Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
363 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 363 conjugacy classes of subgroups — too many to draw. Only its 125 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. C25×C22⋊Q8 | C2 | semidirect |
| 2. #11716508 | C2 | semidirect |
| 4. #11716486 | C2 | semidirect |
| 5. #11716459 | C2 | semidirect |
| 6. #11716458 | C2 | semidirect |
| 7. #11716458 | C2 | semidirect |
| 9. #11716440 | C2 | semidirect |
| 11. C2×Q8×C25 | C22 | semidirect |
| 16. C2×Dic50 | C22 | semidirect |
| 17. C2×Dic50 | C22 | semidirect |
| 18. C4⋊C4×C25 | C22 | semidirect |
| 19. C4⋊C4×C25 | C22 | semidirect |
| 26. C4⋊Dic25 | C22 | semidirect |
| 27. C4⋊Dic25 | C22 | semidirect |
| 28. #87718 | C22 | semidirect |
| 29. #87718 | C22 | semidirect |
| 30. #87718 | C22 | semidirect |
| 35. C22×D25 | Q8 | semidirect |
| 127. C22⋊Q8 | D25 | semidirect |
| 130. C25 | #543 | semidirect |
| 149. C2×Q8 | C2×D25 | semidirect |
| 159. C4⋊C4 | C2×D25 | semidirect |
| 160. C4⋊C4 | C2×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C22⋊Q8 | 2 |
| #11716508 | 2 |
| C2×#87720 | 2 |
| #11716486 | 2 |
| #11716459 | 2 |
| #11716458 | 2 |
| C22⋊C4×D25 | 2 |
| #11716440 | 2 |
| #65968 | 5 |