Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
942 conjugacy classes of subgroups; only the 600 normal subgroups are shown.
This group has 942 conjugacy classes of subgroups — too many to draw. Only its 600 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. C2×#64886 | C2 | direct (N × H) |
| 7. C22×#674 | C4 | semidirect |
| 11. #64886 | C22 | direct (N × H) |
| 22. C2×#674 | C2×C4 | semidirect |
| 44. #674 | C22×C4 | semidirect |
| 79. C22×C5 | #346 | semidirect |
| 103. C2×C5 | C2×#346 | semidirect |
| 119. C5 | C22×#346 | semidirect |
| 120. C22 | #64886 | direct (N × H) |
| 128. C2 | C2×#64886 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#674 | 2 |
| C22×C8×Dic5 | 2 |
| C2×#64886 | 2 |
| C22×#346 | 5 |