Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
380 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 3. C5×#4681 | C2 | semidirect |
| 4. C5×#4680 | C2 | semidirect |
| 5. C3×C5×C82 | C2 | semidirect |
| 16. #68059 | C5 | direct (N × H) |
| 21. C5×C82 | D3 | semidirect |
| 35. #4681 | C2×C5 | semidirect |
| 36. #4680 | C2×C5 | semidirect |
| 37. C3×C82 | C2×C5 | semidirect |
| 83. C82 | C5×D3 | semidirect |
| 154. C3×C5 | #1708 | semidirect |
| 179. C5 | #68059 | direct (N × H) |
| 187. C3 | C5×#1708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4694 | 2 |
| C5×#4693 | 2 |
| C5×#4681 | 2 |
| C5×#4680 | 2 |
| C3×C5×C82 | 2 |
| C5×#1708 | 3 |
| #68059 | 5 |