Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
288 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 71 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. C3×C5×#127 | C2 | semidirect |
| 2. C2×#6716 | C2 | semidirect |
| 3. C2×#6715 | C2 | semidirect |
| 4. #91764 | C2 | semidirect |
| 5. #91087 | C2 | semidirect |
| 17. C5×#127 | D3 | semidirect |
| 32. C3⋊#168 | D4 | semidirect |
| 33. C3×#127 | D5 | semidirect |
| 78. #127 | D15 | semidirect |
| 113. C3×C5 | #496 | semidirect |
| 141. C5 | #5074 | semidirect |
| 150. C3 | #65363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#127 | 2 |
| C2×#6716 | 2 |
| C2×#6715 | 2 |
| #91764 | 2 |
| #91087 | 2 |
| #65363 | 3 |
| #5074 | 5 |