Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
658 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 164 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 |
|---|---|---|
| 9. C2×C5×#97 | C4 | semidirect |
| 10. C2×#3947 | C4 | semidirect |
| 11. C2×C8×Dic5 | C4 | semidirect |
| 12. C2×C4×#168 | C4 | semidirect |
| 15. #64895 | C4 | semidirect |
| 94. C2×#97 | AGL(1,𝔽5) | semidirect |
| 243. C5 | #10814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64997 | 2 |
| C2×#64895 | 2 |
| #10604721 | 2 |
| #10604165 | 2 |
| #10814 | 5 |