Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
363 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 363 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. #11716486 | C2 | semidirect |
| 4. #11716440 | C2 | semidirect |
| 8. C2×Dic50 | C22 | semidirect |
| 12. C4⋊Dic25 | C22 | semidirect |
| 13. #87718 | C22 | semidirect |
| 16. C23×C25 | Q8 | semidirect |
| 63. C25 | #543 | semidirect |
| 86. C23 | Dic50 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊C4×C25 | 2 |
| C2×C22⋊Dic25 | 2 |
| #11716486 | 2 |
| #11716440 | 2 |
| #65817 | 5 |