Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
228 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 3. C2×Dic60 | C2 | semidirect |
| 4. #91102 | C2 | semidirect |
| 5. #91100 | C2 | semidirect |
| 50. C22×C3×C5 | Q16 | semidirect |
| 99. C22×C5 | Dic12 | semidirect |
| 115. C3×C5 | #467 | semidirect |
| 118. C22×C3 | Dic20 | semidirect |
| 144. C5 | #5116 | semidirect |
| 147. C22 | Dic60 | semidirect |
| 154. C3 | #65405 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×C8 | 2 |
| #91813 | 2 |
| C2×Dic60 | 2 |
| #91102 | 2 |
| #91100 | 2 |
| #65405 | 3 |
| #5116 | 5 |