Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
296 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 23. C5×#362 | C4 | semidirect |
| 24. #64785 | C4 | semidirect |
| 25. #64737 | C4 | semidirect |
| 26. #64716 | C4 | semidirect |
| 126. #362 | AGL(1,𝔽5) | semidirect |
| 275. C5 | #13157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604852 | 2 |
| C2×#64910 | 2 |
| #10604115 | 2 |
| #10604091 | 2 |
| D5×#362 | 2 |
| #10598676 | 2 |
| #10598630 | 2 |
| #13157 | 5 |