Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
324 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11716491 | C2 | semidirect |
| 5. #11716486 | C2 | semidirect |
| 6. #11716459 | C2 | semidirect |
| 7. #11716450 | C2 | semidirect |
| 8. #11716447 | C2 | semidirect |
| 9. #11716441 | C2 | semidirect |
| 10. #11716434 | C2 | semidirect |
| 11. C4×Dic50 | C2 | semidirect |
| 135. C4×D4 | D25 | semidirect |
| 137. C25 | #542 | 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 |
| #11716491 | 2 |
| #11716486 | 2 |
| #11716459 | 2 |
| #11716450 | 2 |
| #11716447 | 2 |
| #11716441 | 2 |
| #11716434 | 2 |
| C4×Dic50 | 2 |
| #65895 | 5 |