Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
358 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 96 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. C2×#64851 | C2 | semidirect |
| 4. #10604107 | C2 | semidirect |
| 5. #10598677 | C2 | semidirect |
| 10. C5×#504 | C4 | semidirect |
| 11. #65429 | C4 | semidirect |
| 13. #65196 | C4 | semidirect |
| 17. #65190 | C4 | semidirect |
| 115. #504 | AGL(1,𝔽5) | semidirect |
| 288. C5 | #12841 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#504 | 2 |
| #10604780 | 2 |
| C2×#64851 | 2 |
| #10604107 | 2 |
| #10598677 | 2 |
| #12841 | 5 |