Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 122 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. C5×#5196 | C2 | semidirect |
| 3. C5×#4567 | C2 | semidirect |
| 4. C5×#4506 | C2 | semidirect |
| 5. C5×#4502 | C2 | semidirect |
| 9. C3×C5×Q32 | C4 | semidirect |
| 10. C3×C5×SD32 | C4 | semidirect |
| 11. C3×C5×D16 | C4 | semidirect |
| 17. #71512 | C5 | direct (N × H) |
| 37. #5196 | C2×C5 | semidirect |
| 38. #4567 | C2×C5 | semidirect |
| 39. #4506 | C2×C5 | semidirect |
| 40. #4502 | C2×C5 | semidirect |
| 43. C5×Q32 | Dic3 | semidirect |
| 44. C5×SD32 | Dic3 | semidirect |
| 45. C5×D16 | Dic3 | semidirect |
| 64. C3×Q32 | C4×C5 | semidirect |
| 65. C3×SD32 | C4×C5 | semidirect |
| 66. C3×D16 | C4×C5 | semidirect |
| 121. Q32 | C5×Dic3 | semidirect |
| 122. SD32 | C5×Dic3 | semidirect |
| 123. D16 | C5×Dic3 | semidirect |
| 161. C3×C5 | #2179 | semidirect |
| 184. C5 | #71512 | direct (N × H) |
| 191. C3 | C5×#2179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#508 | 2 |
| C5×#5196 | 2 |
| C5×#4567 | 2 |
| C5×#4506 | 2 |
| C5×#4502 | 2 |
| C5×#2179 | 3 |
| #71512 | 5 |