Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
326 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 89 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. #10602214 | C2 | semidirect |
| 4. C2×#64713 | C2 | semidirect |
| 5. #10601418 | C2 | semidirect |
| 7. C5×#1387 | C2 | semidirect |
| 62. #1387 | D5 | semidirect |
| 259. C5 | #13470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64736 | 2 |
| #10602214 | 2 |
| #10601502 | 2 |
| C2×#64713 | 2 |
| #10601418 | 2 |
| C2×#64711 | 2 |
| C5×#1387 | 2 |
| #13470 | 5 |