Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
495 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 495 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 4. C2×#87718 | C2 | semidirect |
| 5. C2×C4×Dic25 | C2 | semidirect |
| 6. #11716439 | C2 | direct (N × H) |
| 9. C22×Dic25 | C4 | semidirect |
| 16. #87718 | C22 | semidirect |
| 17. C4×Dic25 | C22 | semidirect |
| 28. C2×Dic25 | C2×C4 | semidirect |
| 61. C2×C25 | #117 | semidirect |
| 83. C25 | C2×#117 | semidirect |
| 134. C2 | #11716439 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic25 | 2 |
| C2×C22⋊C4×C25 | 2 |
| C2×C22⋊Dic25 | 2 |
| C2×#87718 | 2 |
| C2×C4×Dic25 | 2 |
| #11716439 | 2 |
| C2×#4023 | 5 |