Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
124 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 124 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. C5×#235 | C2 | semidirect |
| 3. C2×C3×#168 | C2 | semidirect |
| 4. #6663 | C2 | semidirect |
| 5. #6660 | C2 | semidirect |
| 6. #6659 | C2 | semidirect |
| 7. #6654 | C2 | semidirect |
| 27. C2×#168 | D3 | semidirect |
| 36. #235 | D5 | semidirect |
| 83. C3×C5 | #135 | semidirect |
| 110. C5 | #904 | semidirect |
| 118. C3 | #4096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6817 | 2 |
| C5×#235 | 2 |
| C2×C3×#168 | 2 |
| #6663 | 2 |
| #6660 | 2 |
| #6659 | 2 |
| #6654 | 2 |
| #4096 | 3 |
| #904 | 5 |