Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
274 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 2. C5×#2264 | C2 | semidirect |
| 3. #10602300 | C2 | semidirect |
| 4. C2×#64742 | C2 | semidirect |
| 5. #10598320 | C2 | semidirect |
| 6. #10598096 | C2 | semidirect |
| 7. #10598094 | C2 | semidirect |
| 54. #2264 | D5 | semidirect |
| 219. C5 | #13672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613764 | 2 |
| C5×#2264 | 2 |
| #10602300 | 2 |
| C2×#64742 | 2 |
| #10598320 | 2 |
| #10598096 | 2 |
| #10598094 | 2 |
| #13672 | 5 |