Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
292 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D3×D5 |
| commutator, socle, cosocle | C2×C3×C5 | C24 |
| Fitting | C3×C5×D4 | C22 |
| hypercenter | D4 | D3×D5 |
| hypocenter | C3×C5 | 2−1+4 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2 ◁ D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #6819 | C2 | semidirect |
| 2. C5×#237 | C2 | semidirect |
| 3. C3×#711 | C2 | semidirect |
| 4. C2×#1204 | C2 | semidirect |
| 5. #6782 | C2 | semidirect |
| 6. #6780 | C2 | semidirect |
| 7. #6779 | C2 | semidirect |
| 8. #6771 | C2 | semidirect |
| 9. D15⋊Q8 | C2 | semidirect |
| 10. D3×Dic10 | C2 | semidirect |
| 11. D5×Dic6 | C2 | semidirect |
| 43. #711 | D3 | semidirect |
| 65. #237 | D5 | semidirect |
| 144. C3×C5 | 2−1+4 | semidirect |
| 189. C5 | #1010 | semidirect |
| 201. C3 | #4150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6819 | 2 |
| C5×#237 | 2 |
| C3×#711 | 2 |
| C2×#1204 | 2 |
| #6782 | 2 |
| #6780 | 2 |
| #6779 | 2 |
| #6771 | 2 |
| D15⋊Q8 | 2 |
| D3×Dic10 | 2 |
| D5×Dic6 | 2 |
| #4150 | 3 |
| #1010 | 5 |