Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
190 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 3. #10598490 | C2 | semidirect |
| 4. #10598489 | C2 | semidirect |
| 9. C2×C5×C32 | C4 | semidirect |
| 10. C2×#3926 | C4 | semidirect |
| 11. D5×C32 | C4 | semidirect |
| 12. D5×C32 | C4 | semidirect |
| 55. C2×C32 | AGL(1,𝔽5) | semidirect |
| 123. C5 | #13633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604107 | 2 |
| C2×D5×C32 | 2 |
| #10598490 | 2 |
| #10598489 | 2 |
| #13633 | 5 |