Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
285 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 285 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 2. C2×#87712 | C2 | semidirect |
| 3. #11716454 | C2 | semidirect |
| 4. C25×#102 | C2 | semidirect |
| 5. #11716381 | C2 | semidirect |
| 6. #11716369 | C2 | semidirect |
| 7. #11716358 | C2 | semidirect |
| 12. D4×D25 | C4 | semidirect |
| 15. C2×C8×C25 | C22 | semidirect |
| 16. C4⋊C4×C25 | C22 | semidirect |
| 18. C4⋊Dic25 | C22 | semidirect |
| 20. C2×#6014 | C22 | semidirect |
| 111. #102 | D25 | semidirect |
| 112. C25 | #418 | semidirect |
| 138. C2×C8 | C2×D25 | semidirect |
| 140. C4⋊C4 | C2×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D25 | 2 |
| C2×#87712 | 2 |
| #11716454 | 2 |
| C25×#102 | 2 |
| #11716381 | 2 |
| #11716369 | 2 |
| #11716358 | 2 |
| #65059 | 5 |