Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
192 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 78 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. C5×#835 | C2 | semidirect |
| 4. C5×#835 | C2 | semidirect |
| 6. C5×#808 | C2 | semidirect |
| 7. C5×#807 | C2 | semidirect |
| 20. #5045 | C5 | direct (N × H) |
| 43. #835 | C2×C5 | semidirect |
| 44. #835 | C2×C5 | semidirect |
| 46. #808 | C2×C5 | semidirect |
| 47. #807 | C2×C5 | semidirect |
| 141. C3×C5 | #485 | semidirect |
| 174. C5 | #5045 | direct (N × H) |
| 186. C3 | C5×#485 | 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 |
| C5×#926 | 2 |
| C5×#835 | 2 |
| C5×#830 | 2 |
| C5×#808 | 2 |
| C5×#807 | 2 |
| C5×#485 | 3 |
| #5045 | 5 |