Finite Group Databasebeta

← C23×C32×C5×C59 #72198784

Subgroups — C23×C32×C5×C59 #72198784

Order 21240.

384 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C5×C59C314yesmaximal, direct product factor
2C23×C32×C59C511yesmaximal, characteristic, direct product factor, Hall
3C23×C5×C59C3211yescharacteristic, direct product factor, Hall
4C22×C32×C5×C59C217yesmaximal, direct product factor
5C2×C32×C5×C59C2217yesdirect product factor
6C22×C3×C5×C59C2×C3128yesdirect product factor
7C32×C5×C59C2311yescharacteristic, direct product factor, Hall
8C22×C32×C59C2×C517yesdirect product factor
9C2×C3×C5×C59C22×C3128yesdirect product factor
10C23×C3×C59C3×C514yesdirect product factor
11C22×C5×C59C2×C3217yesdirect product factor
12C2×C32×C59C22×C517yesdirect product factor
13C3×C5×C59C23×C314yesdirect product factor
14C22×C3×C59C2×C3×C5128yesdirect product factor
15C2×C5×C59C22×C3217yesdirect product factor
16C32×C59C23×C511yescharacteristic, direct product factor, Hall
17C23×C59C32×C511yescharacteristic, direct product factor, Hall
18C23×C32×C5C5911yesmaximal, characteristic, direct product factor, Hall
19C2×C3×C59C22×C3×C5128yesdirect product factor
20C5×C59C23×C3211yescharacteristic, direct product factor, Hall
21C22×C59C2×C32×C517yesdirect product factor
22C22×C32×C5C2×C5917yesdirect product factor
23C3×C59C23×C3×C514yesdirect product factor
24C23×C3×C5C3×C5914yesdirect product factor
25C2×C59C22×C32×C517yesdirect product factor
26C2×C32×C5C22×C5917yesdirect product factor
27C23×C32C5×C5911yescharacteristic, direct product factor, Hall
28C22×C3×C5C2×C3×C59128yesdirect product factor
29C59C23×C32×C511yescharacteristic, direct product factor, Sylow
30C32×C5C23×C5911yescharacteristic, direct product factor, Hall
31C23×C5C32×C5911yescharacteristic, direct product factor, Hall
32C22×C32C2×C5×C5917yesdirect product factor
33C2×C3×C5C22×C3×C59128yesdirect product factor
34C23×C3C3×C5×C5914yesdirect product factor
35C22×C5C2×C32×C5917yesdirect product factor
36C2×C32C22×C5×C5917yesdirect product factor
37C3×C5C23×C3×C5914yesdirect product factor
38C22×C3C2×C3×C5×C59128yesdirect product factor
39C2×C5C22×C32×C5917yesdirect product factor
40C32C23×C5×C5911yescharacteristic, direct product factor, Sylow
41C23C32×C5×C5911yescharacteristic, direct product factor, Sylow
42C2×C3C22×C3×C5×C59128yesdirect product factor
43C5C23×C32×C5911yescharacteristic, direct product factor, Sylow
44C22C2×C32×C5×C5917yesdirect product factor
45C3C23×C3×C5×C5914yesdirect product factor
46C2C22×C32×C5×C5917yesdirect 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. C23×C3×C5×C59C3direct (N × H)
2. C23×C32×C59C5direct (N × H)
3. C23×C5×C59C32direct (N × H)
4. C22×C32×C5×C59C2direct (N × H)
5. C2×C32×C5×C59C22direct (N × H)
6. C22×C3×C5×C59C2×C3direct (N × H)
7. C32×C5×C59C23direct (N × H)
8. C22×C32×C59C2×C5direct (N × H)
9. C2×C3×C5×C59C22×C3direct (N × H)
10. C23×C3×C59C3×C5direct (N × H)
11. C22×C5×C59C2×C32direct (N × H)
12. C2×C32×C59C22×C5direct (N × H)
13. C3×C5×C59C23×C3direct (N × H)
14. C22×C3×C59C2×C3×C5direct (N × H)
15. C2×C5×C59C22×C32direct (N × H)
16. C32×C59C23×C5direct (N × H)
17. C23×C59C32×C5direct (N × H)
18. C23×C32×C5C59direct (N × H)
19. C2×C3×C59C22×C3×C5direct (N × H)
20. C5×C59C23×C32direct (N × H)
21. C22×C59C2×C32×C5direct (N × H)
22. C22×C32×C5C2×C59direct (N × H)
23. C3×C59C23×C3×C5direct (N × H)
24. C23×C3×C5C3×C59direct (N × H)
25. C2×C59C22×C32×C5direct (N × H)
26. C2×C32×C5C22×C59direct (N × H)
27. C23×C32C5×C59direct (N × H)
28. C22×C3×C5C2×C3×C59direct (N × H)
29. C59C23×C32×C5direct (N × H)
30. C32×C5C23×C59direct (N × H)
31. C23×C5C32×C59direct (N × H)
32. C22×C32C2×C5×C59direct (N × H)
33. C2×C3×C5C22×C3×C59direct (N × H)
34. C23×C3C3×C5×C59direct (N × H)
35. C22×C5C2×C32×C59direct (N × H)
36. C2×C32C22×C5×C59direct (N × H)
37. C3×C5C23×C3×C59direct (N × H)
38. C22×C3C2×C3×C5×C59direct (N × H)
39. C2×C5C22×C32×C59direct (N × H)
40. C32C23×C5×C59direct (N × H)
41. C23C32×C5×C59direct (N × H)
42. C2×C3C22×C3×C5×C59direct (N × H)
43. C5C23×C32×C59direct (N × H)
44. C22C2×C32×C5×C59direct (N × H)
45. C3C23×C3×C5×C59direct (N × H)
46. C2C22×C32×C5×C59direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×C3×C5×C593
C23×C32×C595
C22×C32×C5×C592
C23×C32×C559