Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
474 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 4. #10598031 | C2 | direct (N × H) |
| 8. C2×#4015 | C4 | semidirect |
| 13. #65365 | C4 | semidirect |
| 15. C2×C4×#168 | C4 | semidirect |
| 45. #4015 | C2×C4 | semidirect |
| 51. C4×#168 | C2×C4 | semidirect |
| 259. C2×C5 | #1409 | semidirect |
| 301. C5 | C2×#1409 | semidirect |
| 331. C2 | #10598031 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65365 | 2 |
| C2×C5×#353 | 2 |
| C2×#64765 | 2 |
| #10598031 | 2 |
| C2×#1409 | 5 |