Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
747 conjugacy classes of subgroups; only the 303 normal subgroups are shown.
This group has 747 conjugacy classes of subgroups — too many to draw. Only its 303 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×#1035 | C2 | direct (N × H) |
| 5. C22×#1035 | C4 | direct (N × H) |
| 7. C22×C4×C25 | C4 | semidirect |
| 8. C22×Dic25 | C4 | semidirect |
| 9. C2×C4×D25 | C4 | semidirect |
| 11. C4×#1035 | C22 | direct (N × H) |
| 17. C2×#1035 | C2×C4 | direct (N × H) |
| 19. C2×C4×C25 | C2×C4 | semidirect |
| 20. C2×Dic25 | C2×C4 | semidirect |
| 21. C4×D25 | C2×C4 | semidirect |
| 26. C22×C25 | C42 | semidirect |
| 28. C2×D25 | C42 | semidirect |
| 32. #1035 | C22×C4 | direct (N × H) |
| 33. C4×C25 | C22×C4 | semidirect |
| 34. Dic25 | C22×C4 | semidirect |
| 44. C2×C25 | C2×C42 | semidirect |
| 46. D25 | C2×C42 | semidirect |
| 61. C25 | C22×C42 | semidirect |
| 77. C22×C4 | #1035 | direct (N × H) |
| 92. C2×C4 | C2×#1035 | direct (N × H) |
| 98. C22 | C4×#1035 | direct (N × H) |
| 102. C4 | C22×#1035 | direct (N × H) |
| 105. C2 | C2×C4×#1035 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1035 | 2 |
| C22×C4×D25 | 2 |
| C2×C4×#1035 | 2 |
| C22×C4×AGL(1,𝔽5) | 5 |