Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
376 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 68 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×#568⋊C3 | C2 | semidirect |
| 3. C4×C5×#41⋊C3 | C2 | semidirect |
| 4. C5×#2901 | C3 | semidirect |
| 6. C5×2−1+4⋊C3 | C4 | semidirect |
| 7. C5×#994 | C4 | semidirect |
| 13. #2901⋊C3 | C5 | direct (N × H) |
| 15. C5×#568 | C2×C3 | semidirect |
| 16. C4×C5×#41 | C2×C3 | semidirect |
| 30. #568⋊C3 | C2×C5 | semidirect |
| 31. C4×#41⋊C3 | C2×C5 | semidirect |
| 34. C5×2−1+4 | C3×C4 | semidirect |
| 37. C5×H(5,𝔽2) | C3×C4 | semidirect |
| 56. #2901 | C3×C5 | semidirect |
| 66. 2−1+4⋊C3 | C4×C5 | semidirect |
| 67. #994 | C4×C5 | semidirect |
| 120. #568 | C2×C3×C5 | semidirect |
| 121. C4×#41 | C2×C3×C5 | semidirect |
| 181. 2−1+4 | C3×C4×C5 | semidirect |
| 184. H(5,𝔽2) | C3×C4×C5 | semidirect |
| 331. C5 | #2901⋊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×#568⋊C3 | 2 |
| C4×C5×#41⋊C3 | 2 |
| C5×#2901 | 3 |
| C3×C5×#104 | 4 |
| #2901⋊C3 | 5 |