Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
304 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 304 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 |
|---|---|---|
| 2. C5×#936 | C2 | semidirect |
| 3. C5×#909 | C2 | semidirect |
| 4. C3×C5×#100 | C2 | semidirect |
| 5. C5×#825 | C2 | semidirect |
| 12. C2×C5×Dic6 | C22 | semidirect |
| 13. C3×C5×M16 | C22 | semidirect |
| 15. C4×C5×Dic3 | C22 | semidirect |
| 18. #4746 | C5 | direct (N × H) |
| 23. C5×#100 | D3 | semidirect |
| 39. #936 | C2×C5 | semidirect |
| 40. #909 | C2×C5 | semidirect |
| 41. C3×#100 | C2×C5 | semidirect |
| 42. #825 | C2×C5 | semidirect |
| 51. C5×M16 | C2×D3 | semidirect |
| 69. C2×Dic6 | C22×C5 | semidirect |
| 70. C3×M16 | C22×C5 | semidirect |
| 72. C4×Dic3 | C22×C5 | semidirect |
| 93. #100 | C5×D3 | semidirect |
| 129. M16 | C2×C5×D3 | semidirect |
| 132. C3×C5 | #455 | semidirect |
| 164. C5 | #4746 | direct (N × H) |
| 174. C3 | C5×#455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1004 | 2 |
| C5×#936 | 2 |
| C5×#909 | 2 |
| C3×C5×#100 | 2 |
| C5×#825 | 2 |
| C5×#455 | 3 |
| #4746 | 5 |