Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
248 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×#6718 | C2 | semidirect |
| 2. C5×#944 | C2 | semidirect |
| 5. C2×#6663 | C2 | semidirect |
| 7. #90953 | C2 | semidirect |
| 47. #944 | D5 | semidirect |
| 153. C3×C5 | #497 | semidirect |
| 185. C5 | #5167 | semidirect |
| 195. C3 | #65375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6718 | 2 |
| C5×#944 | 2 |
| C2×C3×#688 | 2 |
| #91364 | 2 |
| C2×#6663 | 2 |
| C2×#6655 | 2 |
| #90953 | 2 |
| #65375 | 3 |
| #5167 | 5 |