Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
858 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 858 conjugacy classes of subgroups — too many to draw. Only its 254 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 |
|---|---|---|
| 10. #64897 | C4 | semidirect |
| 11. C5×#338 | C4 | semidirect |
| 12. #64780 | C4 | semidirect |
| 69. #338 | AGL(1,𝔽5) | direct (N × H) |
| 115. AGL(1,𝔽5) | #338 | direct (N × H) |
| 170. C5 | C4×#338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×AGL(1,𝔽5) | 2 |
| D5⋊#338 | 2 |
| D5×#338 | 2 |
| C4×#338 | 5 |