Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
447 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 447 conjugacy classes of subgroups — too many to draw. Only its 167 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. D25⋊M16 | C2 | direct (N × H) |
| 4. C2×#87735 | C2 | semidirect |
| 5. C2×D25⋊C8 | C2 | semidirect |
| 15. #87739 | C22 | semidirect |
| 16. C2×#6016 | C22 | semidirect |
| 17. #87735 | C22 | semidirect |
| 18. D25⋊C8 | C22 | semidirect |
| 38. #6016 | C23 | semidirect |
| 49. C2×D25 | M16 | semidirect |
| 72. C2×C25 | C2×M16 | semidirect |
| 75. D25 | C2×M16 | semidirect |
| 100. C25 | C22×M16 | semidirect |
| 168. C2 | D25⋊M16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D25 | 2 |
| C2×#87739 | 2 |
| D25⋊M16 | 2 |
| C2×#87735 | 2 |
| C2×D25⋊C8 | 2 |
| C2×D5⋊M16 | 5 |