Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
170 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 5. #64850 | C4 | semidirect |
| 7. C2×C5×C32 | C4 | semidirect |
| 8. C2×#3926 | C4 | semidirect |
| 38. C2×C32 | AGL(1,𝔽5) | semidirect |
| 90. C5 | #7475 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604107 | 2 |
| C2×#64667 | 2 |
| #7475 | 5 |