Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
392 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 2. #10599899 | C2 | semidirect |
| 3. D5×C22⋊C16 | C2 | semidirect |
| 4. C5×#1315 | C2 | semidirect |
| 5. #10598180 | C2 | semidirect |
| 6. #10598016 | C2 | semidirect |
| 7. #10598016 | C2 | semidirect |
| 71. #1315 | D5 | semidirect |
| 323. C5 | #11470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610386 | 2 |
| #10599899 | 2 |
| D5×C22⋊C16 | 2 |
| C5×#1315 | 2 |
| #10598180 | 2 |
| #10598016 | 2 |
| #11470 | 5 |