Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
540 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 111 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×#410 | C2 | semidirect |
| 3. #11751341 | C2 | semidirect |
| 4. #11746295 | C2 | semidirect |
| 7. C22×D60 | C4 | semidirect |
| 9. #91836 | C4 | semidirect |
| 16. #91815 | C4 | semidirect |
| 18. C3×C5×#99 | C22 | semidirect |
| 20. #91118 | C22 | semidirect |
| 23. C5×#410 | D3 | semidirect |
| 54. C3×#410 | D5 | semidirect |
| 69. C5×#99 | C2×D3 | semidirect |
| 113. C3×#99 | C2×D5 | semidirect |
| 145. #410 | D15 | semidirect |
| 235. #99 | C2×D15 | semidirect |
| 316. C3×C5 | #2128 | semidirect |
| 376. C5 | #70061 | semidirect |
| 396. C3 | #10600854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756589 | 2 |
| C3×C5×#410 | 2 |
| #11751341 | 2 |
| #11746295 | 2 |
| #10600854 | 3 |
| #70061 | 5 |