Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
778 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 224 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 |
|---|---|---|
| 3. #10598828 | C2 | direct (N × H) |
| 19. C22×C5×Q8 | C8 | semidirect |
| 50. C2×C5×Q8 | C2×C8 | semidirect |
| 128. C22×Q8 | #170 | semidirect |
| 174. C2×Q8 | C2×#170 | semidirect |
| 203. C2×C5 | #1272 | semidirect |
| 244. C5 | C2×#1272 | semidirect |
| 263. C2 | #10598828 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65519 | 2 |
| C2×#64918 | 2 |
| #10598828 | 2 |
| C2×#1272 | 5 |