Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
366 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 81 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. #10601541 | C2 | semidirect |
| 3. #10601299 | C2 | semidirect |
| 5. #10600672 | C2 | semidirect |
| 7. C5×#1299 | C2 | semidirect |
| 70. #1299 | D5 | semidirect |
| 288. C5 | #10491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611000 | 2 |
| #10601541 | 2 |
| #10601299 | 2 |
| #10601298 | 2 |
| #10600672 | 2 |
| #10600646 | 2 |
| C5×#1299 | 2 |
| #10491 | 5 |