Finite Group Databasebeta

← C32×C5×D11×C31 #44501868

Subgroups — C32×C5×D11×C31 #44501868

Order 30690.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×C11×C31C211yesmaximal, characteristic, complemented, Hall
2C3×C5×D11×C31C314yesmaximal, direct product factor
3C32×D11×C31C511yesmaximal, characteristic, direct product factor, Hall
4C3×C5×C11×C31C2×C314yescomplemented
5C5×D11×C31C3211yescharacteristic, direct product factor, Hall
6C32×C11×C31C2×C511yescharacteristic, complemented, Hall
7C2×C32×C5×C31—111nomaximal, Hall
8C3×D11×C31C3×C514yesdirect product factor
9C5×C11×C31C2×C3211yescharacteristic, complemented, Hall
10C32×C5×C31D1111yescharacteristic, direct product factor, Hall
11C3×C11×C31C2×C3×C514yescomplemented
12C32×C5×D11C3111yesmaximal, characteristic, direct product factor, Hall
13C2×C3×C5×C31—114no—
14D11×C31C32×C511yescharacteristic, direct product factor, Hall
15C2×C32×C31—111noHall
16C32×C5×C11C2×C3111yescharacteristic, complemented, Hall
17C3×C5×C31C3×D1114yesdirect product factor
18C11×C31C2×C32×C511yescharacteristic, complemented, Hall
19C3×C5×D11C3×C3114yesdirect product factor
20C2×C5×C31—111noHall
21C32×C31C5×D1111yescharacteristic, direct product factor, Hall
22C32×D11C5×C3111yescharacteristic, direct product factor, Hall
23C2×C3×C31—114no—
24C3×C5×C11C2×C3×C3114yescomplemented
25C5×C31C32×D1111yescharacteristic, direct product factor, Hall
26C5×D11C32×C3111yescharacteristic, direct product factor, Hall
27C32×C11C2×C5×C3111yescharacteristic, complemented, Hall
28C3×C31C3×C5×D1114yesdirect product factor
29C2×C32×C5—111noHall
30C3×D11C3×C5×C3114yesdirect product factor
31C2×C31—111noHall
32C5×C11C2×C32×C3111yescharacteristic, complemented, Hall
33C32×C5D11×C3111yescharacteristic, direct product factor, Hall
34C3×C11C2×C3×C5×C3114yescomplemented
35C31C32×C5×D1111yescharacteristic, direct product factor, Sylow
36C2×C3×C5—114no—
37D11C32×C5×C3111yescharacteristic, direct product factor, Hall
38C2×C32—111noHall
39C3×C5C3×D11×C3114yesdirect product factor
40C11C2×C32×C5×C3111yescharacteristic, complemented, Sylow
41C2×C5—111noHall
42C32C5×D11×C3111yescharacteristic, direct product factor, Sylow
43C2×C3—114no—
44C5C32×D11×C3111yescharacteristic, direct product factor, Sylow
45C3C3×C5×D11×C3114yesdirect product factor
46C2—111noSylow
subgroupG/H
center, hypercenterC32×C5×C31D11
commutator, cosocle, hypocenterC11C2×C32×C5×C31
FrattiniC1G
Fitting, socleC32×C5×C11×C31C2
LCSG ▷ C11
UCSC1 ◁ C32×C5×C31

Complements

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

NH ≅ G/Ntype
1. C32×C5×C11×C31C2semidirect
2. C3×C5×D11×C31C3direct (N × H)
3. C32×D11×C31C5direct (N × H)
4. C3×C5×C11×C31C2×C3semidirect
5. C5×D11×C31C32direct (N × H)
6. C32×C11×C31C2×C5semidirect
8. C3×D11×C31C3×C5direct (N × H)
9. C5×C11×C31C2×C32semidirect
10. C32×C5×C31D11direct (N × H)
11. C3×C11×C31C2×C3×C5semidirect
12. C32×C5×D11C31direct (N × H)
14. D11×C31C32×C5direct (N × H)
16. C32×C5×C11C2×C31semidirect
17. C3×C5×C31C3×D11direct (N × H)
18. C11×C31C2×C32×C5semidirect
19. C3×C5×D11C3×C31direct (N × H)
21. C32×C31C5×D11direct (N × H)
22. C32×D11C5×C31direct (N × H)
24. C3×C5×C11C2×C3×C31semidirect
25. C5×C31C32×D11direct (N × H)
26. C5×D11C32×C31direct (N × H)
27. C32×C11C2×C5×C31semidirect
28. C3×C31C3×C5×D11direct (N × H)
30. C3×D11C3×C5×C31direct (N × H)
32. C5×C11C2×C32×C31semidirect
33. C32×C5D11×C31direct (N × H)
34. C3×C11C2×C3×C5×C31semidirect
35. C31C32×C5×D11direct (N × H)
37. D11C32×C5×C31direct (N × H)
39. C3×C5C3×D11×C31direct (N × H)
40. C11C2×C32×C5×C31semidirect
42. C32C5×D11×C31direct (N × H)
44. C5C32×D11×C31direct (N × H)
45. C3C3×C5×D11×C31direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×C11×C312
C3×C5×D11×C313
C32×D11×C315
C2×C32×C5×C3111
C32×C5×D1131