Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
832 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 832 conjugacy classes of subgroups — too many to draw. Only its 254 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. C22×C5×Dic10 | C2 | semidirect |
| 3. C2×C5×#687 | C2 | direct (N × H) |
| 4. C22×C5×#168 | C2 | semidirect |
| 11. C2×C5×Dic10 | C22 | semidirect |
| 12. C5×#687 | C22 | direct (N × H) |
| 13. C2×C5×#168 | C22 | semidirect |
| 15. C22×#687 | C5 | direct (N × H) |
| 25. C5×Dic10 | C23 | semidirect |
| 26. C5×#168 | C23 | semidirect |
| 31. C22×Dic10 | C2×C5 | semidirect |
| 34. C2×#687 | C2×C5 | direct (N × H) |
| 35. C22×#168 | C2×C5 | semidirect |
| 38. C22×C52 | SD16 | semidirect |
| 60. C2×Dic10 | C22×C5 | semidirect |
| 63. #687 | C22×C5 | direct (N × H) |
| 64. C2×#168 | C22×C5 | semidirect |
| 67. C2×C52 | C2×SD16 | semidirect |
| 95. Dic10 | C23×C5 | semidirect |
| 97. #168 | C23×C5 | semidirect |
| 102. C52 | C22×SD16 | semidirect |
| 111. C22×C5 | #687 | direct (N × H) |
| 112. C22×C5 | C5×SD16 | semidirect |
| 137. C2×C5 | C2×#687 | direct (N × H) |
| 138. C2×C5 | C2×C5×SD16 | semidirect |
| 153. C5 | C22×#687 | direct (N × H) |
| 154. C5 | C22×C5×SD16 | semidirect |
| 157. C22 | C5×#687 | direct (N × H) |
| 163. C2 | C2×C5×#687 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D4 | 2 |
| C22×C5×Dic10 | 2 |
| C2×C5×#687 | 2 |
| C22×C5×#168 | 2 |
| C22×C5×SD16 | 5 |
| C22×#687 | 5 |