Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
428 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 80 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. #10604765 | C2 | semidirect |
| 4. #10598768 | C2 | semidirect |
| 6. C2×#4094 | C4 | semidirect |
| 10. C5×#408 | C4 | semidirect |
| 11. #65407 | C4 | semidirect |
| 13. C2×C8×Dic5 | C4 | semidirect |
| 104. #408 | AGL(1,𝔽5) | semidirect |
| 260. C5 | #12807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610388 | 2 |
| #10604996 | 2 |
| #10604765 | 2 |
| #10598768 | 2 |
| #12807 | 5 |