Finite Group DatabasebetaFinite Group DatabasebetaOrder 800.
114 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 40 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×Dic50 | C2 | semidirect |
| 3. C22⋊C4×C25 | C2 | semidirect |
| 4. C22⋊Dic25 | C2 | semidirect |
| 5. #87720 | C2 | semidirect |
| 6. #87720 | C2 | semidirect |
| 7. C4×Dic25 | C2 | semidirect |
| 52. C25 | #124 | semidirect |
| 70. C22⋊C4 | D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊D25 | 2 |
| C2×Dic50 | 2 |
| C22⋊C4×C25 | 2 |
| C22⋊Dic25 | 2 |
| #87720 | 2 |
| C4×Dic25 | 2 |
| #4031 | 5 |