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. C3×#66164 | C2 | semidirect |
| 3. C3×#65533 | C2 | semidirect |
| 4. C3×#65529 | C2 | semidirect |
| 5. #10615857 | C3 | direct (N × H) |
| 11. C22×C3×D20 | C22 | semidirect |
| 14. C3×#4083 | C22 | semidirect |
| 16. C3×#4072 | C22 | semidirect |
| 17. C3×#3966 | C22 | semidirect |
| 19. C5×#585 | C2×C3 | semidirect |
| 20. #66164 | C2×C3 | semidirect |
| 21. #65533 | C2×C3 | semidirect |
| 22. #65529 | C2×C3 | 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 | D5 | semidirect |
| 54. C22×D20 | C22×C3 | semidirect |
| 57. #4083 | C22×C3 | semidirect |
| 59. #4072 | C22×C3 | semidirect |
| 60. #3966 | C22×C3 | semidirect |
| 101. C2×C5×Q8 | C3×D4 | semidirect |
| 104. C2×C5×D4 | C3×D4 | semidirect |
| 107. C22×C4×C5 | C3×D4 | semidirect |
| 116. #585 | C3×D5 | semidirect |
| 138. C2×C3×Q8 | C22⋊D5 | semidirect |
| 144. C2×C3×D4 | C22⋊D5 | semidirect |
| 147. C22×C3×C4 | C22⋊D5 | semidirect |
| 227. C2×Q8 | C3×C22⋊D5 | semidirect |
| 233. C2×D4 | C3×C22⋊D5 | semidirect |
| 236. C22×C4 | C3×C22⋊D5 | semidirect |
| 242. C3×C5 | #3027 | semidirect |
| 282. C5 | C3×#3027 | semidirect |
| 294. C3 | #10615857 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#585 | 2 |
| C3×#66164 | 2 |
| C3×#65533 | 2 |
| C3×#65529 | 2 |
| #10615857 | 3 |
| C3×#3027 | 5 |