Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
574 conjugacy classes of subgroups; only the 260 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 260 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 |
|---|---|---|
| 13. #64879 | C4 | semidirect |
| 14. C8×#170 | C4 | semidirect |
| 15. C5×#322 | C4 | semidirect |
| 16. #64675 | C4 | semidirect |
| 17. #64674 | C4 | semidirect |
| 29. C8×AGL(1,𝔽5) | C8 | semidirect |
| 69. #322 | AGL(1,𝔽5) | semidirect |
| 147. C5 | #7841 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10603839 | 2 |
| C4×C8×AGL(1,𝔽5) | 2 |
| #10603807 | 2 |
| C8×D5⋊C8 | 2 |
| D5×#322 | 2 |
| #7841 | 5 |