Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
442 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 91 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×#2145 | C2 | semidirect |
| 3. #10602874 | C2 | semidirect |
| 4. #10602235 | C2 | semidirect |
| 5. #10601456 | C2 | semidirect |
| 6. #10601449 | C2 | semidirect |
| 7. #10598302 | C2 | semidirect |
| 67. C5×#106 | D4 | semidirect |
| 80. #2145 | D5 | semidirect |
| 240. #106 | C22⋊D5 | semidirect |
| 360. C5 | #13416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615635 | 2 |
| C5×#2145 | 2 |
| #10602874 | 2 |
| #10602235 | 2 |
| #10601456 | 2 |
| #10601449 | 2 |
| #10598302 | 2 |
| #13416 | 5 |