Finite Group Databasebeta

← C23×C32×C53 #72187807

Subgroups — C23×C32×C53 #72187807

Order 9000.

6144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C53C217yesmaximal, direct product factor
2C23×C3×C53C314yesmaximal, direct product factor
3C2×C32×C53C2217yesdirect product factor
4C23×C32×C52C5131yesmaximal, direct product factor
5C22×C3×C53C2×C3128yesdirect product factor
6C32×C53C2311yescharacteristic, direct product factor, Hall
7C23×C53C3211yescharacteristic, direct product factor, Hall
8C22×C32×C52C2×C51217yesdirect product factor
9C2×C3×C53C22×C3128yesdirect product factor
10C23×C3×C52C3×C51124yesdirect product factor
11C22×C53C2×C3217yesdirect product factor
12C2×C32×C52C22×C51217yesdirect product factor
13C3×C53C23×C314yesdirect product factor
14C23×C32×C5C52131yesdirect product factor
15C22×C3×C52C2×C3×C51868yesdirect product factor
16C2×C53C22×C3217yesdirect product factor
17C32×C52C23×C5131yesdirect product factor
18C23×C52C32×C5131yesdirect product factor
19C22×C32×C5C2×C521217yesdirect product factor
20C2×C3×C52C22×C3×C51868yesdirect product factor
21C53C23×C3211yescharacteristic, direct product factor, Sylow
22C23×C3×C5C3×C521124yesdirect product factor
23C22×C52C2×C32×C51217yesdirect product factor
24C2×C32×C5C22×C521217yesdirect product factor
25C3×C52C23×C3×C51124yesdirect product factor
26C23×C32C5311yescharacteristic, direct product factor, Hall
27C22×C3×C5C2×C3×C521868yesdirect product factor
28C2×C52C22×C32×C51217yesdirect product factor
29C32×C5C23×C52131yesdirect product factor
30C23×C5C32×C52131yesdirect product factor
31C22×C32C2×C5317yesdirect product factor
32C2×C3×C5C22×C3×C521868yesdirect product factor
33C52C23×C32×C5131yesdirect product factor
34C23×C3C3×C5314yesdirect product factor
35C22×C5C2×C32×C521217yesdirect product factor
36C2×C32C22×C5317yesdirect product factor
37C3×C5C23×C3×C521124yesdirect product factor
38C22×C3C2×C3×C53128yesdirect product factor
39C2×C5C22×C32×C521217yesdirect product factor
40C32C23×C5311yescharacteristic, direct product factor, Sylow
41C23C32×C5311yescharacteristic, direct product factor, Sylow
42C2×C3C22×C3×C53128yesdirect product factor
43C5C23×C32×C52131yesdirect product factor
44C22C2×C32×C5317yesdirect product factor
45C3C23×C3×C5314yesdirect product factor
46C2C22×C32×C5317yesdirect 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. C22×C32×C53C2direct (N × H)
2. C23×C3×C53C3direct (N × H)
3. C2×C32×C53C22direct (N × H)
4. C23×C32×C52C5direct (N × H)
5. C22×C3×C53C2×C3direct (N × H)
6. C32×C53C23direct (N × H)
7. C23×C53C32direct (N × H)
8. C22×C32×C52C2×C5direct (N × H)
9. C2×C3×C53C22×C3direct (N × H)
10. C23×C3×C52C3×C5direct (N × H)
11. C22×C53C2×C32direct (N × H)
12. C2×C32×C52C22×C5direct (N × H)
13. C3×C53C23×C3direct (N × H)
14. C23×C32×C5C52direct (N × H)
15. C22×C3×C52C2×C3×C5direct (N × H)
16. C2×C53C22×C32direct (N × H)
17. C32×C52C23×C5direct (N × H)
18. C23×C52C32×C5direct (N × H)
19. C22×C32×C5C2×C52direct (N × H)
20. C2×C3×C52C22×C3×C5direct (N × H)
21. C53C23×C32direct (N × H)
22. C23×C3×C5C3×C52direct (N × H)
23. C22×C52C2×C32×C5direct (N × H)
24. C2×C32×C5C22×C52direct (N × H)
25. C3×C52C23×C3×C5direct (N × H)
26. C23×C32C53direct (N × H)
27. C22×C3×C5C2×C3×C52direct (N × H)
28. C2×C52C22×C32×C5direct (N × H)
29. C32×C5C23×C52direct (N × H)
30. C23×C5C32×C52direct (N × H)
31. C22×C32C2×C53direct (N × H)
32. C2×C3×C5C22×C3×C52direct (N × H)
33. C52C23×C32×C5direct (N × H)
34. C23×C3C3×C53direct (N × H)
35. C22×C5C2×C32×C52direct (N × H)
36. C2×C32C22×C53direct (N × H)
37. C3×C5C23×C3×C52direct (N × H)
38. C22×C3C2×C3×C53direct (N × H)
39. C2×C5C22×C32×C52direct (N × H)
40. C32C23×C53direct (N × H)
41. C23C32×C53direct (N × H)
42. C2×C3C22×C3×C53direct (N × H)
43. C5C23×C32×C52direct (N × H)
44. C22C2×C32×C53direct (N × H)
45. C3C23×C3×C53direct (N × H)
46. C2C22×C32×C53direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C532
C23×C3×C533
C23×C32×C525