Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
224 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 1. C5×C8×Q16 | C2 | semidirect |
| 4. #10598256 | C2 | semidirect |
| 6. #10597960 | C2 | semidirect |
| 7. #10597929 | C2 | semidirect |
| 47. C8×Q16 | D5 | semidirect |
| 56. C5×Q16 | M16 | semidirect |
| 149. Q16 | #676 | semidirect |
| 194. C5 | #12075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C8×Q16 | 2 |
| C4×#3960 | 2 |
| #10598845 | 2 |
| #10598256 | 2 |
| #10597962 | 2 |
| #10597960 | 2 |
| #10597929 | 2 |
| #12075 | 5 |