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 |
|---|---|---|
| 2. D15⋊Q8 | C2 | semidirect |
| 3. C5×#216 | C2 | semidirect |
| 4. C3×#689 | C2 | semidirect |
| 5. #6660 | C2 | semidirect |
| 6. #6658 | C2 | semidirect |
| 7. #6651 | C2 | semidirect |
| 24. #689 | D3 | semidirect |
| 38. #216 | D5 | semidirect |
| 82. C3×C5 | #137 | semidirect |
| 107. C5 | #918 | semidirect |
| 115. C3 | #4064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6821 | 2 |
| D15⋊Q8 | 2 |
| C5×#216 | 2 |
| C3×#689 | 2 |
| #6660 | 2 |
| #6658 | 2 |
| #6651 | 2 |
| #4064 | 3 |
| #918 | 5 |