Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
759 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 759 conjugacy classes of subgroups — too many to draw. Only its 125 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×C22⋊C4×C25 | C2 | semidirect |
| 3. C2×C22⋊Dic25 | C2 | semidirect |
| 4. C2×#87720 | C2 | semidirect |
| 9. C23×D25 | C4 | semidirect |
| 11. C22×C4×C25 | C22 | semidirect |
| 12. C22×Dic25 | C22 | semidirect |
| 42. C22×C25 | C22⋊C4 | semidirect |
| 52. C2×D25 | C22⋊C4 | semidirect |
| 94. C2×C22⋊C4 | D25 | semidirect |
| 95. C25 | #379 | semidirect |
| 119. C22×C4 | C2×D25 | semidirect |
| 157. C22 | #87720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D25 | 2 |
| C2×C22⋊C4×C25 | 2 |
| C2×C22⋊Dic25 | 2 |
| C2×#87720 | 2 |
| #65244 | 5 |