Finite Group Databasebeta

← C2×C32×C5×C7×C17 #24924210

Subgroups — C2×C32×C5×C7×C17 #24924210

Order 10710.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×C7×C17C211yesmaximal, characteristic, direct product factor, Hall
2C2×C3×C5×C7×C17C314yesmaximal, direct product factor
3C2×C32×C7×C17C511yesmaximal, characteristic, direct product factor, Hall
4C3×C5×C7×C17C2×C314yesdirect product factor
5C2×C32×C5×C17C711yesmaximal, characteristic, direct product factor, Hall
6C2×C5×C7×C17C3211yescharacteristic, direct product factor, Hall
7C32×C7×C17C2×C511yescharacteristic, direct product factor, Hall
8C32×C5×C17C2×C711yescharacteristic, direct product factor, Hall
9C2×C3×C7×C17C3×C514yesdirect product factor
10C2×C32×C5×C7C1711yesmaximal, characteristic, direct product factor, Hall
11C5×C7×C17C2×C3211yescharacteristic, direct product factor, Hall
12C2×C3×C5×C17C3×C714yesdirect product factor
13C3×C7×C17C2×C3×C514yesdirect product factor
14C32×C5×C7C2×C1711yescharacteristic, direct product factor, Hall
15C2×C32×C17C5×C711yescharacteristic, direct product factor, Hall
16C3×C5×C17C2×C3×C714yesdirect product factor
17C2×C7×C17C32×C511yescharacteristic, direct product factor, Hall
18C2×C3×C5×C7C3×C1714yesdirect product factor
19C2×C5×C17C32×C711yescharacteristic, direct product factor, Hall
20C32×C17C2×C5×C711yescharacteristic, direct product factor, Hall
21C2×C32×C7C5×C1711yescharacteristic, direct product factor, Hall
22C7×C17C2×C32×C511yescharacteristic, direct product factor, Hall
23C3×C5×C7C2×C3×C1714yesdirect product factor
24C2×C3×C17C3×C5×C714yesdirect product factor
25C2×C32×C5C7×C1711yescharacteristic, direct product factor, Hall
26C5×C17C2×C32×C711yescharacteristic, direct product factor, Hall
27C2×C5×C7C32×C1711yescharacteristic, direct product factor, Hall
28C32×C7C2×C5×C1711yescharacteristic, direct product factor, Hall
29C3×C17C2×C3×C5×C714yesdirect product factor
30C32×C5C2×C7×C1711yescharacteristic, direct product factor, Hall
31C2×C3×C7C3×C5×C1714yesdirect product factor
32C5×C7C2×C32×C1711yescharacteristic, direct product factor, Hall
33C2×C17C32×C5×C711yescharacteristic, direct product factor, Hall
34C2×C3×C5C3×C7×C1714yesdirect product factor
35C3×C7C2×C3×C5×C1714yesdirect product factor
36C2×C32C5×C7×C1711yescharacteristic, direct product factor, Hall
37C17C2×C32×C5×C711yescharacteristic, direct product factor, Sylow
38C3×C5C2×C3×C7×C1714yesdirect product factor
39C2×C7C32×C5×C1711yescharacteristic, direct product factor, Hall
40C2×C5C32×C7×C1711yescharacteristic, direct product factor, Hall
41C32C2×C5×C7×C1711yescharacteristic, direct product factor, Sylow
42C7C2×C32×C5×C1711yescharacteristic, direct product factor, Sylow
43C2×C3C3×C5×C7×C1714yesdirect product factor
44C5C2×C32×C7×C1711yescharacteristic, direct product factor, Sylow
45C3C2×C3×C5×C7×C1714yesdirect product factor
46C2C32×C5×C7×C1711yescharacteristic, direct product factor, Sylow
subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C32×C5×C7×C17C2direct (N × H)
2. C2×C3×C5×C7×C17C3direct (N × H)
3. C2×C32×C7×C17C5direct (N × H)
4. C3×C5×C7×C17C2×C3direct (N × H)
5. C2×C32×C5×C17C7direct (N × H)
6. C2×C5×C7×C17C32direct (N × H)
7. C32×C7×C17C2×C5direct (N × H)
8. C32×C5×C17C2×C7direct (N × H)
9. C2×C3×C7×C17C3×C5direct (N × H)
10. C2×C32×C5×C7C17direct (N × H)
11. C5×C7×C17C2×C32direct (N × H)
12. C2×C3×C5×C17C3×C7direct (N × H)
13. C3×C7×C17C2×C3×C5direct (N × H)
14. C32×C5×C7C2×C17direct (N × H)
15. C2×C32×C17C5×C7direct (N × H)
16. C3×C5×C17C2×C3×C7direct (N × H)
17. C2×C7×C17C32×C5direct (N × H)
18. C2×C3×C5×C7C3×C17direct (N × H)
19. C2×C5×C17C32×C7direct (N × H)
20. C32×C17C2×C5×C7direct (N × H)
21. C2×C32×C7C5×C17direct (N × H)
22. C7×C17C2×C32×C5direct (N × H)
23. C3×C5×C7C2×C3×C17direct (N × H)
24. C2×C3×C17C3×C5×C7direct (N × H)
25. C2×C32×C5C7×C17direct (N × H)
26. C5×C17C2×C32×C7direct (N × H)
27. C2×C5×C7C32×C17direct (N × H)
28. C32×C7C2×C5×C17direct (N × H)
29. C3×C17C2×C3×C5×C7direct (N × H)
30. C32×C5C2×C7×C17direct (N × H)
31. C2×C3×C7C3×C5×C17direct (N × H)
32. C5×C7C2×C32×C17direct (N × H)
33. C2×C17C32×C5×C7direct (N × H)
34. C2×C3×C5C3×C7×C17direct (N × H)
35. C3×C7C2×C3×C5×C17direct (N × H)
36. C2×C32C5×C7×C17direct (N × H)
37. C17C2×C32×C5×C7direct (N × H)
38. C3×C5C2×C3×C7×C17direct (N × H)
39. C2×C7C32×C5×C17direct (N × H)
40. C2×C5C32×C7×C17direct (N × H)
41. C32C2×C5×C7×C17direct (N × H)
42. C7C2×C32×C5×C17direct (N × H)
43. C2×C3C3×C5×C7×C17direct (N × H)
44. C5C2×C32×C7×C17direct (N × H)
45. C3C2×C3×C5×C7×C17direct (N × H)
46. C2C32×C5×C7×C17direct (N × H)