Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
224 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 62 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×C3×Dic20 | C2 | semidirect |
| 3. #91331 | C2 | semidirect |
| 5. #91098 | C2 | semidirect |
| 7. #90970 | C2 | semidirect |
| 25. C2×Dic20 | D3 | semidirect |
| 155. C3×C5 | #464 | semidirect |
| 190. C5 | #5185 | semidirect |
| 202. C3 | #65056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic20 | 2 |
| #91370 | 2 |
| #91331 | 2 |
| C2×#6656 | 2 |
| #91098 | 2 |
| C5×#821 | 2 |
| #90970 | 2 |
| #65056 | 3 |
| #5185 | 5 |