Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
500 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 110 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×#4751 | C2 | semidirect |
| 3. C3×C5×#355 | C2 | semidirect |
| 4. C5×#4542 | C2 | semidirect |
| 5. C5×#4478 | C2 | semidirect |
| 20. #69165 | C5 | direct (N × H) |
| 25. C5×#355 | D3 | semidirect |
| 52. #4751 | C2×C5 | semidirect |
| 53. C3×#355 | C2×C5 | semidirect |
| 54. #4542 | C2×C5 | semidirect |
| 55. #4478 | C2×C5 | semidirect |
| 137. #355 | C5×D3 | semidirect |
| 284. C3×C5 | #2132 | semidirect |
| 334. C5 | #69165 | direct (N × H) |
| 349. C3 | C5×#2132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5668 | 2 |
| C5×#4751 | 2 |
| C3×C5×#355 | 2 |
| C5×#4542 | 2 |
| C5×#4478 | 2 |
| C5×#2132 | 3 |
| #69165 | 5 |