Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
255 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 255 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×C25 | C2 | semidirect |
| 3. C2×C4×Dic25 | C2 | semidirect |
| 4. #11716373 | C2 | direct (N × H) |
| 10. #87744 | C4 | semidirect |
| 12. C2×D100 | C4 | semidirect |
| 14. C2×Dic50 | C4 | semidirect |
| 16. M16×C25 | C22 | semidirect |
| 19. C4×Dic25 | C22 | semidirect |
| 35. D100 | C2×C4 | semidirect |
| 39. Dic50 | C2×C4 | semidirect |
| 75. C2×C25 | #104 | semidirect |
| 99. C2×M16 | D25 | semidirect |
| 102. C25 | C2×#104 | semidirect |
| 126. M16 | C2×D25 | semidirect |
| 171. C2 | #11716373 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87744 | 2 |
| C2×M16×C25 | 2 |
| C2×C4×Dic25 | 2 |
| #11716373 | 2 |
| C2×#3957 | 5 |