Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 74 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×#65185 | C2 | semidirect |
| 3. #11747560 | C2 | semidirect |
| 4. C2×#90941 | C2 | semidirect |
| 5. #11746318 | C2 | semidirect |
| 6. C5×#4495 | C2 | semidirect |
| 7. #11745885 | C2 | semidirect |
| 13. C2×C3×Dic20 | C22 | semidirect |
| 19. C3×C5×#108 | C22 | semidirect |
| 20. C2×C3⋊#672 | C22 | semidirect |
| 21. C5×#812 | C22 | semidirect |
| 30. #65185 | D3 | semidirect |
| 67. #4495 | D5 | semidirect |
| 75. C2×Dic20 | C2×D3 | semidirect |
| 79. C5×#108 | C2×D3 | semidirect |
| 119. C3×#108 | C2×D5 | semidirect |
| 124. #812 | C2×D5 | semidirect |
| 236. #108 | D3×D5 | semidirect |
| 304. C3×C5 | #2194 | semidirect |
| 349. C5 | #71098 | semidirect |
| 361. C3 | #10600052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11753961 | 2 |
| C3×#65185 | 2 |
| #11747560 | 2 |
| C2×#90941 | 2 |
| #11746318 | 2 |
| C5×#4495 | 2 |
| #11745885 | 2 |
| #10600052 | 3 |
| #71098 | 5 |