Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
204 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 78 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×#334 | C2 | semidirect |
| 3. C5×C4⋊(C3⋊C16) | C2 | semidirect |
| 12. #67467 | C5 | direct (N × H) |
| 15. C5×#334 | D3 | semidirect |
| 30. C3×#334 | C2×C5 | semidirect |
| 31. C4⋊(C3⋊C16) | C2×C5 | semidirect |
| 75. #334 | C5×D3 | semidirect |
| 157. C3×C5 | #1360 | semidirect |
| 188. C5 | #67467 | direct (N × H) |
| 198. C3 | C5×#1360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4696 | 2 |
| C3×C5×#334 | 2 |
| C5×C4⋊(C3⋊C16) | 2 |
| C5×#1360 | 3 |
| #67467 | 5 |