Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
342 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 143 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. #11716486 | C2 | semidirect |
| 5. C2×#87718 | C2 | semidirect |
| 6. #11716452 | C2 | semidirect |
| 7. #11716450 | C2 | semidirect |
| 8. #11716440 | C2 | semidirect |
| 9. #11716440 | C2 | semidirect |
| 10. #11716432 | C2 | semidirect |
| 11. C4×Dic50 | C2 | semidirect |
| 37. D4×C25 | Q8 | semidirect |
| 134. C25 | #554 | semidirect |
| 179. D4 | Dic50 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×C25 | 2 |
| D4×Dic25 | 2 |
| #11716486 | 2 |
| C2×#87718 | 2 |
| #11716452 | 2 |
| #11716450 | 2 |
| #11716440 | 2 |
| #11716432 | 2 |
| C4×Dic50 | 2 |
| #65873 | 5 |