Finite Group Databasebeta

← C22×C32×C5×C72 #22579110

Subgroups — C22×C32×C5×C72 #22579110

Order 8820.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C5×C72C213yesmaximal, direct product factor
2C22×C3×C5×C72C314yesmaximal, direct product factor
3C32×C5×C72C2211yescharacteristic, direct product factor, Hall
4C22×C32×C72C511yesmaximal, characteristic, direct product factor, Hall
5C2×C3×C5×C72C2×C3112yesdirect product factor
6C22×C32×C5×C7C718yesmaximal, direct product factor
7C22×C5×C72C3211yescharacteristic, direct product factor, Hall
8C2×C32×C72C2×C513yesdirect product factor
9C3×C5×C72C22×C314yesdirect product factor
10C2×C32×C5×C7C2×C7124yesdirect product factor
11C22×C3×C72C3×C514yesdirect product factor
12C2×C5×C72C2×C3213yesdirect product factor
13C32×C72C22×C511yescharacteristic, direct product factor, Hall
14C22×C3×C5×C7C3×C7132yesdirect product factor
15C32×C5×C7C22×C718yesdirect product factor
16C2×C3×C72C2×C3×C5112yesdirect product factor
17C22×C32×C7C5×C718yesdirect product factor
18C5×C72C22×C3211yescharacteristic, direct product factor, Hall
19C2×C3×C5×C7C2×C3×C7196yesdirect product factor
20C22×C72C32×C511yescharacteristic, direct product factor, Hall
21C22×C32×C5C7211yescharacteristic, direct product factor, Hall
22C3×C72C22×C3×C514yesdirect product factor
23C22×C5×C7C32×C718yesdirect product factor
24C2×C32×C7C2×C5×C7124yesdirect product factor
25C3×C5×C7C22×C3×C7132yesdirect product factor
26C2×C72C2×C32×C513yesdirect product factor
27C2×C32×C5C2×C7213yesdirect product factor
28C22×C3×C7C3×C5×C7132yesdirect product factor
29C2×C5×C7C2×C32×C7124yesdirect product factor
30C32×C7C22×C5×C718yesdirect product factor
31C22×C3×C5C3×C7214yesdirect product factor
32C72C22×C32×C511yescharacteristic, direct product factor, Sylow
33C32×C5C22×C7211yescharacteristic, direct product factor, Hall
34C2×C3×C7C2×C3×C5×C7196yesdirect product factor
35C22×C32C5×C7211yescharacteristic, direct product factor, Hall
36C5×C7C22×C32×C718yesdirect product factor
37C2×C3×C5C2×C3×C72112yesdirect product factor
38C22×C7C32×C5×C718yesdirect product factor
39C3×C7C22×C3×C5×C7132yesdirect product factor
40C22×C5C32×C7211yescharacteristic, direct product factor, Hall
41C2×C32C2×C5×C7213yesdirect product factor
42C3×C5C22×C3×C7214yesdirect product factor
43C2×C7C2×C32×C5×C7124yesdirect product factor
44C22×C3C3×C5×C7214yesdirect product factor
45C2×C5C2×C32×C7213yesdirect product factor
46C32C22×C5×C7211yescharacteristic, direct product factor, Sylow
47C7C22×C32×C5×C718yesdirect product factor
48C2×C3C2×C3×C5×C72112yesdirect product factor
49C5C22×C32×C7211yescharacteristic, direct product factor, Sylow
50C22C32×C5×C7211yescharacteristic, direct product factor, Sylow
51C3C22×C3×C5×C7214yesdirect product factor
52C2C2×C32×C5×C7213yesdirect product factor
subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C32×C5×C72C2direct (N × H)
2. C22×C3×C5×C72C3direct (N × H)
3. C32×C5×C72C22direct (N × H)
4. C22×C32×C72C5direct (N × H)
5. C2×C3×C5×C72C2×C3direct (N × H)
6. C22×C32×C5×C7C7direct (N × H)
7. C22×C5×C72C32direct (N × H)
8. C2×C32×C72C2×C5direct (N × H)
9. C3×C5×C72C22×C3direct (N × H)
10. C2×C32×C5×C7C2×C7direct (N × H)
11. C22×C3×C72C3×C5direct (N × H)
12. C2×C5×C72C2×C32direct (N × H)
13. C32×C72C22×C5direct (N × H)
14. C22×C3×C5×C7C3×C7direct (N × H)
15. C32×C5×C7C22×C7direct (N × H)
16. C2×C3×C72C2×C3×C5direct (N × H)
17. C22×C32×C7C5×C7direct (N × H)
18. C5×C72C22×C32direct (N × H)
19. C2×C3×C5×C7C2×C3×C7direct (N × H)
20. C22×C72C32×C5direct (N × H)
21. C22×C32×C5C72direct (N × H)
22. C3×C72C22×C3×C5direct (N × H)
23. C22×C5×C7C32×C7direct (N × H)
24. C2×C32×C7C2×C5×C7direct (N × H)
25. C3×C5×C7C22×C3×C7direct (N × H)
26. C2×C72C2×C32×C5direct (N × H)
27. C2×C32×C5C2×C72direct (N × H)
28. C22×C3×C7C3×C5×C7direct (N × H)
29. C2×C5×C7C2×C32×C7direct (N × H)
30. C32×C7C22×C5×C7direct (N × H)
31. C22×C3×C5C3×C72direct (N × H)
32. C72C22×C32×C5direct (N × H)
33. C32×C5C22×C72direct (N × H)
34. C2×C3×C7C2×C3×C5×C7direct (N × H)
35. C22×C32C5×C72direct (N × H)
36. C5×C7C22×C32×C7direct (N × H)
37. C2×C3×C5C2×C3×C72direct (N × H)
38. C22×C7C32×C5×C7direct (N × H)
39. C3×C7C22×C3×C5×C7direct (N × H)
40. C22×C5C32×C72direct (N × H)
41. C2×C32C2×C5×C72direct (N × H)
42. C3×C5C22×C3×C72direct (N × H)
43. C2×C7C2×C32×C5×C7direct (N × H)
44. C22×C3C3×C5×C72direct (N × H)
45. C2×C5C2×C32×C72direct (N × H)
46. C32C22×C5×C72direct (N × H)
47. C7C22×C32×C5×C7direct (N × H)
48. C2×C3C2×C3×C5×C72direct (N × H)
49. C5C22×C32×C72direct (N × H)
50. C22C32×C5×C72direct (N × H)
51. C3C22×C3×C5×C72direct (N × H)
52. C2C2×C32×C5×C72direct (N × H)