Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 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. C5×#2140 | C2 | semidirect |
| 3. C2×#64783 | C2 | semidirect |
| 4. #10602230 | C2 | semidirect |
| 5. #10602220 | C2 | semidirect |
| 6. #10601458 | C2 | semidirect |
| 7. #10598216 | C2 | semidirect |
| 51. C2×C5×C16 | D4 | semidirect |
| 66. #2140 | D5 | semidirect |
| 195. C2×C16 | C22⋊D5 | semidirect |
| 307. C5 | #13396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615567 | 2 |
| C5×#2140 | 2 |
| C2×#64783 | 2 |
| #10602230 | 2 |
| #10602220 | 2 |
| #10601458 | 2 |
| #10598216 | 2 |
| #13396 | 5 |