Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
450 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 4. #10601571 | C2 | semidirect |
| 5. #10601267 | C2 | semidirect |
| 6. C2×#64702 | C2 | semidirect |
| 7. #10598235 | C2 | semidirect |
| 343. C5 | #10550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615019 | 2 |
| C5×#1480 | 2 |
| #10602599 | 2 |
| #10601571 | 2 |
| #10601267 | 2 |
| C2×#64702 | 2 |
| #10598235 | 2 |
| #10550 | 5 |