Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
188 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 188 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×#1200 | C2 | semidirect |
| 3. C2×D3×Dic5 | C2 | semidirect |
| 4. #6714 | C2 | semidirect |
| 5. C5×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C3×C4×Dic5 | C2 | semidirect |
| 7. #6668 | C2 | semidirect |
| 16. #1203 | C4 | semidirect |
| 26. C4×Dic5 | D3 | semidirect |
| 30. C2×D15 | C2×C4 | semidirect |
| 33. C2×C5×D3 | C2×C4 | semidirect |
| 36. C3×Dic5 | C2×C4 | semidirect |
| 37. C3×Dic5 | D4 | semidirect |
| 44. (C2×D3)⋊C4 | D5 | semidirect |
| 82. Dic5 | C4×D3 | semidirect |
| 83. Dic5 | D12 | semidirect |
| 91. C3×C5 | C4×D4 | semidirect |
| 98. C2×D3 | C4×D5 | semidirect |
| 124. C5 | C4×D12 | semidirect |
| 137. C3 | #4027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1203 | 2 |
| C2×#1200 | 2 |
| C2×D3×Dic5 | 2 |
| #6714 | 2 |
| C5×(C2×D3)⋊C4 | 2 |
| C3×C4×Dic5 | 2 |
| #6668 | 2 |
| #4027 | 3 |
| C4×D12 | 5 |