. C3×C13×C31C5×D3semidirect
16. C3⋊D93C5×C13semidirect
17. C3×ΓL(1,𝔽32)D3×C13semidirect
18. C13×C31C5×C3⋊D3semidirect
21. C32×C31C2×C5×C13semidirect
25. ΓL(1,𝔽32)C13×C3⋊D3semidirect
27. C32×C13D31⋊C5semidirect
28. C3×C31C5×D3×C13semidirect
34. C3×C13C3⋊(D31⋊C5)semidirect
35. C31C5×C13×C3⋊D3semidirect
40. C13C3⋊(C3⋊(D31⋊C5))direct (N × H)
42. C32C13×D31⋊C5semidirect
45. C3C13×C3⋊(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
C13×C3⋊(D31⋊C5)3
C13×C3⋊D935
C3⋊(C3⋊(D31⋊C5))13
C5×C13×C3⋊D331