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×#360 | C2 | semidirect |
| 3. #10602871 | C2 | semidirect |
| 4. #10602232 | C2 | semidirect |
| 5. #10601355 | C2 | semidirect |
| 6. C2×#64708 | C2 | semidirect |
| 7. #10598303 | C2 | semidirect |
| 70. C5×#106 | D4 | semidirect |
| 81. C2×#360 | D5 | semidirect |
| 259. #106 | C22⋊D5 | semidirect |
| 398. C5 | #13410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615635 | 2 |
| C2×C5×#360 | 2 |
| #10602871 | 2 |
| #10602232 | 2 |
| #10601355 | 2 |
| C2×#64708 | 2 |
| #10598303 | 2 |
| #13410 | 5 |