Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
448 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 1. C3×C5×Q82 | C2 | semidirect |
| 3. C3×#64768 | C2 | semidirect |
| 4. #10602735 | C3 | direct (N × H) |
| 13. C5×Q82 | C2×C3 | semidirect |
| 15. #64768 | C2×C3 | semidirect |
| 30. C3×Q82 | D5 | semidirect |
| 74. Q82 | C3×D5 | semidirect |
| 151. C3×C5 | #2205 | semidirect |
| 176. C5 | C3×#2205 | semidirect |
| 183. C3 | #10602735 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×Q82 | 2 |
| C3×#65384 | 2 |
| C3×#64768 | 2 |
| #10602735 | 3 |
| C3×#2205 | 5 |