Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
156 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 156 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×C3×C4×D5 | C2 | semidirect |
| 3. #6712 | C2 | semidirect |
| 4. C5×(C2×D3)⋊C4 | C2 | semidirect |
| 5. Dic3⋊Dic5 | C2 | semidirect |
| 6. (C2×D3)⋊Dic5 | C2 | semidirect |
| 7. #6665 | C2 | semidirect |
| 20. C2×C4×D5 | D3 | semidirect |
| 42. (C2×D3)⋊C4 | D5 | semidirect |
| 88. C3×C5 | #123 | semidirect |
| 120. C5 | #929 | semidirect |
| 133. C3 | #4029 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D5 | 2 |
| C2×#1201 | 2 |
| #6712 | 2 |
| C5×(C2×D3)⋊C4 | 2 |
| Dic3⋊Dic5 | 2 |
| (C2×D3)⋊Dic5 | 2 |
| #6665 | 2 |
| #4029 | 3 |
| #929 | 5 |