Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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×#427 | C2 | semidirect |
| 3. #10602756 | C2 | semidirect |
| 4. #10601448 | C2 | semidirect |
| 5. #10601446 | C2 | semidirect |
| 6. #10601391 | C2 | semidirect |
| 7. #10601389 | C2 | semidirect |
| 23. #64712 | C22 | semidirect |
| 24. #64711 | C22 | semidirect |
| 25. #64710 | C22 | semidirect |
| 26. #64709 | C22 | semidirect |
| 60. C2×#427 | D5 | semidirect |
| 265. C5 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#427 | 2 |
| #10615473 | 2 |
| #10602756 | 2 |
| #10601448 | 2 |
| #10601446 | 2 |
| #10601391 | 2 |
| #10601389 | 2 |
| #33647 | 5 |