Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
470 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 144 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×#64885 | C2 | semidirect |
| 3. C2×#64882 | C2 | semidirect |
| 4. #10598801 | C2 | direct (N × H) |
| 17. #64885 | C22 | semidirect |
| 19. #64882 | C22 | semidirect |
| 26. C2×C5×D8 | C8 | semidirect |
| 70. C5×D8 | C2×C8 | semidirect |
| 136. C2×D8 | #170 | semidirect |
| 192. D8 | C2×#170 | semidirect |
| 212. C2×C5 | #1331 | semidirect |
| 246. C5 | C2×#1331 | semidirect |
| 265. C2 | #10598801 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×Dic5 | 2 |
| C2×#64885 | 2 |
| C2×#64882 | 2 |
| #10598801 | 2 |
| C2×#1331 | 5 |