Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
6110 conjugacy classes of subgroups; only the 744 normal subgroups are shown.
This group has 6110 conjugacy classes of subgroups — too many to draw. Only its 744 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 |
|---|---|---|
| 2. C22×C22⋊#170 | C2 | semidirect |
| 3. #10605025 | C2 | direct (N × H) |
| 10. C23×#170 | C22 | semidirect |
| 12. C2×C22⋊#170 | C22 | semidirect |
| 16. C25×C5 | C8 | semidirect |
| 32. C22×#170 | C23 | semidirect |
| 46. C24×C5 | C2×C8 | semidirect |
| 87. C23×C5 | C22⋊C8 | semidirect |
| 107. C25 | #170 | semidirect |
| 133. C22×C5 | C2×C22⋊C8 | semidirect |
| 149. C24 | C2×#170 | semidirect |
| 173. C2×C5 | #1779 | semidirect |
| 187. C23 | C22⋊#170 | semidirect |
| 205. C5 | C2×#1779 | semidirect |
| 213. C22 | C2×C22⋊#170 | semidirect |
| 223. C2 | #10605025 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×Dic5 | 2 |
| C22×C22⋊#170 | 2 |
| #10605025 | 2 |
| C2×#1779 | 5 |