Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
420 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 1. C22×Dic50 | C2 | semidirect |
| 4. #11716486 | C2 | semidirect |
| 5. #11716450 | C2 | semidirect |
| 6. #11716440 | C2 | semidirect |
| 7. #11716431 | C2 | semidirect |
| 8. C4×Dic50 | C2 | semidirect |
| 28. D4×C25 | Q8 | semidirect |
| 40. Dic50 | D4 | direct (N × H) |
| 51. C22×C25 | C2×Q8 | semidirect |
| 56. C4×C25 | C2×Q8 | semidirect |
| 104. C25 | D4×Q8 | semidirect |
| 141. D4 | Dic50 | direct (N × H) |
| 154. C22 | C2×Dic50 | semidirect |
| 161. C4 | C2×Dic50 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic50 | 2 |
| C4×D4×C25 | 2 |
| D4×Dic25 | 2 |
| #11716486 | 2 |
| #11716450 | 2 |
| #11716440 | 2 |
| #11716431 | 2 |
| C4×Dic50 | 2 |
| D4×Dic10 | 5 |