Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
188 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 37 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×#99 | C2 | semidirect |
| 3. #91117 | C2 | semidirect |
| 5. C23×D15 | C4 | semidirect |
| 9. #6719 | C4 | semidirect |
| 14. C5×#99 | D3 | semidirect |
| 28. C3×#99 | D5 | semidirect |
| 71. #99 | D15 | semidirect |
| 108. C3×C5 | AΣL(1,𝔽16) | semidirect |
| 143. C5 | #4471 | semidirect |
| 157. C3 | #64691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91826 | 2 |
| C3×C5×#99 | 2 |
| #91117 | 2 |
| #64691 | 3 |
| #4471 | 5 |