Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
380 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 2. C5×#5424 | C2 | semidirect |
| 3. C5×#5423 | C2 | semidirect |
| 6. C5×2−1+4⋊C3 | C4 | semidirect |
| 7. C5×#994 | C4 | semidirect |
| 13. #73157 | C5 | direct (N × H) |
| 30. #5424 | C2×C5 | semidirect |
| 31. #5423 | C2×C5 | semidirect |
| 34. C5×2−1+4 | Dic3 | semidirect |
| 37. C5×H(5,𝔽2) | Dic3 | semidirect |
| 67. 2−1+4⋊C3 | C4×C5 | semidirect |
| 68. #994 | C4×C5 | semidirect |
| 181. 2−1+4 | C5×Dic3 | semidirect |
| 184. H(5,𝔽2) | C5×Dic3 | semidirect |
| 331. C5 | #73157 | 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×#5424 | 2 |
| C5×#5423 | 2 |
| C5×#1794 | 3 |
| C5×#837 | 4 |
| #73157 | 5 |