Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
310 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 42. C5×#108 | Q8 | semidirect |
| 55. #3944 | Q8 | semidirect |
| 57. C2×#672 | Q8 | semidirect |
| 156. #108 | Dic10 | semidirect |
| 234. C5 | #13460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610276 | 2 |
| C5×#1953 | 2 |
| #10601478 | 2 |
| C2×#64714 | 2 |
| #10598226 | 2 |
| #10598221 | 2 |
| #10598163 | 2 |
| #13460 | 5 |