Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
392 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 88 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. #10604015 | C2 | semidirect |
| 4. #10603819 | C2 | semidirect |
| 6. #10598594 | C2 | semidirect |
| 7. #10598530 | C2 | semidirect |
| 25. C5×Q8⋊C8 | C4 | semidirect |
| 26. Q8⋊#168 | C4 | semidirect |
| 27. #64703 | C4 | semidirect |
| 28. #64679 | C4 | semidirect |
| 139. Q8⋊C8 | AGL(1,𝔽5) | semidirect |
| 333. C5 | #8903 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617190 | 2 |
| #10604455 | 2 |
| #10604015 | 2 |
| #10603819 | 2 |
| #10599022 | 2 |
| #10598594 | 2 |
| #10598530 | 2 |
| #8903 | 5 |