Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
188 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 50 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. #10598275 | C3 | direct (N × H) |
| 5. C3×C5×#125 | C4 | semidirect |
| 7. C3×C5×#97 | C4 | semidirect |
| 22. C5×#125 | C3×C4 | semidirect |
| 24. C5×#97 | C3×C4 | semidirect |
| 36. C3×#125 | Dic5 | semidirect |
| 39. C3×#97 | Dic5 | semidirect |
| 72. #125 | C3×Dic5 | semidirect |
| 75. #97 | C3×Dic5 | semidirect |
| 101. C3×C5 | #1412 | semidirect |
| 123. C5 | C3×#1412 | semidirect |
| 131. C3 | #10598275 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#490 | 2 |
| C3×#64765 | 2 |
| #10598275 | 3 |
| C3×#1412 | 5 |