Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
412 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 82 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. #10604020 | C2 | semidirect |
| 4. #10604019 | C2 | semidirect |
| 6. #10598583 | C2 | semidirect |
| 7. #10598583 | C2 | semidirect |
| 25. C5×#333 | C4 | semidirect |
| 26. #64766 | C4 | semidirect |
| 27. #64705 | C4 | semidirect |
| 28. #64705 | C4 | semidirect |
| 129. #333 | AGL(1,𝔽5) | semidirect |
| 301. C5 | #8934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617378 | 2 |
| #10604663 | 2 |
| #10604020 | 2 |
| #10604019 | 2 |
| #10599275 | 2 |
| #10598583 | 2 |
| #8934 | 5 |