Finite Group Databasebeta

← C32×D5×C11×C31 #44501870

Subgroups — C32×D5×C11×C31 #44501870

Order 30690.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×C11×C31C211yesmaximal, characteristic, complemented, Hall
2C3×D5×C11×C31C314yesmaximal, direct product factor
3C2×C32×C11×C31—51nomaximal, Hall
4C3×C5×C11×C31C2×C314yescomplemented
5D5×C11×C31C3211yescharacteristic, direct product factor, Hall
6C32×C11×C31D511yescharacteristic, direct product factor, Hall
7C32×D5×C31C1111yesmaximal, characteristic, direct product factor, Hall
8C2×C3×C11×C31—54no—
9C5×C11×C31C2×C3211yescharacteristic, complemented, Hall
10C32×C5×C31C2×C1111yescharacteristic, complemented, Hall
11C3×C11×C31C3×D514yesdirect product factor
12C32×D5×C11C3111yesmaximal, characteristic, direct product factor, Hall
13C3×D5×C31C3×C1114yesdirect product factor
14C2×C11×C31—51noHall
15C2×C32×C31—51noHall
16C32×C5×C11C2×C3111yescharacteristic, complemented, Hall
17C3×C5×C31C2×C3×C1114yescomplemented
18C11×C31C32×D511yescharacteristic, direct product factor, Hall
19C3×D5×C11C3×C3114yesdirect product factor
20D5×C31C32×C1111yescharacteristic, direct product factor, Hall
21C32×C31D5×C1111yescharacteristic, direct product factor, Hall
22C2×C32×C11—51noHall
23C2×C3×C31—54no—
24C3×C5×C11C2×C3×C3114yescomplemented
25C5×C31C2×C32×C1111yescharacteristic, complemented, Hall
26D5×C11C32×C3111yescharacteristic, direct product factor, Hall
27C32×C11D5×C3111yescharacteristic, direct product factor, Hall
28C3×C31C3×D5×C1114yesdirect product factor
29C32×D5C11×C3111yescharacteristic, direct product factor, Hall
30C2×C3×C11—54no—
31C2×C31—51noHall
32C5×C11C2×C32×C3111yescharacteristic, complemented, Hall
33C32×C5C2×C11×C3111yescharacteristic, complemented, Hall
34C3×C11C3×D5×C3114yesdirect product factor
35C31C32×D5×C1111yescharacteristic, direct product factor, Sylow
36C3×D5C3×C11×C3114yesdirect product factor
37C2×C11—51noHall
38C2×C32—51noHall
39C3×C5C2×C3×C11×C3114yescomplemented
40C11C32×D5×C3111yescharacteristic, direct product factor, Sylow
41D5C32×C11×C3111yescharacteristic, direct product factor, Hall
42C32D5×C11×C3111yescharacteristic, direct product factor, Sylow
43C2×C3—54no—
44C5C2×C32×C11×C3111yescharacteristic, complemented, Sylow
45C3C3×D5×C11×C3114yesdirect product factor
46C2—51noSylow
subgroupG/H
center, hypercenterC32×C11×C31D5
commutator, cosocle, hypocenterC5C2×C32×C11×C31
FrattiniC1G
Fitting, socleC32×C5×C11×C31C2
LCSG ▷ C5
UCSC1 ◁ C32×C11×C31

Complements

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

NH ≅ G/Ntype
1. C32×C5×C11×C31C2semidirect
2. C3×D5×C11×C31C3direct (N × H)
4. C3×C5×C11×C31C2×C3semidirect
5. D5×C11×C31C32direct (N × H)
6. C32×C11×C31D5direct (N × H)
7. C32×D5×C31C11direct (N × H)
9. C5×C11×C31C2×C32semidirect
10. C32×C5×C31C2×C11semidirect
11. C3×C11×C31C3×D5direct (N × H)
12. C32×D5×C11C31direct (N × H)
13. C3×D5×C31C3×C11direct (N × H)
16. C32×C5×C11C2×C31semidirect
17. C3×C5×C31C2×C3×C11semidirect
18. C11×C31C32×D5direct (N × H)
19. C3×D5×C11C3×C31direct (N × H)
20. D5×C31C32×C11direct (N × H)
21. C32×C31D5×C11direct (N × H)
24. C3×C5×C11C2×C3×C31semidirect
25. C5×C31C2×C32×C11semidirect
26. D5×C11C32×C31direct (N × H)
27. C32×C11D5×C31direct (N × H)
28. C3×C31C3×D5×C11direct (N × H)
29. C32×D5C11×C31direct (N × H)
32. C5×C11C2×C32×C31semidirect
33. C32×C5C2×C11×C31semidirect
34. C3×C11C3×D5×C31direct (N × H)
35. C31C32×D5×C11direct (N × H)
36. C3×D5C3×C11×C31direct (N × H)
39. C3×C5C2×C3×C11×C31semidirect
40. C11C32×D5×C31direct (N × H)
41. D5C32×C11×C31direct (N × H)
42. C32D5×C11×C31direct (N × H)
44. C5C2×C32×C11×C31semidirect
45. C3C3×D5×C11×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×D5×C11×C313
C2×C32×C11×C315
C32×D5×C3111
C32×D5×C1131