Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
664 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 173 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. #11717448 | C2 | semidirect |
| 3. #11717435 | C2 | semidirect |
| 4. D5⋊#704 | C2 | semidirect |
| 5. #11717361 | C2 | semidirect |
| 6. D5⋊#700 | C2 | semidirect |
| 7. D5⋊(D5⋊C8) | C2 | semidirect |
| 19. #87867 | C22 | semidirect |
| 20. #87863 | C22 | semidirect |
| 21. #87862 | C22 | semidirect |
| 22. #87860 | C22 | semidirect |
| 23. #87856 | C22 | semidirect |
| 24. #87855 | C22 | semidirect |
| 25. #87834 | C22 | semidirect |
| 26. D5⋊#170 | C22 | semidirect |
| 52. #6034 | C23 | semidirect |
| 53. #6033 | C23 | semidirect |
| 73. D52 | M16 | semidirect |
| 113. C5⋊D5 | C2×M16 | semidirect |
| 115. C5×D5 | C2×M16 | semidirect |
| 169. C52 | C22×M16 | semidirect |
| 230. D5 | D5⋊M16 | semidirect |
| 258. C5 | C2×D5⋊M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D52 | 2 |
| #11717448 | 2 |
| #11717435 | 2 |
| D5⋊#704 | 2 |
| #11717361 | 2 |
| D5⋊#700 | 2 |
| D5⋊(D5⋊C8) | 2 |
| C2×D5⋊M16 | 5 |