Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
296 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 3. C2×C5×#216 | C2 | semidirect |
| 5. C5×#810 | C2 | semidirect |
| 18. #5050 | C5 | direct (N × H) |
| 39. C2×#216 | C2×C5 | semidirect |
| 41. #810 | C2×C5 | semidirect |
| 56. C22×C3×C5 | Q16 | semidirect |
| 111. C22×C5 | #216 | semidirect |
| 129. C3×C5 | #451 | semidirect |
| 132. C22×C3 | C5×Q16 | semidirect |
| 160. C5 | #5050 | direct (N × H) |
| 163. C22 | C5×#216 | semidirect |
| 170. C3 | C5×#451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×Dic6 | 2 |
| C3×C5×C22⋊Q8 | 2 |
| C2×C5×#216 | 2 |
| C5×#830 | 2 |
| C5×#810 | 2 |
| C5×#451 | 3 |
| #5050 | 5 |