Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
414 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 77 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. #10601621 | C2 | semidirect |
| 3. #10601609 | C2 | semidirect |
| 4. #10601590 | C2 | semidirect |
| 5. #10600281 | C2 | semidirect |
| 6. #10600262 | C2 | semidirect |
| 7. C5×#1285 | C2 | semidirect |
| 79. #1285 | D5 | semidirect |
| 356. C5 | #10508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611080 | 2 |
| #10601621 | 2 |
| #10601609 | 2 |
| #10601590 | 2 |
| #10600281 | 2 |
| #10600262 | 2 |
| C5×#1285 | 2 |
| #10508 | 5 |