Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
492 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 134 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×#4833 | C2 | semidirect |
| 3. C3×C5×#331 | C2 | semidirect |
| 4. C5×#4544 | C2 | semidirect |
| 5. C5×#4481 | C2 | semidirect |
| 18. #68382 | C5 | direct (N × H) |
| 23. C5×#331 | D3 | semidirect |
| 40. #4833 | C2×C5 | semidirect |
| 41. C3×#331 | C2×C5 | semidirect |
| 42. #4544 | C2×C5 | semidirect |
| 43. #4481 | C2×C5 | semidirect |
| 104. #331 | C5×D3 | semidirect |
| 208. C3×C5 | #1543 | semidirect |
| 246. C5 | #68382 | direct (N × H) |
| 258. C3 | C5×#1543 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5716 | 2 |
| C5×#4833 | 2 |
| C3×C5×#331 | 2 |
| C5×#4544 | 2 |
| C5×#4481 | 2 |
| C5×#1543 | 3 |
| #68382 | 5 |