Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
248 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 72 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×C3×Dic20 | C2 | semidirect |
| 3. #91389 | C2 | semidirect |
| 5. C2×#6662 | C2 | semidirect |
| 7. C5×#815 | C2 | semidirect |
| 24. C2×Dic20 | D3 | semidirect |
| 52. #815 | D5 | semidirect |
| 153. C3×C5 | #497 | semidirect |
| 185. C5 | #5190 | semidirect |
| 195. C3 | #65004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6706 | 2 |
| C2×C3×Dic20 | 2 |
| #91389 | 2 |
| #91374 | 2 |
| C2×#6662 | 2 |
| C2×#6658 | 2 |
| C5×#815 | 2 |
| #65004 | 3 |
| #5190 | 5 |