Finite Group Databasebeta

← C32×C11×D31⋊C5 #44501779

Subgroups — C32×C11×D31⋊C5 #44501779

Order 30690.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C11×ΓL(1,𝔽32)C211yesmaximal, characteristic, complemented, Hall
2C3×C11×D31⋊C5C314yesmaximal, direct product factor
3C32×C11×D31C511yesmaximal, characteristic, complemented, Hall
4C3×C11×ΓL(1,𝔽32)C2×C314yescomplemented
5C11×D31⋊C5C3211yescharacteristic, direct product factor, Hall
6C32×C11×C31C2×C511yescharacteristic, complemented, Hall
7C32×D31⋊C5C1111yesmaximal, characteristic, direct product factor, Hall
8C3×C11×D31C3×C514yescomplemented
9C11×ΓL(1,𝔽32)C2×C3211yescharacteristic, complemented, Hall
10C32×ΓL(1,𝔽32)C2×C1111yescharacteristic, complemented, Hall
11C3×C11×C31C2×C3×C514yescomplemented
12C2×C32×C5×C11—311nomaximal, Hall
13C3×D31⋊C5C3×C1114yesdirect product factor
14C11×D31C32×C511yescharacteristic, complemented, Hall
15C32×D31C5×C1111yescharacteristic, complemented, Hall
16C32×C5×C11—311noHall
17C3×ΓL(1,𝔽32)C2×C3×C1114yescomplemented
18C11×C31C2×C32×C511yescharacteristic, complemented, Hall
19C2×C3×C5×C11—314no—
20D31⋊C5C32×C1111yescharacteristic, direct product factor, Hall
21C32×C31C2×C5×C1111yescharacteristic, complemented, Hall
22C2×C32×C11—311noHall
23C3×D31C3×C5×C1114yescomplemented
24C3×C5×C11—314no—
25ΓL(1,𝔽32)C2×C32×C1111yescharacteristic, complemented, Hall
26C2×C5×C11—311noHall
27C32×C11D31⋊C511yescharacteristic, direct product factor, Hall
28C3×C31C2×C3×C5×C1114yescomplemented
29C2×C32×C5—311noHall
30C2×C3×C11—314no—
31D31C32×C5×C1111yescharacteristic, complemented, Hall
32C5×C11—311noHall
33C32×C5—311noHall
34C3×C11C3×D31⋊C514yesdirect product factor
35C31C2×C32×C5×C1111yescharacteristic, complemented, Sylow
36C2×C3×C5—314no—
37C2×C11—311noHall
38C2×C32—311noHall
39C3×C5—314no—
40C11C32×D31⋊C511yescharacteristic, direct product factor, Sylow
41C2×C5—311noHall
42C32C11×D31⋊C511yescharacteristic, direct product factor, Sylow
43C2×C3—314no—
44C5—311noSylow
45C3C3×C11×D31⋊C514yesdirect product factor
46C2—311noSylow
subgroupG/H
center, hypercenterC32×C11D31⋊C5
commutator, cosocle, hypocenterC31C2×C32×C5×C11
FrattiniC1G
Fitting, socleC32×C11×C31C2×C5
LCSG ▷ C31
UCSC1 ◁ C32×C11

Complements

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

NH ≅ G/Ntype
1. C32×C11×ΓL(1,𝔽32)C2semidirect
2. C3×C11×D31⋊C5C3direct (N × H)
3. C32×C11×D31C5semidirect
4. C3×C11×ΓL(1,𝔽32)C2×C3semidirect
5. C11×D31⋊C5C32direct (N × H)
6. C32×C11×C31C2×C5semidirect
7. C32×D31⋊C5C11direct (N × H)
8. C3×C11×D31C3×C5semidirect
9. C11×ΓL(1,𝔽32)C2×C32semidirect
10. C32×ΓL(1,𝔽32)C2×C11semidirect
11. C3×C11×C31C2×C3×C5semidirect
13. C3×D31⋊C5C3×C11direct (N × H)
14. C11×D31C32×C5semidirect
15. C32×D31C5×C11semidirect
17. C3×ΓL(1,𝔽32)C2×C3×C11semidirect
18. C11×C31C2×C32×C5semidirect
20. D31⋊C5C32×C11direct (N × H)
21. C32×C31C2×C5×C11semidirect
23. C3×D31C3×C5×C11semidirect
25. ΓL(1,𝔽32)C2×C32×C11semidirect
27. C32×C11D31⋊C5direct (N × H)
28. C3×C31C2×C3×C5×C11semidirect
31. D31C32×C5×C11semidirect
34. C3×C11C3×D31⋊C5direct (N × H)
35. C31C2×C32×C5×C11semidirect
40. C11C32×D31⋊C5direct (N × H)
42. C32C11×D31⋊C5direct (N × H)
45. C3C3×C11×D31⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C11×ΓL(1,𝔽32)2
C3×C11×D31⋊C53
C32×C11×D315
C32×D31⋊C511
C2×C32×C5×C1131