Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
124 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 40 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. C5×#239 | C2 | semidirect |
| 2. #6769 | C2 | semidirect |
| 3. #6717 | C2 | semidirect |
| 4. C3×#689 | C2 | semidirect |
| 5. #6656 | C2 | semidirect |
| 6. #6654 | C2 | semidirect |
| 7. D3×#168 | C2 | semidirect |
| 23. #689 | D3 | semidirect |
| 36. #239 | D5 | semidirect |
| 83. C3×C5 | #135 | semidirect |
| 110. C5 | #919 | semidirect |
| 118. C3 | #4096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#239 | 2 |
| #6769 | 2 |
| #6717 | 2 |
| C3×#689 | 2 |
| #6656 | 2 |
| #6654 | 2 |
| D3×#168 | 2 |
| #4096 | 3 |
| #919 | 5 |