Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
320 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 122 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×#4682 | C2 | semidirect |
| 3. C5×#4562 | C2 | semidirect |
| 4. C4×C5×C3⋊C16 | C2 | semidirect |
| 14. #71288 | C5 | direct (N × H) |
| 32. #4682 | C2×C5 | semidirect |
| 33. #4562 | C2×C5 | semidirect |
| 34. C4×C3⋊C16 | C2×C5 | semidirect |
| 158. C3×C5 | #2240 | semidirect |
| 188. C5 | #71288 | direct (N × H) |
| 198. C3 | C5×#2240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#493 | 2 |
| C5×#4682 | 2 |
| C5×#4562 | 2 |
| C4×C5×C3⋊C16 | 2 |
| C5×#2240 | 3 |
| #71288 | 5 |