Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
120 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 38 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. Q8×D15 | C2 | semidirect |
| 3. C5×#216 | C2 | semidirect |
| 4. C3×#688 | C2 | semidirect |
| 5. #6663 | C2 | semidirect |
| 6. #6657 | C2 | semidirect |
| 7. #6651 | C2 | semidirect |
| 25. #688 | D3 | semidirect |
| 38. #216 | D5 | semidirect |
| 82. C3×C5 | #137 | semidirect |
| 107. C5 | #915 | semidirect |
| 115. C3 | #4064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D15 | 2 |
| #6766 | 2 |
| C5×#216 | 2 |
| C3×#688 | 2 |
| #6663 | 2 |
| #6657 | 2 |
| #6651 | 2 |
| #4064 | 3 |
| #915 | 5 |