Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
402 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 12. C2×C5×Q32 | C4 | semidirect |
| 13. C2×#3961 | C4 | semidirect |
| 18. C2×Dic40 | C4 | semidirect |
| 106. C2×Q32 | AGL(1,𝔽5) | semidirect |
| 249. C5 | #13244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×Q32 | 2 |
| #10604852 | 2 |
| D5⋊#362 | 2 |
| D5⋊#368 | 2 |
| #10604098 | 2 |
| #13244 | 5 |