Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
228 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 90 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×C5×#216 | C2 | semidirect |
| 5. C5×#835 | C2 | semidirect |
| 6. C5×#810 | C2 | semidirect |
| 7. C5×#807 | C2 | semidirect |
| 22. #5051 | C5 | direct (N × H) |
| 46. C2×#216 | C2×C5 | semidirect |
| 49. #835 | C2×C5 | semidirect |
| 50. #810 | C2×C5 | semidirect |
| 51. #807 | C2×C5 | semidirect |
| 68. C22×C3×C5 | Q16 | semidirect |
| 133. C22×C5 | #216 | semidirect |
| 155. C3×C5 | #467 | semidirect |
| 158. C22×C3 | C5×Q16 | semidirect |
| 190. C5 | #5051 | direct (N × H) |
| 193. C22 | C5×#216 | semidirect |
| 202. C3 | C5×#467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C22⋊Q8 | 2 |
| C2×C5×#216 | 2 |
| C5×#924 | 2 |
| C22×C5×C3⋊C8 | 2 |
| C5×#835 | 2 |
| C5×#810 | 2 |
| C5×#807 | 2 |
| C5×#467 | 3 |
| #5051 | 5 |