Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
456 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 90 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×#497 | C2 | semidirect |
| 3. C5×#5089 | C2 | semidirect |
| 4. C5×#4540 | C2 | semidirect |
| 5. C5×#4464 | C2 | semidirect |
| 9. C3×C5×C4⋊Q8 | C22 | semidirect |
| 16. C3×C5×#97 | C22 | semidirect |
| 19. C5×#803 | C22 | semidirect |
| 20. #71329 | C5 | direct (N × H) |
| 22. C5×#497 | D3 | semidirect |
| 47. C3×#497 | C2×C5 | semidirect |
| 48. #5089 | C2×C5 | semidirect |
| 49. #4540 | C2×C5 | semidirect |
| 50. #4464 | C2×C5 | semidirect |
| 53. C5×C4⋊Q8 | C2×D3 | semidirect |
| 63. C5×#97 | C2×D3 | semidirect |
| 86. C3×C4⋊Q8 | C22×C5 | semidirect |
| 93. C3×#97 | C22×C5 | semidirect |
| 96. #803 | C22×C5 | semidirect |
| 118. #497 | C5×D3 | semidirect |
| 175. C4⋊Q8 | C2×C5×D3 | semidirect |
| 185. #97 | C2×C5×D3 | semidirect |
| 241. C3×C5 | #1659 | semidirect |
| 281. C5 | #71329 | direct (N × H) |
| 294. C3 | C5×#1659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5683 | 2 |
| C3×C5×#497 | 2 |
| C5×#5089 | 2 |
| C5×#4540 | 2 |
| C5×#4464 | 2 |
| C5×#1659 | 3 |
| #71329 | 5 |