Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
412 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 160 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. #91470 | C2 | semidirect |
| 6. #91468 | C2 | semidirect |
| 7. #91388 | C2 | semidirect |
| 8. #91384 | C2 | semidirect |
| 36. C2×C3×C4×C5 | Q8 | semidirect |
| 101. C2×C4×C5 | Dic6 | semidirect |
| 124. C2×C3×C4 | Dic10 | semidirect |
| 159. C3×C5 | #544 | semidirect |
| 183. C2×C4 | #1204 | semidirect |
| 190. C5 | #5519 | semidirect |
| 202. C3 | #65834 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91815 | 2 |
| C2×C5×C4⋊Dic3 | 2 |
| C3×#4072 | 2 |
| #91575 | 2 |
| #91470 | 2 |
| #91468 | 2 |
| #91388 | 2 |
| #91384 | 2 |
| #65834 | 3 |
| #5519 | 5 |