Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
444 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|---|
| 5. #91468 | C2 | semidirect |
| 6. C4×#1204 | C2 | semidirect |
| 7. #91388 | C2 | semidirect |
| 33. C2×C3×C4×C5 | Q8 | semidirect |
| 91. C2×C4×C5 | Dic6 | semidirect |
| 113. C2×C3×C4 | Dic10 | semidirect |
| 143. C3×C5 | #533 | semidirect |
| 163. C2×C4 | #1204 | semidirect |
| 169. C5 | #5470 | semidirect |
| 179. C3 | #65851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91815 | 2 |
| C5×#926 | 2 |
| C2×C3×C4×Dic5 | 2 |
| #91574 | 2 |
| #91468 | 2 |
| C4×#1204 | 2 |
| #91388 | 2 |
| #65851 | 3 |
| #5470 | 5 |