Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
456 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 70 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. #11750816 | C2 | semidirect |
| 3. #11746909 | C2 | semidirect |
| 4. #11746893 | C2 | semidirect |
| 5. C5×#4464 | C2 | semidirect |
| 6. C3×#64684 | C2 | semidirect |
| 7. #11745848 | C2 | semidirect |
| 12. #91758 | C22 | semidirect |
| 21. C3×C5×#97 | C22 | semidirect |
| 22. C5×#803 | C22 | semidirect |
| 23. C3×#3935 | C22 | semidirect |
| 35. #64684 | D3 | semidirect |
| 71. #4464 | D5 | semidirect |
| 85. C5×#97 | C2×D3 | semidirect |
| 90. #3935 | C2×D3 | semidirect |
| 132. C3×#97 | C2×D5 | semidirect |
| 137. #803 | C2×D5 | semidirect |
| 266. #97 | D3×D5 | semidirect |
| 347. C3×C5 | #1659 | semidirect |
| 405. C5 | #68352 | semidirect |
| 424. C3 | #10599145 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752772 | 2 |
| #11750816 | 2 |
| #11746909 | 2 |
| #11746893 | 2 |
| C5×#4464 | 2 |
| C3×#64684 | 2 |
| #11745848 | 2 |
| #10599145 | 3 |
| #68352 | 5 |