Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
212 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 69 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. #91796 | C2 | semidirect |
| 3. C3×C5×#108 | C2 | semidirect |
| 4. #91109 | C2 | semidirect |
| 5. C8×Dic15 | C2 | semidirect |
| 12. Dic60 | C4 | semidirect |
| 13. D120 | C4 | semidirect |
| 14. #6706 | C4 | semidirect |
| 20. C5×#108 | D3 | semidirect |
| 36. C3×#108 | D5 | semidirect |
| 79. #108 | D15 | semidirect |
| 112. C3×C5 | #443 | semidirect |
| 136. C5 | #4895 | semidirect |
| 143. C3 | #65184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91796 | 2 |
| #91793 | 2 |
| C3×C5×#108 | 2 |
| #91109 | 2 |
| C8×Dic15 | 2 |
| #65184 | 3 |
| #4895 | 5 |