Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
564 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 114 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×#5040 | C2 | semidirect |
| 3. C5×#4979 | C2 | semidirect |
| 4. C5×#4537 | C2 | semidirect |
| 5. C5×#4528 | C2 | semidirect |
| 20. #71880 | C5 | direct (N × H) |
| 50. #5040 | C2×C5 | semidirect |
| 51. #4979 | C2×C5 | semidirect |
| 52. #4537 | C2×C5 | semidirect |
| 53. #4528 | C2×C5 | semidirect |
| 83. C2×C3×C4×C5 | SD16 | semidirect |
| 195. C2×C4×C5 | #214 | semidirect |
| 232. C2×C3×C4 | C5×SD16 | semidirect |
| 280. C3×C5 | #1604 | semidirect |
| 324. C2×C4 | C5×#214 | semidirect |
| 333. C5 | #71880 | direct (N × H) |
| 348. C3 | C5×#1604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#537 | 2 |
| C5×#5040 | 2 |
| C5×#4979 | 2 |
| C5×#4537 | 2 |
| C5×#4528 | 2 |
| C5×#1604 | 3 |
| #71880 | 5 |