Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 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. #10599841 | C2 | semidirect |
| 5. #10598049 | C2 | semidirect |
| 6. #10598045 | C2 | semidirect |
| 7. C16×#168 | C2 | semidirect |
| 73. C5×C16 | SD16 | semidirect |
| 111. #168 | M32 | semidirect |
| 168. C16 | #687 | semidirect |
| 194. C5 | #12051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2169 | 2 |
| C8×#687 | 2 |
| #10599841 | 2 |
| D4⋊#672 | 2 |
| #10598049 | 2 |
| #10598045 | 2 |
| C16×#168 | 2 |
| #12051 | 5 |