Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
302 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 4. C5×#519 | C4 | semidirect |
| 8. C2×#3968 | C4 | semidirect |
| 11. #64928 | C4 | semidirect |
| 13. #64927 | C4 | semidirect |
| 75. #519 | AGL(1,𝔽5) | semidirect |
| 220. C5 | #7489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64928 | 2 |
| C2×#64927 | 2 |
| #10602454 | 2 |
| #7489 | 5 |