Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
450 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 128 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. #10598690 | C2 | semidirect |
| 107. C2×C4×C5 | M32 | semidirect |
| 212. C2×C4 | #3998 | semidirect |
| 222. C5 | #11440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#168 | 2 |
| #10604872 | 2 |
| #10598690 | 2 |
| #11440 | 5 |