Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
390 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 87 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×#2138 | C2 | semidirect |
| 3. #10602873 | C2 | semidirect |
| 4. #10602202 | C2 | semidirect |
| 5. #10601458 | C2 | semidirect |
| 6. #10601443 | C2 | semidirect |
| 7. #10598299 | C2 | semidirect |
| 71. #2138 | D5 | semidirect |
| 327. C5 | #13406 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615659 | 2 |
| C5×#2138 | 2 |
| #10602873 | 2 |
| #10602202 | 2 |
| #10601458 | 2 |
| #10601443 | 2 |
| #10598299 | 2 |
| #13406 | 5 |