Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
392 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 3. #10603893 | C2 | semidirect |
| 4. #10603774 | C2 | semidirect |
| 6. #10598557 | C2 | semidirect |
| 7. #10598510 | C2 | semidirect |
| 9. #65788 | C4 | semidirect |
| 10. Q8×#170 | C4 | semidirect |
| 16. #65705 | C4 | semidirect |
| 17. #65702 | C4 | semidirect |
| 23. #64927 | C4 | semidirect |
| 28. #64870 | C4 | semidirect |
| 344. C5 | #8248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617265 | 2 |
| #10604505 | 2 |
| #10603893 | 2 |
| #10603774 | 2 |
| #10599101 | 2 |
| #10598557 | 2 |
| #10598510 | 2 |
| #8248 | 5 |