Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1798 conjugacy classes of subgroups; only the 400 normal subgroups are shown.
This group has 1798 conjugacy classes of subgroups — too many to draw. Only its 400 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 |
|---|---|---|
| 8. C2×C5×C4⋊Q8 | C4 | semidirect |
| 9. C2×#4090 | C4 | semidirect |
| 12. C2×#4034 | C4 | semidirect |
| 14. C2×#4015 | C4 | semidirect |
| 30. C2×C4⋊AGL(1,𝔽5) | Q8 | semidirect |
| 92. C2×C4⋊Q8 | AGL(1,𝔽5) | semidirect |
| 246. C5 | #14161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×C4⋊Q8 | 2 |
| C2×C4×C4⋊AGL(1,𝔽5) | 2 |
| #10604988 | 2 |
| #10604342 | 2 |
| #14161 | 5 |