Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
224 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 56 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×#65208 | C2 | semidirect |
| 2. D5×D48 | C2 | semidirect |
| 3. #11746342 | C2 | semidirect |
| 4. C5×#4521 | C2 | semidirect |
| 5. #11745819 | C2 | semidirect |
| 6. #11745818 | C2 | semidirect |
| 7. #11745815 | C2 | semidirect |
| 11. C3×C5×Q32 | C22 | semidirect |
| 15. C3×D80 | C22 | semidirect |
| 18. C3⋊#3926 | C22 | semidirect |
| 19. C5×C3⋊C32 | C22 | semidirect |
| 21. #65208 | D3 | semidirect |
| 42. #4521 | D5 | semidirect |
| 48. C5×Q32 | C2×D3 | semidirect |
| 53. D80 | C2×D3 | semidirect |
| 71. C3×Q32 | C2×D5 | semidirect |
| 79. C3⋊C32 | C2×D5 | semidirect |
| 130. Q32 | D3×D5 | semidirect |
| 174. C3×C5 | #2263 | semidirect |
| 204. C5 | #71509 | semidirect |
| 213. C3 | #10600173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65208 | 2 |
| D5×D48 | 2 |
| #11746342 | 2 |
| C5×#4521 | 2 |
| #11745819 | 2 |
| #11745818 | 2 |
| #11745815 | 2 |
| #10600173 | 3 |
| #71509 | 5 |