Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
600 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 161 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×#87862 | C2 | semidirect |
| 3. #11717435 | C2 | semidirect |
| 4. #11717373 | C2 | semidirect |
| 5. #11717361 | C2 | semidirect |
| 6. #11717360 | C2 | semidirect |
| 7. D5⋊(D5⋊C8) | C2 | semidirect |
| 17. C2×#6034 | C22 | semidirect |
| 20. #87862 | C22 | semidirect |
| 21. #87860 | C22 | semidirect |
| 22. #87856 | C22 | semidirect |
| 24. #87834 | C22 | semidirect |
| 25. D5⋊#170 | C22 | semidirect |
| 97. C5⋊D5 | #131 | semidirect |
| 140. C52 | C2×#131 | semidirect |
| 211. C5 | D5⋊#131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717471 | 2 |
| C2×#87862 | 2 |
| #11717435 | 2 |
| #11717373 | 2 |
| #11717361 | 2 |
| #11717360 | 2 |
| D5⋊(D5⋊C8) | 2 |
| D5⋊#131 | 5 |