Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
470 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 108 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. #10598619 | C2 | semidirect |
| 10. C2×C5×#107 | C4 | semidirect |
| 11. C2×#3950 | C4 | semidirect |
| 15. D5×#107 | C4 | semidirect |
| 99. C2×#107 | AGL(1,𝔽5) | semidirect |
| 264. C5 | #12866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×#107 | 2 |
| #10604723 | 2 |
| D5⋊(C22⋊C16) | 2 |
| #10598619 | 2 |
| #12866 | 5 |