Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 106 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×#5195 | C2 | semidirect |
| 3. C5×#5137 | C2 | semidirect |
| 4. C5×#4566 | C2 | semidirect |
| 5. C5×#4553 | C2 | semidirect |
| 14. C2×C5×Dic12 | C22 | semidirect |
| 17. C5×#817 | C22 | semidirect |
| 19. C5×#812 | C22 | semidirect |
| 20. #72113 | C5 | direct (N × H) |
| 51. #5195 | C2×C5 | semidirect |
| 52. #5137 | C2×C5 | semidirect |
| 53. #4566 | C2×C5 | semidirect |
| 54. #4553 | C2×C5 | semidirect |
| 97. C2×Dic12 | C22×C5 | semidirect |
| 100. #817 | C22×C5 | semidirect |
| 102. #812 | C22×C5 | semidirect |
| 261. C3×C5 | #2191 | semidirect |
| 302. C5 | #72113 | direct (N × H) |
| 314. C3 | C5×#2191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#575 | 2 |
| C5×#5195 | 2 |
| C5×#5137 | 2 |
| C5×#4566 | 2 |
| C5×#4553 | 2 |
| C5×#2191 | 3 |
| #72113 | 5 |