Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
412 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 4. #10598267 | C2 | semidirect |
| 5. C22×C5×Q16 | C4 | semidirect |
| 10. C5×#467 | C4 | semidirect |
| 12. C2×C5×#107 | C4 | semidirect |
| 92. C22×Q16 | Dic5 | semidirect |
| 98. #467 | Dic5 | semidirect |
| 100. C2×#107 | Dic5 | semidirect |
| 265. C5 | #11889 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#467 | 2 |
| #10602763 | 2 |
| #10602756 | 2 |
| #10598267 | 2 |
| #11889 | 5 |