Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
448 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 154 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. C5×#4694 | C2 | semidirect |
| 3. C5×#4693 | C2 | semidirect |
| 4. C5×#4682 | C2 | semidirect |
| 5. C3×C5×C82 | C2 | semidirect |
| 16. #68058 | C5 | direct (N × H) |
| 21. C5×C82 | D3 | semidirect |
| 35. #4694 | C2×C5 | semidirect |
| 36. #4693 | C2×C5 | semidirect |
| 37. #4682 | C2×C5 | semidirect |
| 38. C3×C82 | C2×C5 | semidirect |
| 59. C3×C5×C8 | D8 | semidirect |
| 60. C3×C5×C8 | SD16 | semidirect |
| 86. C82 | C5×D3 | semidirect |
| 117. C5×C8 | #204 | semidirect |
| 118. C5×C8 | D24 | semidirect |
| 142. C3×C8 | C5×D8 | semidirect |
| 143. C3×C8 | C5×SD16 | semidirect |
| 164. C3×C5 | #1706 | semidirect |
| 187. C8 | C5×#204 | semidirect |
| 188. C8 | C5×D24 | semidirect |
| 193. C5 | #68058 | direct (N × H) |
| 202. C3 | C5×#1706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4695 | 2 |
| C5×#4694 | 2 |
| C5×#4693 | 2 |
| C5×#4682 | 2 |
| C3×C5×C82 | 2 |
| C5×#1706 | 3 |
| #68058 | 5 |