Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
231 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 231 conjugacy classes of subgroups — too many to draw. Only its 79 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. C25×#117 | C2 | semidirect |
| 3. C2×#87716 | C2 | semidirect |
| 4. #11716353 | C2 | semidirect |
| 9. #87744 | C4 | semidirect |
| 11. C2×D100 | C4 | semidirect |
| 13. C2×Dic50 | C4 | semidirect |
| 16. C42×C25 | C22 | semidirect |
| 18. #87716 | C22 | semidirect |
| 98. #117 | D25 | semidirect |
| 100. C25 | #421 | semidirect |
| 127. C42 | C2×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87744 | 2 |
| C25×#117 | 2 |
| C2×#87716 | 2 |
| #11716353 | 2 |
| #65294 | 5 |