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 |
|---|---|---|
| 5. C3×C5×#125 | C4 | semidirect |
| 7. C3×C5×#97 | C4 | semidirect |
| 9. #67784 | C5 | direct (N × H) |
| 22. C5×#125 | Dic3 | semidirect |
| 25. C5×#97 | Dic3 | semidirect |
| 36. C3×#125 | C4×C5 | semidirect |
| 38. C3×#97 | C4×C5 | semidirect |
| 72. #125 | C5×Dic3 | semidirect |
| 75. #97 | C5×Dic3 | semidirect |
| 101. C3×C5 | #1412 | semidirect |
| 123. C5 | #67784 | direct (N × H) |
| 131. C3 | C5×#1412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#490 | 2 |
| C5×#4545 | 2 |
| C5×#1412 | 3 |
| #67784 | 5 |