Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
434 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 2. C2×#64888 | C2 | semidirect |
| 3. C2×#64883 | C2 | semidirect |
| 4. #10598800 | C2 | direct (N × H) |
| 17. #64888 | C22 | semidirect |
| 19. #64883 | C22 | semidirect |
| 222. C2×C5 | #1360 | semidirect |
| 255. C5 | C2×#1360 | semidirect |
| 273. C2 | #10598800 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65444 | 2 |
| C2×#64888 | 2 |
| C2×#64883 | 2 |
| #10598800 | 2 |
| C2×#1360 | 5 |