Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
486 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 184 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×#64886 | C2 | semidirect |
| 5. #10598777 | C2 | semidirect |
| 8. C22×#674 | C4 | semidirect |
| 15. C22⋊#674 | C4 | semidirect |
| 71. #674 | C22⋊C4 | semidirect |
| 131. C22×C5 | #346 | semidirect |
| 194. C5 | #12611 | semidirect |
| 198. C22 | #64886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#674 | 2 |
| C2×C22⋊#674 | 2 |
| C2×#64886 | 2 |
| #10600740 | 2 |
| #10598777 | 2 |
| #12611 | 5 |