Finite Group Databasebeta

← C22×C5×C11×C13⋊C3 #22575181

Subgroups — C22×C5×C11×C13⋊C3 #22575181

Order 8580.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×C11×C13⋊C3C213yesmaximal, direct product factor
2C22×C5×C11×C13C311yesmaximal, characteristic, complemented, Hall
3C5×C11×C13⋊C3C2211yescharacteristic, direct product factor, Hall
4C22×C11×C13⋊C3C511yesmaximal, characteristic, direct product factor, Hall
5C2×C5×C11×C13C2×C313yescomplemented
6C2×C11×C13⋊C3C2×C513yesdirect product factor
7C22×C5×C13⋊C3C1111yesmaximal, characteristic, direct product factor, Hall
8C5×C11×C13C22×C311yescharacteristic, complemented, Hall
9C22×C3×C5×C11—131nomaximal, Hall
10C22×C11×C13C3×C511yescharacteristic, complemented, Hall
11C11×C13⋊C3C22×C511yescharacteristic, direct product factor, Hall
12C2×C5×C13⋊C3C2×C1113yesdirect product factor
13C2×C3×C5×C11—133no—
14C2×C11×C13C2×C3×C513yescomplemented
15C22×C5×C13C3×C1111yescharacteristic, complemented, Hall
16C22×C5×C11C13⋊C311yescharacteristic, direct product factor, Hall
17C5×C13⋊C3C22×C1111yescharacteristic, direct product factor, Hall
18C3×C5×C11—131noHall
19C22×C13⋊C3C5×C1111yescharacteristic, direct product factor, Hall
20C11×C13C22×C3×C511yescharacteristic, complemented, Hall
21C22×C3×C11—131noHall
22C2×C5×C13C2×C3×C1113yescomplemented
23C2×C5×C11C2×C13⋊C313yesdirect product factor
24C2×C13⋊C3C2×C5×C1113yesdirect product factor
25C2×C3×C11—133no—
26C5×C13C22×C3×C1111yescharacteristic, complemented, Hall
27C22×C3×C5—131noHall
28C5×C11C22×C13⋊C311yescharacteristic, direct product factor, Hall
29C22×C13C3×C5×C1111yescharacteristic, complemented, Hall
30C22×C11C5×C13⋊C311yescharacteristic, direct product factor, Hall
31C13⋊C3C22×C5×C1111yescharacteristic, direct product factor, Hall
32C3×C11—131noHall
33C2×C3×C5—133no—
34C2×C13C2×C3×C5×C1113yescomplemented
35C2×C11C2×C5×C13⋊C313yesdirect product factor
36C22×C5C11×C13⋊C311yescharacteristic, direct product factor, Hall
37C3×C5—131noHall
38C13C22×C3×C5×C1111yescharacteristic, complemented, Sylow
39C22×C3—131noHall
40C11C22×C5×C13⋊C311yescharacteristic, direct product factor, Sylow
41C2×C5C2×C11×C13⋊C313yesdirect product factor
42C2×C3—133no—
43C5C22×C11×C13⋊C311yescharacteristic, direct product factor, Sylow
44C22C5×C11×C13⋊C311yescharacteristic, direct product factor, Sylow
45C3—131noSylow
46C2C2×C5×C11×C13⋊C313yesdirect product factor
subgroupG/H
center, hypercenterC22×C5×C11C13⋊C3
commutator, hypocenterC13C22×C3×C5×C11
FrattiniC1G
Fitting, socleC22×C5×C11×C13C3
LCSG ▷ C13
UCSC1 ◁ C22×C5×C11

Complements

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

NH ≅ G/Ntype
1. C2×C5×C11×C13⋊C3C2direct (N × H)
2. C22×C5×C11×C13C3semidirect
3. C5×C11×C13⋊C3C22direct (N × H)
4. C22×C11×C13⋊C3C5direct (N × H)
5. C2×C5×C11×C13C2×C3semidirect
6. C2×C11×C13⋊C3C2×C5direct (N × H)
7. C22×C5×C13⋊C3C11direct (N × H)
8. C5×C11×C13C22×C3semidirect
10. C22×C11×C13C3×C5semidirect
11. C11×C13⋊C3C22×C5direct (N × H)
12. C2×C5×C13⋊C3C2×C11direct (N × H)
14. C2×C11×C13C2×C3×C5semidirect
15. C22×C5×C13C3×C11semidirect
16. C22×C5×C11C13⋊C3direct (N × H)
17. C5×C13⋊C3C22×C11direct (N × H)
19. C22×C13⋊C3C5×C11direct (N × H)
20. C11×C13C22×C3×C5semidirect
22. C2×C5×C13C2×C3×C11semidirect
23. C2×C5×C11C2×C13⋊C3direct (N × H)
24. C2×C13⋊C3C2×C5×C11direct (N × H)
26. C5×C13C22×C3×C11semidirect
28. C5×C11C22×C13⋊C3direct (N × H)
29. C22×C13C3×C5×C11semidirect
30. C22×C11C5×C13⋊C3direct (N × H)
31. C13⋊C3C22×C5×C11direct (N × H)
34. C2×C13C2×C3×C5×C11semidirect
35. C2×C11C2×C5×C13⋊C3direct (N × H)
36. C22×C5C11×C13⋊C3direct (N × H)
38. C13C22×C3×C5×C11semidirect
40. C11C22×C5×C13⋊C3direct (N × H)
41. C2×C5C2×C11×C13⋊C3direct (N × H)
43. C5C22×C11×C13⋊C3direct (N × H)
44. C22C5×C11×C13⋊C3direct (N × H)
46. C2C2×C5×C11×C13⋊C3direct (N × H)