Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
360 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 3. #10602221 | C2 | semidirect |
| 4. #10600572 | C2 | semidirect |
| 6. C5×#1376 | C2 | semidirect |
| 7. #10598308 | C2 | semidirect |
| 19. #64736 | C4 | semidirect |
| 64. #1376 | D5 | semidirect |
| 274. C5 | #13136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64736 | 2 |
| #10602233 | 2 |
| #10602221 | 2 |
| #10600572 | 2 |
| #10600569 | 2 |
| C5×#1376 | 2 |
| #10598308 | 2 |
| #13136 | 5 |