Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
188 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 40 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. #10598738 | C3 | direct (N × H) |
| 4. C3×C5×#125 | C4 | semidirect |
| 8. C3×#3935 | C4 | semidirect |
| 21. C5×#125 | C3×C4 | semidirect |
| 25. #3935 | C3×C4 | semidirect |
| 36. C3×#125 | AGL(1,𝔽5) | semidirect |
| 72. #125 | C3×AGL(1,𝔽5) | semidirect |
| 101. C3×C5 | #1412 | semidirect |
| 123. C5 | C3×#1412 | semidirect |
| 131. C3 | #10598738 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65356 | 2 |
| C3×#64853 | 2 |
| #10598738 | 3 |
| C3×#1412 | 5 |