Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
204 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 70 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. C3×C5×#364 | C2 | semidirect |
| 3. C5×#4463 | C2 | semidirect |
| 12. #67570 | C5 | direct (N × H) |
| 15. C5×#364 | D3 | semidirect |
| 30. C3×#364 | C2×C5 | semidirect |
| 31. #4463 | C2×C5 | semidirect |
| 75. #364 | C5×D3 | semidirect |
| 152. C3×C5 | #1359 | semidirect |
| 179. C5 | #67570 | direct (N × H) |
| 187. C3 | C5×#1359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4693 | 2 |
| C3×C5×#364 | 2 |
| C5×#4463 | 2 |
| C5×#1359 | 3 |
| #67570 | 5 |