Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
584 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 159 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. C2×#87867 | C2 | semidirect |
| 3. C2×#87860 | C2 | semidirect |
| 4. #11717373 | C2 | semidirect |
| 5. D5⋊#704 | C2 | semidirect |
| 6. #11717371 | C2 | semidirect |
| 17. #87867 | C22 | semidirect |
| 18. C2×#6034 | C22 | semidirect |
| 20. #87860 | C22 | semidirect |
| 21. C2×#6033 | C22 | semidirect |
| 22. #87834 | C22 | semidirect |
| 23. D5⋊#170 | C22 | semidirect |
| 133. C52 | #568 | semidirect |
| 203. C5 | #66256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87880 | 2 |
| C2×#87867 | 2 |
| C2×#87860 | 2 |
| #11717373 | 2 |
| D5⋊#704 | 2 |
| #11717371 | 2 |
| #66256 | 5 |