Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
270 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 112 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. #10598525 | C2 | semidirect |
| 4. #10598524 | C2 | semidirect |
| 89. C5×C8 | M32 | semidirect |
| 93. #168 | M32 | semidirect |
| 176. C8 | #3990 | semidirect |
| 178. C5 | #12004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10603827 | 2 |
| C82×D5 | 2 |
| #10598525 | 2 |
| #10598524 | 2 |
| #12004 | 5 |