Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
136 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 44 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. #6817 | C2 | semidirect |
| 2. C2×C5×D12 | C2 | semidirect |
| 3. C3×#681 | C2 | semidirect |
| 4. #6659 | C2 | semidirect |
| 5. #6654 | C2 | semidirect |
| 10. D60 | C22 | semidirect |
| 12. Dic30 | C22 | semidirect |
| 15. C3×#168 | C22 | semidirect |
| 21. #681 | D3 | semidirect |
| 30. C2×D12 | D5 | semidirect |
| 42. #168 | C2×D3 | semidirect |
| 69. C3×C5 | AGL(1,ℤ/8) | semidirect |
| 94. C5 | #908 | semidirect |
| 102. C3 | #4078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6817 | 2 |
| C2×C5×D12 | 2 |
| C3×#681 | 2 |
| #6659 | 2 |
| #6654 | 2 |
| #4078 | 3 |
| #908 | 5 |