Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
472 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 198 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×#936 | C2 | semidirect |
| 3. C5×#935 | C2 | semidirect |
| 4. C5×D4×Dic3 | C2 | semidirect |
| 5. C4×C5×Dic6 | C2 | semidirect |
| 17. #5713 | C5 | direct (N × H) |
| 33. #936 | C2×C5 | semidirect |
| 34. #935 | C2×C5 | semidirect |
| 35. D4×Dic3 | C2×C5 | semidirect |
| 36. C4×Dic6 | C2×C5 | semidirect |
| 108. C3×C5 | #559 | semidirect |
| 131. C5 | #5713 | direct (N × H) |
| 139. C3 | C5×#559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#127 | 2 |
| C5×#936 | 2 |
| C5×#935 | 2 |
| C5×D4×Dic3 | 2 |
| C4×C5×Dic6 | 2 |
| C5×#559 | 3 |
| #5713 | 5 |