Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1276 conjugacy classes of subgroups; only the 260 normal subgroups are shown.
This group has 1276 conjugacy classes of subgroups — too many to draw. Only its 260 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. #10604384 | C2 | semidirect |
| 4. #10604219 | C2 | semidirect |
| 7. C5×#518 | C4 | semidirect |
| 8. #66132 | C4 | semidirect |
| 12. #65850 | C4 | semidirect |
| 14. C2×#4023 | C4 | semidirect |
| 113. #518 | AGL(1,𝔽5) | semidirect |
| 292. C5 | #20710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617757 | 2 |
| C2×#65771 | 2 |
| #10604384 | 2 |
| #10604219 | 2 |
| #20710 | 5 |