Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
376 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 99 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×#460 | C2 | semidirect |
| 3. #11751128 | C2 | semidirect |
| 4. Q8×C3⋊#168 | C2 | semidirect |
| 5. #11746365 | C2 | semidirect |
| 6. #11746306 | C2 | semidirect |
| 7. #11746300 | C2 | semidirect |
| 25. C5×#460 | D3 | semidirect |
| 52. C3×#460 | D5 | semidirect |
| 78. C3×C5×Q8 | D8 | semidirect |
| 98. C3⋊#168 | SD16 | semidirect |
| 136. #460 | D15 | semidirect |
| 178. C5×Q8 | #213 | semidirect |
| 222. C3×Q8 | #686 | semidirect |
| 277. C3×C5 | #1668 | semidirect |
| 300. Q8 | #6715 | semidirect |
| 326. C5 | #71021 | semidirect |
| 341. C3 | #10601814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#460 | 2 |
| #11751174 | 2 |
| #11751128 | 2 |
| Q8×C3⋊#168 | 2 |
| #11746365 | 2 |
| #11746306 | 2 |
| #11746300 | 2 |
| #10601814 | 3 |
| #71021 | 5 |