Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
314 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 6. C22×#674 | C4 | semidirect |
| 13. C22⋊#674 | C4 | semidirect |
| 49. C5×C22⋊C4 | C16 | semidirect |
| 168. C22⋊C4 | #674 | semidirect |
| 208. C5 | #7199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#674 | 2 |
| C22⋊C4×#168 | 2 |
| #7199 | 5 |