Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
380 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 86 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. #10598605 | C2 | semidirect |
| 5. #10598604 | C2 | semidirect |
| 11. C2×C5×#106 | C4 | semidirect |
| 12. #65395 | C4 | semidirect |
| 16. #65149 | C4 | semidirect |
| 18. D5×#106 | C4 | semidirect |
| 120. C2×#106 | AGL(1,𝔽5) | semidirect |
| 286. C5 | #12873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610847 | 2 |
| #10604727 | 2 |
| #10604713 | 2 |
| #10598605 | 2 |
| #10598604 | 2 |
| #12873 | 5 |