Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1506 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 1506 conjugacy classes of subgroups — too many to draw. Only its 242 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. C22×#4133 | C2 | semidirect |
| 2. C2×#65692 | C2 | semidirect |
| 4. #10604983 | C2 | semidirect |
| 5. #10604236 | C2 | semidirect |
| 6. #10603786 | C2 | semidirect |
| 7. #10603775 | C2 | semidirect |
| 43. C2×D5⋊C8 | D4 | semidirect |
| 121. C23×C5 | #131 | semidirect |
| 139. C2×Dic5 | #131 | semidirect |
| 246. C23 | #4133 | semidirect |
| 270. C5 | #21442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4133 | 2 |
| C2×#65692 | 2 |
| #10608508 | 2 |
| #10604983 | 2 |
| #10604236 | 2 |
| #10603786 | 2 |
| #10603775 | 2 |
| #21442 | 5 |