Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
328 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3×C4×C5 | C2 | semidirect |
| 2. C2×C5×#67 | C2 | semidirect |
| 3. C5×#235 | C2 | direct (N × H) |
| 4. C2×C5×D12 | C2 | semidirect |
| 5. C2×C4×C5×D3 | C2 | semidirect |
| 6. C2×C5×Dic6 | C2 | semidirect |
| 12. C2×C3×C4×C5 | C22 | semidirect |
| 13. C5×#67 | C22 | semidirect |
| 15. C5×D12 | C22 | semidirect |
| 16. C4×C5×D3 | C22 | semidirect |
| 17. C5×Dic6 | C22 | semidirect |
| 18. C2×#235 | C5 | direct (N × H) |
| 24. C22×C4×C5 | D3 | semidirect |
| 33. C22×C3×C4 | C2×C5 | semidirect |
| 34. C2×#67 | C2×C5 | semidirect |
| 35. #235 | C2×C5 | direct (N × H) |
| 36. C2×D12 | C2×C5 | semidirect |
| 37. C2×C4×D3 | C2×C5 | semidirect |
| 38. C2×Dic6 | C2×C5 | semidirect |
| 48. C2×C4×C5 | C2×D3 | semidirect |
| 51. C2×C3×C5 | #41 | semidirect |
| 58. C2×C3×C4 | C22×C5 | semidirect |
| 59. #67 | C22×C5 | semidirect |
| 61. D12 | C22×C5 | semidirect |
| 62. C4×D3 | C22×C5 | semidirect |
| 63. Dic6 | C22×C5 | semidirect |
| 77. C22×C4 | C5×D3 | semidirect |
| 78. C3×C5 | C2×#41 | semidirect |
| 89. C2×C5 | #235 | direct (N × H) |
| 100. C2×C4 | C2×C5×D3 | semidirect |
| 102. C2×C3 | C5×#41 | semidirect |
| 105. C5 | C2×#235 | direct (N × H) |
| 114. C3 | C2×C5×#41 | semidirect |
| 117. C2 | C5×#235 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×C5 | 2 |
| C2×C5×#67 | 2 |
| C5×#235 | 2 |
| C2×C5×D12 | 2 |
| C2×C4×C5×D3 | 2 |
| C2×C5×Dic6 | 2 |
| C2×C5×#41 | 3 |
| C2×#235 | 5 |