Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
356 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 25. C5×#332 | C4 | semidirect |
| 26. #64767 | C4 | semidirect |
| 27. #64706 | C4 | semidirect |
| 28. #64702 | C4 | semidirect |
| 126. #332 | AGL(1,𝔽5) | semidirect |
| 278. C5 | #8936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617383 | 2 |
| #10604665 | 2 |
| #10604020 | 2 |
| #10604019 | 2 |
| #10599212 | 2 |
| #10598583 | 2 |
| #8936 | 5 |