Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
882 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 882 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 1. C2×C5⋊#564 | C2 | semidirect |
| 4. C2×#64763 | C2 | semidirect |
| 5. #10602043 | C2 | direct (N × H) |
| 6. C2×#64685 | C2 | semidirect |
| 11. C5⋊#564 | C22 | semidirect |
| 25. #64763 | C22 | semidirect |
| 26. #64685 | C22 | semidirect |
| 236. C2×C5 | #1658 | semidirect |
| 261. C5 | C2×#1658 | semidirect |
| 276. C2 | #10602043 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5⋊#564 | 2 |
| C2×C5×#490 | 2 |
| C2×#65360 | 2 |
| C2×#64763 | 2 |
| #10602043 | 2 |
| C2×#64685 | 2 |
| C2×#1658 | 5 |