Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
664 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 134 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×#65124 | C2 | semidirect |
| 3. C3×C5×#331 | C2 | semidirect |
| 4. C3×#64764 | C2 | semidirect |
| 5. C3×#64705 | C2 | semidirect |
| 6. #10599180 | C3 | direct (N × H) |
| 14. C3×C5×C4⋊C8 | C22 | semidirect |
| 17. C3×C4⋊#168 | C22 | semidirect |
| 20. #65124 | C2×C3 | semidirect |
| 21. C5×#331 | C2×C3 | semidirect |
| 22. #64764 | C2×C3 | semidirect |
| 23. #64705 | C2×C3 | semidirect |
| 45. C3×#331 | D5 | semidirect |
| 53. C5×C4⋊C8 | C22×C3 | semidirect |
| 56. C4⋊#168 | C22×C3 | semidirect |
| 88. C3×C4⋊C8 | C2×D5 | semidirect |
| 112. #331 | C3×D5 | semidirect |
| 173. C4⋊C8 | C2×C3×D5 | semidirect |
| 233. C3×C5 | #1555 | semidirect |
| 279. C5 | C3×#1555 | semidirect |
| 293. C3 | #10599180 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D5×#127 | 2 |
| C3×#65124 | 2 |
| C3×C5×#331 | 2 |
| C3×#64764 | 2 |
| C3×#64705 | 2 |
| #10599180 | 3 |
| C3×#1555 | 5 |