Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
274 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 274 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 |
|---|---|---|
| 17. C5×#368 | C4 | semidirect |
| 18. #64726 | C4 | semidirect |
| 19. #64713 | C4 | semidirect |
| 83. #368 | AGL(1,𝔽5) | semidirect |
| 191. C5 | #13171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64849 | 2 |
| #10604098 | 2 |
| #10604088 | 2 |
| D5×#368 | 2 |
| #10598629 | 2 |
| #13171 | 5 |