Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 98 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. C3×C5×#470 | C2 | semidirect |
| 3. C5×#5179 | C2 | semidirect |
| 4. C5×#4553 | C2 | semidirect |
| 5. C5×#4488 | C2 | semidirect |
| 8. C2×C3×C5×Q16 | C22 | semidirect |
| 15. C3×C5×#106 | C22 | semidirect |
| 19. C5×#812 | C22 | semidirect |
| 20. #71091 | C5 | direct (N × H) |
| 23. C5×#470 | D3 | semidirect |
| 51. C3×#470 | C2×C5 | semidirect |
| 52. #5179 | C2×C5 | semidirect |
| 53. #4553 | C2×C5 | semidirect |
| 54. #4488 | C2×C5 | semidirect |
| 60. C2×C5×Q16 | C2×D3 | semidirect |
| 66. C5×#106 | C2×D3 | semidirect |
| 91. C2×C3×Q16 | C22×C5 | semidirect |
| 98. C3×#106 | C22×C5 | semidirect |
| 102. #812 | C22×C5 | semidirect |
| 129. #470 | C5×D3 | semidirect |
| 193. C2×Q16 | C2×C5×D3 | semidirect |
| 199. #106 | C2×C5×D3 | semidirect |
| 261. C3×C5 | #2191 | semidirect |
| 302. C5 | #71091 | 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 |
|---|---|
| C5×#5748 | 2 |
| C3×C5×#470 | 2 |
| C5×#5179 | 2 |
| C5×#4553 | 2 |
| C5×#4488 | 2 |
| C5×#2191 | 3 |
| #71091 | 5 |