Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 94 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×#510 | C2 | semidirect |
| 3. C3×#65478 | C2 | semidirect |
| 4. C3×#65468 | C2 | semidirect |
| 5. C3×#64786 | C2 | semidirect |
| 6. C3×#64738 | C2 | semidirect |
| 7. C3×#64734 | C2 | semidirect |
| 8. #10602315 | C3 | direct (N × H) |
| 11. C2×C3×C5×Q16 | C22 | semidirect |
| 22. C3×C5×M32 | C22 | semidirect |
| 26. C3×#3949 | C22 | semidirect |
| 27. C3×#3944 | C22 | semidirect |
| 30. C5×#510 | C2×C3 | semidirect |
| 31. #65478 | C2×C3 | semidirect |
| 32. #65468 | C2×C3 | semidirect |
| 33. #64786 | C2×C3 | semidirect |
| 34. #64738 | C2×C3 | semidirect |
| 35. #64734 | C2×C3 | semidirect |
| 71. C3×#510 | D5 | semidirect |
| 78. C2×C5×Q16 | C22×C3 | semidirect |
| 89. C5×M32 | C22×C3 | semidirect |
| 93. #3949 | C22×C3 | semidirect |
| 94. #3944 | C22×C3 | semidirect |
| 132. C2×C3×Q16 | C2×D5 | semidirect |
| 140. C3×M32 | C2×D5 | semidirect |
| 178. #510 | C3×D5 | semidirect |
| 265. C2×Q16 | C2×C3×D5 | semidirect |
| 273. M32 | C2×C3×D5 | semidirect |
| 355. C3×C5 | #2191 | semidirect |
| 407. C5 | C3×#2191 | semidirect |
| 421. C3 | #10602315 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66102 | 2 |
| C3×C5×#510 | 2 |
| C3×#65478 | 2 |
| C3×#65468 | 2 |
| C3×#64786 | 2 |
| C3×#64738 | 2 |
| C3×#64734 | 2 |
| #10602315 | 3 |
| C3×#2191 | 5 |