Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
535 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 535 conjugacy classes of subgroups — too many to draw. Only its 170 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. #11717428 | C2 | semidirect |
| 3. C5×#4133 | C2 | semidirect |
| 4. D5⋊#676 | C2 | semidirect |
| 5. #11717329 | C2 | semidirect |
| 6. D5×#700 | C2 | semidirect |
| 7. #11717327 | C2 | semidirect |
| 15. #87849 | C22 | semidirect |
| 16. D5⋊#168 | C22 | semidirect |
| 17. C5×#700 | C22 | semidirect |
| 18. C5×D5⋊C8 | C22 | semidirect |
| 21. #87828 | C22 | semidirect |
| 22. #87828 | C22 | semidirect |
| 23. D5×#170 | C22 | semidirect |
| 45. #4133 | D5 | semidirect |
| 85. #700 | C2×D5 | semidirect |
| 87. D5⋊C8 | C2×D5 | semidirect |
| 144. C52 | #568 | semidirect |
| 207. C5 | #66084 | semidirect |
| 208. C5 | #66264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717484 | 2 |
| #11717428 | 2 |
| C5×#4133 | 2 |
| D5⋊#676 | 2 |
| #11717329 | 2 |
| D5×#700 | 2 |
| #11717327 | 2 |
| #66264 | 5 |
| #66084 | 5 |