Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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. #91103 | C2 | semidirect |
| 13. C5×M32 | D3 | semidirect |
| 23. C3×M32 | D5 | semidirect |
| 51. M32 | D15 | semidirect |
| 74. C3×C5 | #361 | semidirect |
| 93. C5 | #4516 | semidirect |
| 99. C3 | #64736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D120 | 2 |
| C3×C5×M32 | 2 |
| #91103 | 2 |
| #64736 | 3 |
| #4516 | 5 |