Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
178 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 9. #64850 | C4 | semidirect |
| 10. #64849 | C4 | semidirect |
| 11. C5×M64 | C4 | semidirect |
| 12. #64719 | C4 | semidirect |
| 56. M64 | AGL(1,𝔽5) | semidirect |
| 136. C5 | #7477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604107 | 2 |
| C2×#64850 | 2 |
| D5×M64 | 2 |
| #7477 | 5 |