Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
152 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 58 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. C4×Dic15 | C2 | semidirect |
| 4. C3×#683 | C2 | semidirect |
| 5. #6668 | C2 | semidirect |
| 7. Dic3×Dic5 | C2 | semidirect |
| 16. D3×Dic5 | C4 | semidirect |
| 22. #683 | D3 | semidirect |
| 80. C3×C5 | #117 | semidirect |
| 107. C5 | #892 | semidirect |
| 118. C3 | #4023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Dic5 | 2 |
| C4×Dic15 | 2 |
| C5×(C2×D3)⋊C4 | 2 |
| C3×#683 | 2 |
| #6668 | 2 |
| (C2×D3)⋊Dic5 | 2 |
| Dic3×Dic5 | 2 |
| #4023 | 3 |
| #892 | 5 |