Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
231 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 231 conjugacy classes of subgroups — too many to draw. Only its 57 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. #11716549 | C2 | semidirect |
| 3. D25⋊M16 | C2 | semidirect |
| 4. #11716423 | C2 | semidirect |
| 5. C2×D4×C25 | C4 | semidirect |
| 10. #87746 | C4 | semidirect |
| 13. C2×Dic50 | C4 | semidirect |
| 17. C4×#1035 | C22 | semidirect |
| 18. #87735 | C22 | semidirect |
| 100. C25 | #421 | semidirect |
| 119. C2×D4 | #1035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87746 | 2 |
| #11716549 | 2 |
| D25⋊M16 | 2 |
| #11716423 | 2 |
| #65769 | 5 |