Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
712 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 123 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. #10597942 | C2 | direct (N × H) |
| 8. C22×C4⋊Dic5 | C4 | semidirect |
| 11. C2×#3963 | C4 | semidirect |
| 14. #65238 | C4 | semidirect |
| 44. C2×C4⋊Dic5 | C2×C4 | semidirect |
| 51. #3963 | C2×C4 | semidirect |
| 295. C2×C5 | #1352 | semidirect |
| 354. C5 | C2×#1352 | semidirect |
| 397. C2 | #10597942 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65238 | 2 |
| C2×C5×#323 | 2 |
| C2×#64746 | 2 |
| #10597942 | 2 |
| C2×#1352 | 5 |