Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
440 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 440 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 |
|---|---|---|
| 1. #11756511 | C2 | semidirect |
| 2. C3×#65431 | C2 | semidirect |
| 3. #11747543 | C2 | semidirect |
| 4. C2×#90938 | C2 | semidirect |
| 5. C5×#4561 | C2 | semidirect |
| 6. #11745919 | C2 | semidirect |
| 7. #11745907 | C2 | semidirect |
| 18. C2×C3×D40 | C22 | semidirect |
| 19. C5×#812 | C22 | semidirect |
| 20. C2×C5×C3⋊C16 | C22 | semidirect |
| 22. C3×#3951 | C22 | semidirect |
| 28. #65431 | D3 | semidirect |
| 65. #4561 | D5 | semidirect |
| 77. C2×D40 | C2×D3 | semidirect |
| 81. #3951 | C2×D3 | semidirect |
| 124. #812 | C2×D5 | semidirect |
| 125. C2×C3⋊C16 | C2×D5 | semidirect |
| 307. C3×C5 | #2192 | semidirect |
| 355. C5 | #71094 | semidirect |
| 368. C3 | #10599919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756511 | 2 |
| C3×#65431 | 2 |
| #11747543 | 2 |
| C2×#90938 | 2 |
| C5×#4561 | 2 |
| #11745919 | 2 |
| #11745907 | 2 |
| #10599919 | 3 |
| #71094 | 5 |