Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
396 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 79 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. #10600478 | C2 | semidirect |
| 3. #10599432 | C2 | semidirect |
| 5. C5×#1272 | C2 | semidirect |
| 7. #10597969 | C2 | semidirect |
| 63. #1272 | D5 | semidirect |
| 340. C5 | #7805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10608332 | 2 |
| #10600478 | 2 |
| #10599432 | 2 |
| #10599428 | 2 |
| C5×#1272 | 2 |
| #10597970 | 2 |
| #10597969 | 2 |
| #7805 | 5 |