Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
388 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 3. #10601476 | C2 | semidirect |
| 4. #10601456 | C2 | semidirect |
| 6. C5×#1389 | C2 | semidirect |
| 7. #10598303 | C2 | semidirect |
| 23. #64708 | C4 | semidirect |
| 64. #1389 | D5 | semidirect |
| 268. C5 | #12944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65183 | 2 |
| #10602241 | 2 |
| #10601476 | 2 |
| #10601456 | 2 |
| #10601449 | 2 |
| C5×#1389 | 2 |
| #10598303 | 2 |
| #12944 | 5 |