Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
690 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 105 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. #10605735 | C2 | semidirect |
| 3. C5×#1519 | C2 | semidirect |
| 4. #10602468 | C2 | semidirect |
| 5. C2×#64688 | C2 | semidirect |
| 6. #10598167 | C2 | semidirect |
| 7. #10598116 | C2 | semidirect |
| 13. #65512 | C4 | semidirect |
| 18. #65282 | C4 | semidirect |
| 63. C5×#95 | D4 | semidirect |
| 67. #3963 | D4 | semidirect |
| 73. #1519 | D5 | semidirect |
| 267. #95 | C22⋊D5 | semidirect |
| 449. C5 | #9205 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614441 | 2 |
| #10605735 | 2 |
| C5×#1519 | 2 |
| #10602468 | 2 |
| C2×#64688 | 2 |
| #10598167 | 2 |
| #10598116 | 2 |
| #9205 | 5 |