Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 120 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. C3×Q8×D5 | C2 | semidirect |
| 3. #6718 | C2 | semidirect |
| 4. C5×#215 | C2 | semidirect |
| 5. #6662 | C2 | semidirect |
| 6. #6656 | C2 | semidirect |
| 7. #6649 | C2 | semidirect |
| 21. Q8×D5 | D3 | semidirect |
| 40. #215 | D5 | semidirect |
| 82. C3×C5 | #137 | semidirect |
| 107. C5 | #942 | semidirect |
| 115. C3 | #4061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×D5 | 2 |
| #6772 | 2 |
| #6718 | 2 |
| C5×#215 | 2 |
| #6662 | 2 |
| #6656 | 2 |
| #6649 | 2 |
| #4061 | 3 |
| #942 | 5 |