Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
668 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 116 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. C5×#5945 | C2 | semidirect |
| 2. C5×#578⋊C3 | C2 | semidirect |
| 3. C5×#577⋊C3 | C2 | semidirect |
| 4. C5×#576⋊C3 | C2 | semidirect |
| 5. C2×C5×#131⋊C3 | C2 | semidirect |
| 6. C5×#3584 | C3 | semidirect |
| 8. C5×2−1+4⋊C3 | C22 | semidirect |
| 9. C5×#994 | C22 | semidirect |
| 13. C5×#131⋊C3 | C22 | semidirect |
| 14. C5×#131⋊C3 | C22 | semidirect |
| 15. #3584⋊C3 | C5 | direct (N × H) |
| 16. C5×#585 | C2×C3 | semidirect |
| 18. C5×#578 | C2×C3 | semidirect |
| 20. C5×#577 | C2×C3 | semidirect |
| 22. C5×#576 | C2×C3 | semidirect |
| 26. C2×C5×#131 | C2×C3 | semidirect |
| 37. #5945 | C2×C5 | semidirect |
| 38. #578⋊C3 | C2×C5 | semidirect |
| 39. #577⋊C3 | C2×C5 | semidirect |
| 40. #576⋊C3 | C2×C5 | semidirect |
| 41. C2×#131⋊C3 | C2×C5 | semidirect |
| 80. #3584 | C3×C5 | semidirect |
| 90. 2−1+4⋊C3 | C22×C5 | semidirect |
| 91. #994 | C22×C5 | semidirect |
| 95. #131⋊C3 | C22×C5 | semidirect |
| 96. #131⋊C3 | C22×C5 | semidirect |
| 153. #585 | C2×C3×C5 | semidirect |
| 155. #578 | C2×C3×C5 | semidirect |
| 157. #577 | C2×C3×C5 | semidirect |
| 159. #576 | C2×C3×C5 | semidirect |
| 163. C2×#131 | C2×C3×C5 | semidirect |
| 389. C5 | #3584⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5945 | 2 |
| C5×#578⋊C3 | 2 |
| C5×#577⋊C3 | 2 |
| C5×#576⋊C3 | 2 |
| C2×C5×#131⋊C3 | 2 |
| C5×#3584 | 3 |
| C3×C5×#135 | 4 |
| #3584⋊C3 | 5 |