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. C3×#64683 | C2 | semidirect |
| 4. #10598061 | C3 | direct (N × H) |
| 14. C5×#364 | C2×C3 | semidirect |
| 15. #64683 | C2×C3 | semidirect |
| 31. C3×#364 | D5 | semidirect |
| 75. #364 | C3×D5 | semidirect |
| 152. C3×C5 | #1359 | semidirect |
| 179. C5 | C3×#1359 | semidirect |
| 187. C3 | #10598061 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64982 | 2 |
| C3×C5×#364 | 2 |
| C3×#64683 | 2 |
| #10598061 | 3 |
| C3×#1359 | 5 |