Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1480 conjugacy classes of subgroups; only the 352 normal subgroups are shown.
This group has 1480 conjugacy classes of subgroups — too many to draw. Only its 352 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×D5×Dic5 | C2 | semidirect |
| 3. C2×C22⋊#1039 | C2 | semidirect |
| 4. C2×C5×C22⋊Dic5 | C2 | semidirect |
| 5. D5×C22⋊Dic5 | C2 | direct (N × H) |
| 6. C2×#87778 | C2 | semidirect |
| 9. C23×C5×D5 | C4 | semidirect |
| 13. C22×#1039 | C22 | semidirect |
| 14. C22×C5×Dic5 | C22 | semidirect |
| 16. C2×D5×Dic5 | C22 | semidirect |
| 17. C22⋊#1039 | C22 | semidirect |
| 18. C5×C22⋊Dic5 | C22 | semidirect |
| 19. #87778 | C22 | semidirect |
| 23. C23×C52 | C2×C4 | semidirect |
| 30. C22×C5×D5 | C2×C4 | semidirect |
| 31. C22×C5×D5 | C2×C4 | semidirect |
| 36. C2×#1039 | C23 | semidirect |
| 38. C2×C5×Dic5 | C23 | semidirect |
| 50. C2×C22⋊Dic5 | D5 | direct (N × H) |
| 56. C22×C52 | C22×C4 | semidirect |
| 62. C2×C5×D5 | C22⋊C4 | semidirect |
| 64. C2×C5×D5 | C22×C4 | semidirect |
| 77. C23×D5 | Dic5 | semidirect |
| 87. C22×Dic5 | C2×D5 | semidirect |
| 95. C22⋊Dic5 | C2×D5 | direct (N × H) |
| 99. C2×C52 | C2×C22⋊C4 | semidirect |
| 103. C5×D5 | C2×C22⋊C4 | semidirect |
| 119. C23×C5 | C4×D5 | semidirect |
| 120. C23×C5 | C2×Dic5 | semidirect |
| 129. C22×D5 | C2×Dic5 | semidirect |
| 130. C22×D5 | C2×Dic5 | semidirect |
| 144. C2×Dic5 | C22×D5 | semidirect |
| 152. C52 | C22×C22⋊C4 | semidirect |
| 171. C22×C5 | C2×C4×D5 | semidirect |
| 174. C22×C5 | C22×Dic5 | semidirect |
| 181. C2×D5 | C22⋊Dic5 | direct (N × H) |
| 183. C2×D5 | C22×Dic5 | semidirect |
| 211. C2×C5 | D5×C22⋊C4 | semidirect |
| 212. C2×C5 | C2×C22⋊Dic5 | semidirect |
| 218. D5 | C2×C22⋊Dic5 | direct (N × H) |
| 229. C23 | D5×Dic5 | semidirect |
| 238. C5 | C2×D5×C22⋊C4 | semidirect |
| 239. C5 | C22×C22⋊Dic5 | semidirect |
| 250. C22 | C2×D5×Dic5 | semidirect |
| 258. C2 | D5×C22⋊Dic5 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C5×D5 | 2 |
| C22×D5×Dic5 | 2 |
| C2×C22⋊#1039 | 2 |
| C2×C5×C22⋊Dic5 | 2 |
| D5×C22⋊Dic5 | 2 |
| C2×#87778 | 2 |
| C22×C22⋊Dic5 | 5 |
| C2×D5×C22⋊C4 | 5 |