Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 80 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. C5×#5143 | C2 | semidirect |
| 3. #11747562 | C2 | semidirect |
| 4. C2×#90945 | C2 | semidirect |
| 5. C3×#64781 | C2 | semidirect |
| 6. #11745920 | C2 | semidirect |
| 7. #11745908 | C2 | semidirect |
| 18. C2×C5×Dic12 | C22 | semidirect |
| 20. C5×#819 | C22 | semidirect |
| 21. C3×#3944 | C22 | semidirect |
| 22. C2×C3×#672 | C22 | semidirect |
| 31. #64781 | D3 | semidirect |
| 62. #5143 | D5 | semidirect |
| 83. #3944 | C2×D3 | semidirect |
| 84. C2×#672 | C2×D3 | semidirect |
| 114. C2×Dic12 | C2×D5 | semidirect |
| 122. #819 | C2×D5 | semidirect |
| 304. C3×C5 | #2194 | semidirect |
| 349. C5 | #69128 | semidirect |
| 361. C3 | #10601891 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756511 | 2 |
| C5×#5143 | 2 |
| #11747562 | 2 |
| C2×#90945 | 2 |
| C3×#64781 | 2 |
| #11745920 | 2 |
| #11745908 | 2 |
| #10601891 | 3 |
| #69128 | 5 |