Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
508 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 508 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×#4837 | C2 | semidirect |
| 3. C3×C5×#333 | C2 | semidirect |
| 4. C5×#4546 | C2 | semidirect |
| 5. C5×#4485 | C2 | semidirect |
| 18. #68489 | C5 | direct (N × H) |
| 22. C5×#333 | D3 | semidirect |
| 41. #4837 | C2×C5 | semidirect |
| 42. C3×#333 | C2×C5 | semidirect |
| 43. #4546 | C2×C5 | semidirect |
| 44. #4485 | C2×C5 | semidirect |
| 105. #333 | C5×D3 | semidirect |
| 212. C3×C5 | #1560 | semidirect |
| 250. C5 | #68489 | direct (N × H) |
| 262. C3 | C5×#1560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5725 | 2 |
| C5×#4837 | 2 |
| C3×C5×#333 | 2 |
| C5×#4546 | 2 |
| C5×#4485 | 2 |
| C5×#1560 | 3 |
| #68489 | 5 |