Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
348 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 75 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×#1569 | C2 | semidirect |
| 3. #10601318 | C2 | semidirect |
| 5. #10600656 | C2 | semidirect |
| 7. #10598244 | C2 | semidirect |
| 76. #1569 | D5 | semidirect |
| 308. C5 | #10497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611049 | 2 |
| C5×#1569 | 2 |
| #10601318 | 2 |
| #10601297 | 2 |
| #10600656 | 2 |
| #10600652 | 2 |
| #10598244 | 2 |
| #10497 | 5 |