Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
200 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 43 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 |
|---|---|---|
| 16. C2×C42×C5 | C8 | semidirect |
| 68. C2×C42 | #168 | semidirect |
| 124. C5 | #7348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1820 | 2 |
| #10598118 | 2 |
| #7348 | 5 |