Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
240 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 3. #10601704 | C2 | semidirect |
| 4. Q16×#168 | C2 | semidirect |
| 6. #10598056 | C2 | semidirect |
| 7. #10598045 | C2 | semidirect |
| 59. C5×Q16 | SD16 | semidirect |
| 155. Q16 | #687 | semidirect |
| 200. C5 | #12419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2207 | 2 |
| #10602067 | 2 |
| #10601704 | 2 |
| Q16×#168 | 2 |
| #10598281 | 2 |
| #10598056 | 2 |
| #10598045 | 2 |
| #12419 | 5 |