Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
260 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 74 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. C23×C5×D3 | C2 | semidirect |
| 2. C2×C5×#67 | C2 | semidirect |
| 3. C2×C5×D12 | C2 | semidirect |
| 4. C3×C5×C22⋊C4 | C2 | semidirect |
| 5. C5×(C2×D3)⋊C4 | C2 | semidirect |
| 11. C22×C5×D3 | C22 | semidirect |
| 12. C2×C3×C4×C5 | C22 | semidirect |
| 14. C2×C5×Dic3 | C22 | semidirect |
| 16. #882 | C5 | direct (N × H) |
| 21. C5×C22⋊C4 | D3 | semidirect |
| 23. C22×C3×C5 | D4 | semidirect |
| 30. C2×C5×D3 | D4 | semidirect |
| 33. C23×D3 | C2×C5 | semidirect |
| 34. C2×#67 | C2×C5 | semidirect |
| 35. C2×D12 | C2×C5 | semidirect |
| 36. C3×C22⋊C4 | C2×C5 | semidirect |
| 37. (C2×D3)⋊C4 | C2×C5 | semidirect |
| 46. C2×C4×C5 | C2×D3 | semidirect |
| 57. C22×D3 | C22×C5 | semidirect |
| 58. C2×C3×C4 | C22×C5 | semidirect |
| 60. C2×Dic3 | C22×C5 | semidirect |
| 69. C22×C5 | D12 | semidirect |
| 77. C22⋊C4 | C5×D3 | semidirect |
| 78. C3×C5 | #120 | semidirect |
| 80. C22×C3 | C5×D4 | semidirect |
| 87. C2×D3 | C5×D4 | semidirect |
| 103. C2×C4 | C2×C5×D3 | semidirect |
| 109. C5 | #882 | direct (N × H) |
| 117. C22 | C5×D12 | semidirect |
| 121. C3 | C5×#120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×D3 | 2 |
| C2×C5×#67 | 2 |
| C2×C5×D12 | 2 |
| C3×C5×C22⋊C4 | 2 |
| C5×(C2×D3)⋊C4 | 2 |
| C5×#120 | 3 |
| #882 | 5 |