Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
444 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 444 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. #10600620 | C2 | semidirect |
| 4. C2×#64685 | C2 | semidirect |
| 6. #10600341 | C2 | semidirect |
| 7. C5×#1295 | C2 | semidirect |
| 79. #1295 | D5 | semidirect |
| 378. C5 | #10426 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10605986 | 2 |
| #10600620 | 2 |
| #10600614 | 2 |
| C2×#64685 | 2 |
| C2×#64684 | 2 |
| #10600341 | 2 |
| C5×#1295 | 2 |
| #10426 | 5 |