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×#87863 | C2 | semidirect |
| 3. #11717435 | C2 | semidirect |
| 4. #11717373 | C2 | semidirect |
| 5. D5⋊#700 | C2 | semidirect |
| 6. #11717358 | C2 | semidirect |
| 16. C2×#6034 | C22 | semidirect |
| 18. #87863 | C22 | semidirect |
| 19. #87860 | C22 | semidirect |
| 21. #87855 | C22 | semidirect |
| 22. #87834 | C22 | semidirect |
| 23. D5⋊#170 | C22 | semidirect |
| 136. C52 | #568 | semidirect |
| 205. C5 | #66264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717471 | 2 |
| C2×#87863 | 2 |
| #11717435 | 2 |
| #11717373 | 2 |
| D5⋊#700 | 2 |
| #11717358 | 2 |
| #66264 | 5 |