Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
456 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 456 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. #10604731 | C2 | semidirect |
| 4. #10604722 | C2 | semidirect |
| 5. #10598786 | C2 | semidirect |
| 6. C2×C5×#131 | C4 | semidirect |
| 13. #65523 | C4 | semidirect |
| 17. #65408 | C4 | semidirect |
| 20. #65390 | C4 | semidirect |
| 120. C2×#131 | AGL(1,𝔽5) | semidirect |
| 338. C5 | #8626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615525 | 2 |
| #10604991 | 2 |
| #10604731 | 2 |
| #10604722 | 2 |
| #10598786 | 2 |
| #8626 | 5 |