Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
690 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 120 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. C2×C5×2−1+4⋊C3 | C2 | semidirect |
| 2. C2×C5×#994 | C2 | semidirect |
| 3. C5×#577⋊C3 | C2 | direct (N × H) |
| 4. C2×C5×#131⋊C3 | C2 | semidirect |
| 5. C2×C5×#577 | C3 | semidirect |
| 7. C5×2−1+4⋊C3 | C22 | semidirect |
| 9. C5×#994 | C22 | semidirect |
| 14. C5×#131⋊C3 | C22 | semidirect |
| 15. C2×#577⋊C3 | C5 | direct (N × H) |
| 17. C2×C5×H(5,𝔽2) | C2×C3 | semidirect |
| 19. C5×#577 | C2×C3 | semidirect |
| 24. C2×C5×#131 | C2×C3 | semidirect |
| 34. C2×2−1+4⋊C3 | C2×C5 | semidirect |
| 35. C2×#994 | C2×C5 | semidirect |
| 36. #577⋊C3 | C2×C5 | direct (N × H) |
| 37. C2×#131⋊C3 | C2×C5 | semidirect |
| 45. C5×H(5,𝔽2) | C22×C3 | semidirect |
| 69. C5×#131 | C22×C3 | semidirect |
| 72. C2×#577 | C3×C5 | semidirect |
| 83. 2−1+4⋊C3 | C22×C5 | semidirect |
| 85. #994 | C22×C5 | semidirect |
| 90. #131⋊C3 | C22×C5 | semidirect |
| 148. C2×H(5,𝔽2) | C2×C3×C5 | semidirect |
| 150. #577 | C2×C3×C5 | semidirect |
| 155. C2×#131 | C2×C3×C5 | semidirect |
| 221. H(5,𝔽2) | C22×C3×C5 | semidirect |
| 245. #131 | C22×C3×C5 | semidirect |
| 343. C2×C5 | #577⋊C3 | direct (N × H) |
| 391. C5 | C2×#577⋊C3 | direct (N × H) |
| 413. C2 | C5×#577⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×2−1+4⋊C3 | 2 |
| C2×C5×#994 | 2 |
| C5×#577⋊C3 | 2 |
| C2×C5×#131⋊C3 | 2 |
| C2×C5×#577 | 3 |
| C2×C3×C5×SD16 | 4 |
| C2×#577⋊C3 | 5 |