Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
240 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 240 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 |
|---|---|---|
| 2. C3×#64853 | C2 | semidirect |
| 3. #10598747 | C3 | direct (N × H) |
| 4. C3×C5×#127 | C4 | semidirect |
| 8. C3×C4×#168 | C4 | semidirect |
| 11. #64853 | C2×C3 | semidirect |
| 22. C5×#127 | C3×C4 | semidirect |
| 26. C4×#168 | C3×C4 | semidirect |
| 40. C3×#127 | AGL(1,𝔽5) | semidirect |
| 81. #127 | C3×AGL(1,𝔽5) | semidirect |
| 114. C3×C5 | #1408 | semidirect |
| 141. C5 | C3×#1408 | semidirect |
| 150. C3 | #10598747 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65362 | 2 |
| C3×#64853 | 2 |
| #10598747 | 3 |
| C3×#1408 | 5 |