Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
274 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 274 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 |
|---|---|---|
| 1. C5×C8×Q16 | C2 | semidirect |
| 2. #10601707 | C2 | semidirect |
| 4. #10597964 | C2 | semidirect |
| 5. #10597931 | C2 | semidirect |
| 38. C8×Q16 | D5 | semidirect |
| 46. C5×Q16 | D8 | semidirect |
| 92. C5×C8 | SD32 | semidirect |
| 129. Q16 | D40 | semidirect |
| 168. C8 | #3960 | semidirect |
| 171. C5 | #12425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C8×Q16 | 2 |
| #10601707 | 2 |
| #10598855 | 2 |
| #10597964 | 2 |
| #10597931 | 2 |
| #12425 | 5 |