Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
414 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 2. #10604806 | C2 | semidirect |
| 3. #10604801 | C2 | semidirect |
| 4. #10604788 | C2 | semidirect |
| 5. #10604786 | C2 | semidirect |
| 6. #10604104 | C2 | semidirect |
| 7. #10604101 | C2 | semidirect |
| 18. C2×C5×D16 | C4 | semidirect |
| 19. C2×#3959 | C4 | semidirect |
| 20. C2×#3958 | C4 | semidirect |
| 25. C2×#3932 | C4 | semidirect |
| 150. C2×D16 | AGL(1,𝔽5) | semidirect |
| 364. C5 | #13247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65200 | 2 |
| #10604806 | 2 |
| #10604801 | 2 |
| #10604788 | 2 |
| #10604786 | 2 |
| #10604104 | 2 |
| #10604101 | 2 |
| #13247 | 5 |