Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
696 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 172 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. #11717454 | C2 | semidirect |
| 3. #11717452 | C2 | semidirect |
| 4. #11717448 | C2 | semidirect |
| 5. C2×#87862 | C2 | semidirect |
| 13. #87867 | C22 | semidirect |
| 14. C2×#6034 | C22 | semidirect |
| 15. #87863 | C22 | semidirect |
| 18. #87862 | C22 | semidirect |
| 72. C5⋊D5 | #131 | semidirect |
| 104. C52 | C2×#131 | semidirect |
| 157. C5 | D5⋊#131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×C5⋊D5 | 2 |
| #11717454 | 2 |
| #11717452 | 2 |
| #11717448 | 2 |
| C2×#87862 | 2 |
| D5⋊#131 | 5 |