Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
540 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 144 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. C2×C5×D3×Q8 | C2 | semidirect |
| 3. #91836 | C2 | semidirect |
| 4. C3×#4090 | C2 | semidirect |
| 5. #91424 | C2 | semidirect |
| 6. #91385 | C2 | semidirect |
| 7. #91375 | C2 | semidirect |
| 8. #91371 | C2 | semidirect |
| 9. #91351 | C2 | semidirect |
| 37. #4090 | D3 | semidirect |
| 59. C2×D3×Q8 | D5 | semidirect |
| 198. C3×C5 | #536 | semidirect |
| 237. C5 | #5724 | semidirect |
| 250. C3 | #66150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D3×Q8 | 2 |
| C2×#6769 | 2 |
| #91836 | 2 |
| C3×#4090 | 2 |
| #91424 | 2 |
| #91385 | 2 |
| #91375 | 2 |
| #91371 | 2 |
| #91351 | 2 |
| #66150 | 3 |
| #5724 | 5 |