Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
387 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 387 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 3. C2×C4×Dic25 | C2 | semidirect |
| 4. #11716379 | C2 | semidirect |
| 7. C22×C4×C25 | C4 | semidirect |
| 11. C22⋊Dic25 | C4 | direct (N × H) |
| 26. C2×Dic25 | C2×C4 | semidirect |
| 34. C22×C25 | C42 | semidirect |
| 40. C4×C25 | C22⋊C4 | semidirect |
| 73. C25 | C4×C22⋊C4 | semidirect |
| 88. C22×C4 | Dic25 | semidirect |
| 115. C22 | C4×Dic25 | semidirect |
| 122. C4 | C22⋊Dic25 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C25 | 2 |
| C2×C22⋊Dic25 | 2 |
| C2×C4×Dic25 | 2 |
| #11716379 | 2 |
| C4×C22⋊Dic5 | 5 |