Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 77 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. #91096 | C2 | semidirect |
| 4. #91082 | C2 | semidirect |
| 5. C16×D15 | C2 | semidirect |
| 14. C3×C5×C16 | C22 | semidirect |
| 15. C3⋊#672 | C22 | semidirect |
| 18. C5×M32 | D3 | semidirect |
| 34. C3×M32 | D5 | semidirect |
| 45. C5×C16 | C2×D3 | semidirect |
| 63. C3×C16 | C2×D5 | semidirect |
| 79. M32 | D15 | direct (N × H) |
| 84. D15 | M32 | direct (N × H) |
| 112. C16 | C2×D15 | semidirect |
| 113. C3×C5 | C2×M32 | semidirect |
| 141. C5 | D3×M32 | semidirect |
| 150. C3 | D5×M32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D15 | 2 |
| C3×C5×M32 | 2 |
| #91096 | 2 |
| #91082 | 2 |
| C16×D15 | 2 |
| D5×M32 | 3 |
| D3×M32 | 5 |