Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
438 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
| 16. C2×Dic40 | C4 | semidirect |
| 93. C2×Q32 | AGL(1,𝔽5) | semidirect |
| 108. C2×AGL(1,𝔽5) | Q32 | semidirect |
| 236. C5 | #13236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×Q32 | 2 |
| #10604848 | 2 |
| C2×#64908 | 2 |
| C2×#64849 | 2 |
| C2×C16×AGL(1,𝔽5) | 2 |
| #13236 | 5 |