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. C4×D4×C25 | C2 | semidirect |
| 3. #11716498 | C2 | semidirect |
| 4. C4×C22⋊D25 | C2 | semidirect |
| 5. #11716488 | C2 | semidirect |
| 6. #11716459 | C2 | semidirect |
| 7. #11716452 | C2 | semidirect |
| 8. #11716445 | C2 | semidirect |
| 9. #11716441 | C2 | semidirect |
| 10. C42×D25 | C2 | semidirect |
| 11. C4×Dic50 | C2 | semidirect |
| 136. C4×D4 | 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 |
|---|---|
| C4×D4×C25 | 2 |
| #11716500 | 2 |
| #11716498 | 2 |
| C4×C22⋊D25 | 2 |
| #11716488 | 2 |
| #11716459 | 2 |
| #11716452 | 2 |
| #11716445 | 2 |
| #11716441 | 2 |
| C42×D25 | 2 |
| C4×Dic50 | 2 |
| #65891 | 5 |