Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
496 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 163 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. #92101 | C2 | semidirect |
| 2. C3×C5×#131 | C2 | semidirect |
| 3. #91798 | C2 | semidirect |
| 4. C2×Dic60 | C2 | semidirect |
| 5. #91793 | C2 | semidirect |
| 20. C5×#131 | D3 | semidirect |
| 36. C3×#131 | D5 | semidirect |
| 83. #131 | D15 | semidirect |
| 114. C3×C5 | #578 | semidirect |
| 137. C5 | #5753 | semidirect |
| 143. C3 | #66087 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #92101 | 2 |
| C3×C5×#131 | 2 |
| #91798 | 2 |
| C2×Dic60 | 2 |
| #91793 | 2 |
| #66087 | 3 |
| #5753 | 5 |