Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
342 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 17. #64884 | C4 | semidirect |
| 18. #64881 | C4 | semidirect |
| 23. C5×#335 | C4 | semidirect |
| 24. #64700 | C4 | semidirect |
| 25. #64700 | C4 | semidirect |
| 26. #64678 | C4 | semidirect |
| 103. #335 | AGL(1,𝔽5) | semidirect |
| 239. C5 | #8270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604012 | 2 |
| #10604010 | 2 |
| #10603839 | 2 |
| #10603814 | 2 |
| #10599360 | 2 |
| #10598583 | 2 |
| #8270 | 5 |