Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
454 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 89 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×#2148 | C2 | semidirect |
| 3. #10602873 | C2 | semidirect |
| 4. C2×#64736 | C2 | semidirect |
| 5. #10601499 | C2 | semidirect |
| 6. C2×#64715 | C2 | semidirect |
| 7. #10598304 | C2 | semidirect |
| 63. #3951 | D4 | semidirect |
| 70. #2148 | D5 | semidirect |
| 326. C5 | #13417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615637 | 2 |
| C5×#2148 | 2 |
| #10602873 | 2 |
| C2×#64736 | 2 |
| #10601499 | 2 |
| C2×#64715 | 2 |
| #10598304 | 2 |
| #13417 | 5 |