Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
156 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 2. C2×C4×C5×D3 | C2 | semidirect |
| 3. C3×C5×C4⋊C4 | C2 | semidirect |
| 4. C5×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C5×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C5×(C2×D3)⋊C4 | C2 | semidirect |
| 7. C5×Dic3⋊C4 | C2 | semidirect |
| 18. #894 | C5 | direct (N × H) |
| 22. C5×C4⋊C4 | D3 | semidirect |
| 39. C2×C4×D3 | C2×C5 | semidirect |
| 40. C3×C4⋊C4 | C2×C5 | semidirect |
| 41. (C2×D3)⋊C4 | C2×C5 | semidirect |
| 42. (C2×D3)⋊C4 | C2×C5 | semidirect |
| 43. (C2×D3)⋊C4 | C2×C5 | semidirect |
| 44. Dic3⋊C4 | C2×C5 | semidirect |
| 84. C4⋊C4 | C5×D3 | semidirect |
| 88. C3×C5 | #123 | semidirect |
| 120. C5 | #894 | direct (N × H) |
| 133. C3 | C5×#123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D12 | 2 |
| C2×C4×C5×D3 | 2 |
| C3×C5×C4⋊C4 | 2 |
| C5×(C2×D3)⋊C4 | 2 |
| C5×Dic3⋊C4 | 2 |
| C5×#123 | 3 |
| #894 | 5 |