Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
720 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 196 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. C5×#5753 | C2 | semidirect |
| 2. C3×#66086 | C2 | semidirect |
| 3. #11751241 | C2 | semidirect |
| 4. #11747550 | C2 | semidirect |
| 5. C2×#90940 | C2 | semidirect |
| 6. #11747539 | C2 | semidirect |
| 7. #11747538 | C2 | semidirect |
| 13. C2×C5×Dic12 | C22 | semidirect |
| 14. C5×#904 | C22 | semidirect |
| 18. #91096 | C22 | semidirect |
| 19. C2×C3⋊#672 | C22 | semidirect |
| 20. #90946 | C22 | semidirect |
| 21. #90941 | C22 | semidirect |
| 22. #90940 | C22 | semidirect |
| 23. #90940 | C22 | semidirect |
| 24. #90937 | C22 | semidirect |
| 27. #66086 | D3 | semidirect |
| 55. #5753 | D5 | semidirect |
| 102. C2×Dic12 | C2×D5 | semidirect |
| 103. #904 | C2×D5 | semidirect |
| 251. C3×C5 | #3416 | semidirect |
| 285. C5 | #84008 | semidirect |
| 294. C3 | #10615747 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5753 | 2 |
| C3×#66086 | 2 |
| #11751241 | 2 |
| #11747550 | 2 |
| C2×#90940 | 2 |
| #11747539 | 2 |
| #11747538 | 2 |
| #10615747 | 3 |
| #84008 | 5 |