Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
288 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 72 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. #91764 | C2 | semidirect |
| 2. C3×#4020 | C2 | semidirect |
| 3. C2×#6657 | C2 | semidirect |
| 4. C2×#6653 | C2 | semidirect |
| 5. C5×#803 | C2 | semidirect |
| 20. #4020 | D3 | semidirect |
| 32. C5×C3⋊C8 | D4 | semidirect |
| 37. #803 | D5 | semidirect |
| 95. C3⋊C8 | D20 | semidirect |
| 113. C3×C5 | #496 | semidirect |
| 141. C5 | #5074 | semidirect |
| 150. C3 | #65001 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91764 | 2 |
| C3×#4020 | 2 |
| C2×#6657 | 2 |
| C2×#6653 | 2 |
| C5×#803 | 2 |
| #65001 | 3 |
| #5074 | 5 |