Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
418 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 4. #10598813 | C2 | semidirect |
| 5. C22×C5×Q16 | C4 | semidirect |
| 14. #65477 | C4 | semidirect |
| 16. C2×#3950 | C4 | semidirect |
| 92. C22×Q16 | AGL(1,𝔽5) | semidirect |
| 270. C5 | #11887 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65477 | 2 |
| #10604723 | 2 |
| D5⋊(C22⋊C16) | 2 |
| #10598813 | 2 |
| #11887 | 5 |