Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
460 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 20. C2×C5×Q32 | C4 | semidirect |
| 21. C2×#3961 | C4 | semidirect |
| 22. C2×#3961 | C4 | semidirect |
| 25. C2×Dic40 | C4 | semidirect |
| 141. C2×Q32 | AGL(1,𝔽5) | semidirect |
| 338. C5 | #13020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617434 | 2 |
| C2×D5×Q32 | 2 |
| #10604852 | 2 |
| D5⋊#362 | 2 |
| #10604832 | 2 |
| #10598665 | 2 |
| #10598662 | 2 |
| #13020 | 5 |