Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
496 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 496 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×#64994 | C2 | semidirect |
| 3. #11746870 | C2 | semidirect |
| 4. #11746285 | C2 | semidirect |
| 5. C5×#4464 | C2 | semidirect |
| 6. #11745848 | C2 | semidirect |
| 7. #11745847 | C2 | semidirect |
| 20. C3×C5×#97 | C22 | semidirect |
| 21. #91087 | C22 | semidirect |
| 22. C5×#803 | C22 | semidirect |
| 25. C3×#3935 | C22 | semidirect |
| 31. #64994 | D3 | semidirect |
| 71. #4464 | D5 | semidirect |
| 84. C5×#97 | C2×D3 | semidirect |
| 90. #3935 | C2×D3 | semidirect |
| 134. C3×#97 | C2×D5 | semidirect |
| 138. #803 | C2×D5 | semidirect |
| 269. #97 | D3×D5 | semidirect |
| 352. C3×C5 | #1533 | semidirect |
| 412. C5 | #70808 | semidirect |
| 432. C3 | #10599140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#875 | 2 |
| C3×#64994 | 2 |
| #11746870 | 2 |
| #11746285 | 2 |
| C5×#4464 | 2 |
| #11745848 | 2 |
| #11745847 | 2 |
| #10599140 | 3 |
| #70808 | 5 |