Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
495 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 495 conjugacy classes of subgroups — too many to draw. Only its 167 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. #11716549 | C2 | direct (N × H) |
| 4. C2×C4⋊#1035 | C2 | semidirect |
| 5. C2×C4×#1035 | C2 | semidirect |
| 8. C22×C4×C25 | C4 | semidirect |
| 9. C22×Dic25 | C4 | semidirect |
| 10. C2×C4×D25 | C4 | semidirect |
| 11. C2×C4×D25 | C4 | semidirect |
| 12. C2×C4×D25 | C4 | semidirect |
| 17. C4⋊#1035 | C22 | semidirect |
| 18. C4×#1035 | C22 | semidirect |
| 30. C2×C4×C25 | C2×C4 | semidirect |
| 33. C2×Dic25 | C2×C4 | semidirect |
| 36. C4×D25 | C2×C4 | semidirect |
| 37. C4×D25 | C2×C4 | semidirect |
| 75. C2×C25 | #117 | semidirect |
| 78. D25 | #117 | semidirect |
| 105. C25 | C2×#117 | semidirect |
| 130. C22×C4 | #1035 | semidirect |
| 159. C2×C4 | C2×#1035 | semidirect |
| 180. C2 | #11716549 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D25 | 2 |
| C2×C22⋊#1035 | 2 |
| #11716549 | 2 |
| C2×C4⋊#1035 | 2 |
| C2×C4×#1035 | 2 |
| C2×#4130 | 5 |