Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
351 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 351 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. #11716509 | C2 | semidirect |
| 3. Q8×Dic25 | C2 | semidirect |
| 5. C2×C4×Dic25 | C2 | semidirect |
| 6. #11716460 | C2 | semidirect |
| 7. #11716455 | C2 | semidirect |
| 8. #11716454 | C2 | semidirect |
| 9. #11716452 | C2 | semidirect |
| 10. #11716448 | C2 | semidirect |
| 11. #11716443 | C2 | semidirect |
| 132. C22⋊Q8 | D25 | semidirect |
| 139. C25 | #529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C22⋊Q8 | 2 |
| #11716509 | 2 |
| Q8×Dic25 | 2 |
| #11716492 | 2 |
| C2×C4×Dic25 | 2 |
| #11716460 | 2 |
| #11716455 | 2 |
| #11716454 | 2 |
| #11716452 | 2 |
| #11716448 | 2 |
| #11716443 | 2 |
| #65958 | 5 |