Finite Group Databasebeta

← C32×C7×D5×C31 #34086308

Subgroups — C32×C7×D5×C31 #34086308

Order 19530.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×C7×C31C211yesmaximal, characteristic, complemented, Hall
2C3×C7×D5×C31C314yesmaximal, direct product factor
3C2×C32×C7×C31—51nomaximal, Hall
4C3×C5×C7×C31C2×C314yescomplemented
5C32×D5×C31C711yesmaximal, characteristic, direct product factor, Hall
6C7×D5×C31C3211yescharacteristic, direct product factor, Hall
7C32×C7×C31D511yescharacteristic, direct product factor, Hall
8C32×C5×C31C2×C711yescharacteristic, complemented, Hall
9C2×C3×C7×C31—54no—
10C5×C7×C31C2×C3211yescharacteristic, complemented, Hall
11C3×D5×C31C3×C714yesdirect product factor
12C3×C7×C31C3×D514yesdirect product factor
13C32×C7×D5C3111yesmaximal, characteristic, direct product factor, Hall
14C2×C32×C31—51noHall
15C3×C5×C31C2×C3×C714yescomplemented
16C2×C7×C31—51noHall
17C32×C5×C7C2×C3111yescharacteristic, complemented, Hall
18D5×C31C32×C711yescharacteristic, direct product factor, Hall
19C32×C31C7×D511yescharacteristic, direct product factor, Hall
20C7×C31C32×D511yescharacteristic, direct product factor, Hall
21C3×C7×D5C3×C3114yesdirect product factor
22C2×C3×C31—54no—
23C5×C31C2×C32×C711yescharacteristic, complemented, Hall
24C2×C32×C7—51noHall
25C3×C5×C7C2×C3×C3114yescomplemented
26C3×C31C3×C7×D514yesdirect product factor
27C32×D5C7×C3111yescharacteristic, direct product factor, Hall
28C7×D5C32×C3111yescharacteristic, direct product factor, Hall
29C32×C7D5×C3111yescharacteristic, direct product factor, Hall
30C2×C31—51noHall
31C32×C5C2×C7×C3111yescharacteristic, complemented, Hall
32C2×C3×C7—54no—
33C5×C7C2×C32×C3111yescharacteristic, complemented, Hall
34C31C32×C7×D511yescharacteristic, direct product factor, Sylow
35C3×D5C3×C7×C3114yesdirect product factor
36C3×C7C3×D5×C3114yesdirect product factor
37C2×C32—51noHall
38C3×C5C2×C3×C7×C3114yescomplemented
39C2×C7—51noHall
40D5C32×C7×C3111yescharacteristic, direct product factor, Hall
41C32C7×D5×C3111yescharacteristic, direct product factor, Sylow
42C7C32×D5×C3111yescharacteristic, direct product factor, Sylow
43C2×C3—54no—
44C5C2×C32×C7×C3111yescharacteristic, complemented, Sylow
45C3C3×C7×D5×C3114yesdirect product factor
46C2—51noSylow
subgroupG/H
center, hypercenterC32×C7×C31D5
commutator, cosocle, hypocenterC5C2×C32×C7×C31
FrattiniC1G
Fitting, socleC32×C5×C7×C31C2
LCSG ▷ C5
UCSC1 ◁ C32×C7×C31

Complements

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

NH ≅ G/Ntype
1. C32×C5×C7×C31C2semidirect
2. C3×C7×D5×C31C3direct (N × H)
4. C3×C5×C7×C31C2×C3semidirect
5. C32×D5×C31C7direct (N × H)
6. C7×D5×C31C32direct (N × H)
7. C32×C7×C31D5direct (N × H)
8. C32×C5×C31C2×C7semidirect
10. C5×C7×C31C2×C32semidirect
11. C3×D5×C31C3×C7direct (N × H)
12. C3×C7×C31C3×D5direct (N × H)
13. C32×C7×D5C31direct (N × H)
15. C3×C5×C31C2×C3×C7semidirect
17. C32×C5×C7C2×C31semidirect
18. D5×C31C32×C7direct (N × H)
19. C32×C31C7×D5direct (N × H)
20. C7×C31C32×D5direct (N × H)
21. C3×C7×D5C3×C31direct (N × H)
23. C5×C31C2×C32×C7semidirect
25. C3×C5×C7C2×C3×C31semidirect
26. C3×C31C3×C7×D5direct (N × H)
27. C32×D5C7×C31direct (N × H)
28. C7×D5C32×C31direct (N × H)
29. C32×C7D5×C31direct (N × H)
31. C32×C5C2×C7×C31semidirect
33. C5×C7C2×C32×C31semidirect
34. C31C32×C7×D5direct (N × H)
35. C3×D5C3×C7×C31direct (N × H)
36. C3×C7C3×D5×C31direct (N × H)
38. C3×C5C2×C3×C7×C31semidirect
40. D5C32×C7×C31direct (N × H)
41. C32C7×D5×C31direct (N × H)
42. C7C32×D5×C31direct (N × H)
44. C5C2×C32×C7×C31semidirect
45. C3C3×C7×D5×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×C7×C312
C3×C7×D5×C313
C2×C32×C7×C315
C32×D5×C317
C32×C7×D531