Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
890 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 160 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. #10605010 | C2 | semidirect |
| 3. #10605009 | C2 | semidirect |
| 4. C2×#64932 | C2 | semidirect |
| 5. #10605007 | C2 | semidirect |
| 15. C2×#3998 | C22 | semidirect |
| 16. C2×#3998 | C22 | semidirect |
| 17. C22×#674 | C22 | semidirect |
| 310. C5 | #12685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619197 | 2 |
| #10605010 | 2 |
| #10605009 | 2 |
| C2×#64932 | 2 |
| #10605007 | 2 |
| #12685 | 5 |