Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
386 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 386 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. #10602235 | C2 | semidirect |
| 3. C2×#64735 | C2 | semidirect |
| 4. #10601511 | C2 | semidirect |
| 5. C2×#64717 | C2 | semidirect |
| 6. C2×#64713 | C2 | semidirect |
| 7. C5×#1385 | C2 | semidirect |
| 75. #1385 | D5 | semidirect |
| 328. C5 | #13392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610987 | 2 |
| #10602235 | 2 |
| C2×#64735 | 2 |
| #10601511 | 2 |
| C2×#64717 | 2 |
| C2×#64713 | 2 |
| C5×#1385 | 2 |
| #13392 | 5 |