Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
320 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 1. C3×C5×#500 | C2 | semidirect |
| 4. C3×#64766 | C2 | semidirect |
| 5. C3×#64678 | C2 | semidirect |
| 6. #10602165 | C3 | direct (N × H) |
| 19. C5×#500 | C2×C3 | semidirect |
| 22. #64766 | C2×C3 | semidirect |
| 23. #64678 | C2×C3 | semidirect |
| 37. C3×#500 | D5 | semidirect |
| 93. #500 | C3×D5 | semidirect |
| 191. C3×C5 | #1675 | semidirect |
| 226. C5 | C3×#1675 | semidirect |
| 238. C3 | #10602165 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#500 | 2 |
| C3×#65373 | 2 |
| C3×C8×D20 | 2 |
| C3×#64766 | 2 |
| C3×#64678 | 2 |
| #10602165 | 3 |
| C3×#1675 | 5 |