Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1544 conjugacy classes of subgroups; only the 322 normal subgroups are shown.
This group has 1544 conjugacy classes of subgroups — too many to draw. Only its 322 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 |
|---|---|---|
| 1. C3×C5×#585 | C2 | semidirect |
| 2. C5×#5830 | C2 | semidirect |
| 3. C5×#5244 | C2 | semidirect |
| 4. C5×#5240 | C2 | semidirect |
| 11. C22×C5×D12 | C22 | semidirect |
| 14. C5×#937 | C22 | semidirect |
| 16. C5×#926 | C22 | semidirect |
| 17. C5×#834 | C22 | semidirect |
| 18. #84126 | C5 | direct (N × H) |
| 19. C5×#585 | D3 | semidirect |
| 30. C2×C3×C5×Q8 | D4 | semidirect |
| 33. C2×C3×C5×D4 | D4 | semidirect |
| 36. C22×C3×C4×C5 | D4 | semidirect |
| 45. C3×#585 | C2×C5 | semidirect |
| 46. #5830 | C2×C5 | semidirect |
| 47. #5244 | C2×C5 | semidirect |
| 48. #5240 | C2×C5 | semidirect |
| 87. C22×D12 | C22×C5 | semidirect |
| 90. #937 | C22×C5 | semidirect |
| 92. #926 | C22×C5 | semidirect |
| 93. #834 | C22×C5 | semidirect |
| 101. C2×C5×Q8 | #67 | semidirect |
| 107. C2×C5×D4 | #67 | semidirect |
| 110. C22×C4×C5 | #67 | semidirect |
| 116. #585 | C5×D3 | semidirect |
| 138. C2×C3×Q8 | C5×D4 | semidirect |
| 141. C2×C3×D4 | C5×D4 | semidirect |
| 144. C22×C3×C4 | C5×D4 | semidirect |
| 227. C2×Q8 | C5×#67 | semidirect |
| 233. C2×D4 | C5×#67 | semidirect |
| 236. C22×C4 | C5×#67 | semidirect |
| 242. C3×C5 | #3027 | semidirect |
| 282. C5 | #84126 | direct (N × H) |
| 294. C3 | C5×#3027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#585 | 2 |
| C5×#5830 | 2 |
| C5×#5244 | 2 |
| C5×#5240 | 2 |
| C5×#3027 | 3 |
| #84126 | 5 |