Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
294 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 294 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×#64877 | C2 | semidirect |
| 3. C22×#3928 | C2 | semidirect |
| 4. #10598669 | C2 | direct (N × H) |
| 15. #64877 | C22 | semidirect |
| 19. C2×#3928 | C22 | semidirect |
| 177. C2×C5 | #1401 | semidirect |
| 202. C5 | C2×#1401 | semidirect |
| 217. C2 | #10598669 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65196 | 2 |
| C2×#64877 | 2 |
| C22×#3928 | 2 |
| #10598669 | 2 |
| C2×#1401 | 5 |