Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
332 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 170 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C5 | C23×D3 |
| commutator, cosocle | C2×C3 | C24×C5 |
| Frattini | C2 | C23×C5×D3 |
| Fitting | C2×C3×C5×D4 | C2 |
| socle | C2×C3×C5 | C24 |
| hypercenter | C2×C5×D4 | D3 |
| hypocenter | C3 | C5×H(5,𝔽2) |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C5 ◁ C2×C5×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C5×D4 | C2 | semidirect |
| 2. C2×C5×#67 | C2 | semidirect |
| 3. C5×#237 | C2 | semidirect |
| 4. C5×D3×D4 | C2 | semidirect |
| 5. C5×#235 | C2 | semidirect |
| 7. C23×C3×C5 | C22 | semidirect |
| 8. C22×C5×D3 | C22 | semidirect |
| 9. C3×C5×D4 | C22 | semidirect |
| 10. C2×C3×C4×C5 | C22 | semidirect |
| 11. C5×#67 | C22 | semidirect |
| 12. C5×#67 | C22 | semidirect |
| 13. C2×C5×Dic3 | C22 | semidirect |
| 14. C5×D12 | C22 | semidirect |
| 15. C4×C5×D3 | C22 | semidirect |
| 16. C5×Dic6 | C22 | semidirect |
| 17. #1004 | C5 | direct (N × H) |
| 22. C2×C5×D4 | D3 | semidirect |
| 30. C2×C3×D4 | C2×C5 | semidirect |
| 31. C2×#67 | C2×C5 | semidirect |
| 32. #237 | C2×C5 | semidirect |
| 33. D3×D4 | C2×C5 | semidirect |
| 34. #235 | C2×C5 | semidirect |
| 36. C23×C5 | C2×D3 | semidirect |
| 41. C5×D4 | C2×D3 | semidirect |
| 44. C2×C4×C5 | C2×D3 | semidirect |
| 50. C23×C3 | C22×C5 | semidirect |
| 51. C22×D3 | C22×C5 | semidirect |
| 52. C3×D4 | C22×C5 | semidirect |
| 53. C2×C3×C4 | C22×C5 | semidirect |
| 54. #67 | C22×C5 | semidirect |
| 55. #67 | C22×C5 | semidirect |
| 56. C2×Dic3 | C22×C5 | semidirect |
| 57. D12 | C22×C5 | semidirect |
| 58. C4×D3 | C22×C5 | semidirect |
| 59. Dic6 | C22×C5 | semidirect |
| 71. C2×D4 | C5×D3 | semidirect |
| 72. C3×C5 | H(5,𝔽2) | semidirect |
| 85. C23 | C2×C5×D3 | semidirect |
| 90. D4 | C2×C5×D3 | semidirect |
| 93. C2×C4 | C2×C5×D3 | semidirect |
| 98. C5 | #1004 | direct (N × H) |
| 106. C3 | C5×H(5,𝔽2) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×D4 | 2 |
| C2×C5×#67 | 2 |
| C5×#237 | 2 |
| C5×D3×D4 | 2 |
| C5×#235 | 2 |
| C5×H(5,𝔽2) | 3 |
| #1004 | 5 |