Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
198 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 70. C5×C16 | Q16 | semidirect |
| 153. C16 | #689 | semidirect |
| 175. C5 | #12459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×C16 | 2 |
| #10601738 | 2 |
| #10601737 | 2 |
| #10599839 | 2 |
| #10598056 | 2 |
| #10598055 | 2 |
| #10597992 | 2 |
| #12459 | 5 |