Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
510 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 144 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. C2×#64860 | C2 | semidirect |
| 4. #10598699 | C2 | semidirect |
| 14. C22⋊#674 | C4 | semidirect |
| 36. C2×#674 | C2×C4 | semidirect |
| 145. C22×C5 | #347 | semidirect |
| 221. C5 | #12605 | semidirect |
| 227. C22 | #64860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3935 | 2 |
| #10604872 | 2 |
| C2×#64860 | 2 |
| #10598699 | 2 |
| #12605 | 5 |