Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
392 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 182 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. C5×#944 | C2 | semidirect |
| 4. C5×#879 | C2 | semidirect |
| 5. C5×#878 | C2 | semidirect |
| 6. C5×#870 | C2 | semidirect |
| 22. #5672 | C5 | direct (N × H) |
| 40. #944 | C2×C5 | semidirect |
| 42. #879 | C2×C5 | semidirect |
| 43. #878 | C2×C5 | semidirect |
| 44. #870 | C2×C5 | semidirect |
| 133. C3×C5 | #563 | semidirect |
| 158. C5 | #5672 | direct (N × H) |
| 167. C3 | C5×#563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#124 | 2 |
| C5×#944 | 2 |
| C5×#935 | 2 |
| C5×#879 | 2 |
| C5×#878 | 2 |
| C5×#870 | 2 |
| C5×#563 | 3 |
| #5672 | 5 |