Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
152 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 48 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. C2×#1204 | C2 | semidirect |
| 3. #6719 | C2 | semidirect |
| 4. C5×#217 | C2 | semidirect |
| 5. #6665 | C2 | semidirect |
| 6. #6665 | C2 | semidirect |
| 7. Dic3×Dic5 | C2 | semidirect |
| 43. #217 | D5 | semidirect |
| 88. C3×C5 | #124 | semidirect |
| 120. C5 | #936 | semidirect |
| 133. C3 | #4031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C22⋊D5 | 2 |
| C2×#1204 | 2 |
| #6719 | 2 |
| C5×#217 | 2 |
| #6665 | 2 |
| Dic3×Dic5 | 2 |
| #4031 | 3 |
| #936 | 5 |