Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
364 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 90 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⋊#564 | C2 | semidirect |
| 4. C3×C5×#330 | C2 | semidirect |
| 5. C3×#64685 | C2 | semidirect |
| 6. #10599168 | C3 | direct (N × H) |
| 19. C5⋊#564 | C2×C3 | semidirect |
| 22. C5×#330 | C2×C3 | semidirect |
| 23. #64685 | C2×C3 | semidirect |
| 43. C3×#330 | D5 | semidirect |
| 96. #330 | C3×D5 | semidirect |
| 177. C3×C5 | #1658 | semidirect |
| 202. C5 | C3×#1658 | semidirect |
| 211. C3 | #10599168 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5⋊#564 | 2 |
| C3×#65356 | 2 |
| C3×#65002 | 2 |
| C3×C5×#330 | 2 |
| C3×#64685 | 2 |
| #10599168 | 3 |
| C3×#1658 | 5 |