Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
462 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×C5×#359 | C2 | semidirect |
| 3. #10602871 | C2 | semidirect |
| 4. C2×#64729 | C2 | semidirect |
| 5. #10601494 | C2 | semidirect |
| 6. C2×#64715 | C2 | semidirect |
| 7. #10598296 | C2 | semidirect |
| 61. C5×#108 | D4 | semidirect |
| 73. C2×#359 | D5 | semidirect |
| 224. #108 | C22⋊D5 | semidirect |
| 350. C5 | #13411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615637 | 2 |
| C2×C5×#359 | 2 |
| #10602871 | 2 |
| C2×#64729 | 2 |
| #10601494 | 2 |
| C2×#64715 | 2 |
| #10598296 | 2 |
| #13411 | 5 |