Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
364 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 80 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. #10604028 | C2 | semidirect |
| 4. #10604016 | C2 | semidirect |
| 6. #10598597 | C2 | semidirect |
| 7. #10598583 | C2 | semidirect |
| 23. C5×#332 | C4 | semidirect |
| 24. #64767 | C4 | semidirect |
| 25. #64705 | C4 | semidirect |
| 26. #64705 | C4 | semidirect |
| 127. #332 | AGL(1,𝔽5) | semidirect |
| 318. C5 | #9581 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604663 | 2 |
| #10604644 | 2 |
| #10604028 | 2 |
| #10604016 | 2 |
| #10599210 | 2 |
| #10598597 | 2 |
| #10598583 | 2 |
| #9581 | 5 |