Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 1. C5×#904 | C2 | semidirect |
| 2. C2×C5×D24 | C2 | semidirect |
| 3. C3×C5×M32 | C2 | semidirect |
| 4. C5×#800 | C2 | semidirect |
| 5. C5×D48 | C2 | semidirect |
| 10. C5×Dic12 | C22 | semidirect |
| 13. C5×D24 | C22 | semidirect |
| 15. C3×C5×C16 | C22 | semidirect |
| 16. #4908 | C5 | direct (N × H) |
| 21. C5×M32 | D3 | semidirect |
| 32. #904 | C2×C5 | semidirect |
| 33. C2×D24 | C2×C5 | semidirect |
| 34. C3×M32 | C2×C5 | semidirect |
| 35. #800 | C2×C5 | semidirect |
| 36. D48 | C2×C5 | semidirect |
| 45. C5×C16 | C2×D3 | semidirect |
| 57. Dic12 | C22×C5 | semidirect |
| 60. D24 | C22×C5 | semidirect |
| 62. C3×C16 | C22×C5 | semidirect |
| 77. M32 | C5×D3 | semidirect |
| 107. C16 | C2×C5×D3 | semidirect |
| 108. C3×C5 | #509 | semidirect |
| 134. C5 | #4908 | direct (N × H) |
| 142. C3 | C5×#509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#904 | 2 |
| C2×C5×D24 | 2 |
| C3×C5×M32 | 2 |
| C5×#800 | 2 |
| C5×D48 | 2 |
| C5×#509 | 3 |
| #4908 | 5 |