Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
508 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 508 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×#5033 | C2 | semidirect |
| 3. C5×#4981 | C2 | semidirect |
| 4. C5×#4537 | C2 | semidirect |
| 5. C5×#4528 | C2 | semidirect |
| 20. #71874 | C5 | direct (N × H) |
| 48. #5033 | C2×C5 | semidirect |
| 49. #4981 | C2×C5 | semidirect |
| 50. #4537 | C2×C5 | semidirect |
| 51. #4528 | C2×C5 | semidirect |
| 266. C3×C5 | #1610 | semidirect |
| 317. C5 | #71874 | direct (N × H) |
| 332. C3 | C5×#1610 | 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×#5033 | 2 |
| C5×#4981 | 2 |
| C5×#4537 | 2 |
| C5×#4528 | 2 |
| C5×#1610 | 3 |
| #71874 | 5 |