Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
478 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 84 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. #10604665 | C2 | semidirect |
| 4. #10604648 | C2 | semidirect |
| 6. #10598592 | C2 | semidirect |
| 7. #10598583 | C2 | semidirect |
| 20. C5×#475 | C4 | semidirect |
| 21. #65376 | C4 | semidirect |
| 22. #65320 | C4 | semidirect |
| 25. #65130 | C4 | semidirect |
| 147. #475 | AGL(1,𝔽5) | semidirect |
| 383. C5 | #8971 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617205 | 2 |
| #10612728 | 2 |
| #10604665 | 2 |
| #10604648 | 2 |
| C4×#4010 | 2 |
| #10598592 | 2 |
| #10598583 | 2 |
| #8971 | 5 |