Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
387 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 387 conjugacy classes of subgroups — too many to draw. Only its 153 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×#87739 | C2 | semidirect |
| 3. #11716550 | C2 | semidirect |
| 4. D25⋊M16 | C2 | semidirect |
| 13. #87739 | C22 | semidirect |
| 14. C2×#6016 | C22 | semidirect |
| 15. #87735 | C22 | semidirect |
| 16. D25⋊C8 | C22 | semidirect |
| 78. C25 | #568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87746 | 2 |
| C2×#87739 | 2 |
| #11716550 | 2 |
| D25⋊M16 | 2 |
| #66256 | 5 |