Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
414 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 414 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×#64889 | C2 | semidirect |
| 3. C2×C8×#170 | C2 | semidirect |
| 4. #10598623 | C2 | direct (N × H) |
| 17. #64889 | C22 | semidirect |
| 19. C8×#170 | C22 | semidirect |
| 31. C2×Dic20 | C8 | semidirect |
| 34. #4050 | C8 | semidirect |
| 36. C2×D40 | C8 | semidirect |
| 88. Dic20 | C2×C8 | semidirect |
| 90. D40 | C2×C8 | semidirect |
| 231. C2×C5 | #1335 | semidirect |
| 264. C5 | C2×#1335 | semidirect |
| 281. C2 | #10598623 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65184 | 2 |
| C2×#64889 | 2 |
| C2×C8×#170 | 2 |
| #10598623 | 2 |
| C2×#1335 | 5 |