Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
462 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 116 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. #10604114 | C2 | semidirect |
| 5. #10598670 | C2 | semidirect |
| 17. #64912 | C4 | semidirect |
| 18. #64891 | C4 | semidirect |
| 21. C5×#349 | C4 | semidirect |
| 22. #64773 | C4 | semidirect |
| 23. #64734 | C4 | semidirect |
| 125. #349 | AGL(1,𝔽5) | semidirect |
| 302. C5 | #12608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65728 | 2 |
| D5⋊#349 | 2 |
| #10604114 | 2 |
| D5×#349 | 2 |
| #10598670 | 2 |
| #12608 | 5 |