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. C3×#709 | C2 | semidirect |
| 3. C2×C5×C3⋊C8 | C2 | semidirect |
| 4. #6662 | C2 | semidirect |
| 5. #6658 | C2 | semidirect |
| 6. #6657 | C2 | semidirect |
| 7. #6653 | C2 | semidirect |
| 22. #709 | D3 | semidirect |
| 41. C2×C3⋊C8 | D5 | semidirect |
| 83. C3×C5 | #135 | semidirect |
| 110. C5 | #950 | semidirect |
| 118. C3 | #4050 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6817 | 2 |
| C3×#709 | 2 |
| C2×C5×C3⋊C8 | 2 |
| #6662 | 2 |
| #6658 | 2 |
| #6657 | 2 |
| #6653 | 2 |
| #4050 | 3 |
| #950 | 5 |