Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 106 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. C3×C5×M32 | C2 | semidirect |
| 3. C5×#812 | C2 | semidirect |
| 4. C5×#798 | C2 | semidirect |
| 5. C5×D3×C16 | C2 | semidirect |
| 14. C3×C5×C16 | C22 | semidirect |
| 15. C5×C3⋊C16 | C22 | semidirect |
| 16. D3×M32 | C5 | direct (N × H) |
| 20. C5×M32 | D3 | direct (N × H) |
| 34. C3×M32 | C2×C5 | semidirect |
| 35. #812 | C2×C5 | semidirect |
| 36. #798 | C2×C5 | semidirect |
| 37. D3×C16 | C2×C5 | semidirect |
| 46. C5×C16 | C2×D3 | semidirect |
| 63. C3×C16 | C22×C5 | semidirect |
| 64. C3⋊C16 | C22×C5 | semidirect |
| 79. M32 | C5×D3 | direct (N × H) |
| 84. C5×D3 | M32 | direct (N × H) |
| 112. C16 | C2×C5×D3 | semidirect |
| 113. C3×C5 | C2×M32 | semidirect |
| 140. D3 | C5×M32 | direct (N × H) |
| 141. C5 | D3×M32 | direct (N × H) |
| 150. C3 | C2×C5×M32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D3×C8 | 2 |
| C3×C5×M32 | 2 |
| C5×#812 | 2 |
| C5×#798 | 2 |
| C5×D3×C16 | 2 |
| C2×C5×M32 | 3 |
| D3×M32 | 5 |