Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
188 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×C5×#67 | C2 | semidirect |
| 2. C2×C5×#67 | C2 | semidirect |
| 3. C2×C5×D12 | C2 | semidirect |
| 4. C2×C4×C5×D3 | C2 | semidirect |
| 5. C3×C5×C22⋊C4 | C2 | semidirect |
| 6. C5×(C2×D3)⋊C4 | C2 | semidirect |
| 7. C5×Dic3⋊C4 | C2 | semidirect |
| 20. #884 | C5 | direct (N × H) |
| 27. C5×C22⋊C4 | D3 | semidirect |
| 37. C2×C5×D3 | D4 | semidirect |
| 41. C5×Dic3 | D4 | semidirect |
| 42. C2×#67 | C2×C5 | semidirect |
| 43. C2×#67 | C2×C5 | semidirect |
| 44. C2×D12 | C2×C5 | semidirect |
| 45. C2×C4×D3 | C2×C5 | semidirect |
| 46. C3×C22⋊C4 | C2×C5 | semidirect |
| 47. (C2×D3)⋊C4 | C2×C5 | semidirect |
| 48. Dic3⋊C4 | C2×C5 | semidirect |
| 98. C22⋊C4 | C5×D3 | semidirect |
| 99. C3×C5 | #121 | semidirect |
| 109. C2×D3 | C5×D4 | semidirect |
| 113. Dic3 | C5×D4 | semidirect |
| 137. C5 | #884 | direct (N × H) |
| 152. C3 | C5×#121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#67 | 2 |
| C2×C5×D12 | 2 |
| C2×C4×C5×D3 | 2 |
| C3×C5×C22⋊C4 | 2 |
| C5×(C2×D3)⋊C4 | 2 |
| C5×Dic3⋊C4 | 2 |
| C5×#121 | 3 |
| #884 | 5 |