Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
316 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 97 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. #10601476 | C2 | semidirect |
| 5. C4×#3951 | C2 | semidirect |
| 6. #10598224 | C2 | semidirect |
| 7. #10598149 | C2 | semidirect |
| 19. #64785 | C4 | semidirect |
| 20. #64783 | C4 | semidirect |
| 264. C5 | #13137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1974 | 2 |
| #10602874 | 2 |
| #10602873 | 2 |
| #10601476 | 2 |
| C4×#3951 | 2 |
| #10598224 | 2 |
| #10598149 | 2 |
| #13137 | 5 |