Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
438 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 85 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. #10611068 | C2 | semidirect |
| 3. #10601621 | C2 | semidirect |
| 4. #10601610 | C2 | semidirect |
| 5. #10601601 | C2 | semidirect |
| 6. C5×#1308 | C2 | semidirect |
| 7. #10598248 | C2 | semidirect |
| 72. #1308 | D5 | semidirect |
| 305. C5 | #9333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611080 | 2 |
| #10611068 | 2 |
| #10601621 | 2 |
| #10601610 | 2 |
| #10601601 | 2 |
| C5×#1308 | 2 |
| #10598248 | 2 |
| #9333 | 5 |