Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
152 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 48 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×Dic6 | C2 | semidirect |
| 3. #6714 | C2 | semidirect |
| 4. C3×#685 | C2 | semidirect |
| 5. #6667 | C2 | semidirect |
| 6. #6665 | C2 | semidirect |
| 7. Dic3×Dic5 | C2 | semidirect |
| 24. #685 | D3 | semidirect |
| 39. C2×Dic6 | D5 | semidirect |
| 88. C3×C5 | #124 | semidirect |
| 120. C5 | #885 | semidirect |
| 133. C3 | #4093 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Dic6 | 2 |
| C2×#1202 | 2 |
| #6714 | 2 |
| C3×#685 | 2 |
| #6667 | 2 |
| #6665 | 2 |
| Dic3×Dic5 | 2 |
| #4093 | 3 |
| #885 | 5 |