Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
540 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 96 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. #11749173 | C2 | semidirect |
| 3. #11746366 | C2 | semidirect |
| 4. C3×#64765 | C2 | semidirect |
| 5. #11746007 | C2 | semidirect |
| 8. C2×C5×D3×D4 | C4 | semidirect |
| 13. C5×#936 | C4 | semidirect |
| 14. C5×#875 | C4 | semidirect |
| 15. C5×#872 | C4 | semidirect |
| 17. #91118 | C22 | semidirect |
| 18. C3×#3966 | C22 | semidirect |
| 25. #64765 | D3 | semidirect |
| 66. #3966 | C2×D3 | semidirect |
| 93. C2×D3×D4 | Dic5 | semidirect |
| 98. #936 | Dic5 | semidirect |
| 100. #875 | Dic5 | semidirect |
| 101. #872 | Dic5 | semidirect |
| 280. C3×C5 | #2128 | semidirect |
| 334. C5 | #69152 | semidirect |
| 352. C3 | #10602654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5715 | 2 |
| #11749173 | 2 |
| #11746366 | 2 |
| C3×#64765 | 2 |
| #11746007 | 2 |
| #10602654 | 3 |
| #69152 | 5 |