Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
420 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 2. #10604727 | C2 | semidirect |
| 4. #10598768 | C2 | semidirect |
| 5. C2×#4047 | C4 | semidirect |
| 10. C2×C5×#97 | C4 | semidirect |
| 11. #65399 | C4 | semidirect |
| 13. #65213 | C4 | semidirect |
| 101. C2×#97 | AGL(1,𝔽5) | semidirect |
| 250. C5 | #12808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610222 | 2 |
| #10604727 | 2 |
| #10604142 | 2 |
| #10598768 | 2 |
| #12808 | 5 |