Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
456 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 72 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×#5055 | C2 | semidirect |
| 3. #11747097 | C2 | semidirect |
| 4. #11746914 | C2 | semidirect |
| 5. C3×#64760 | C2 | semidirect |
| 6. #11745848 | C2 | semidirect |
| 7. #11745848 | C2 | semidirect |
| 18. C5×#869 | C22 | semidirect |
| 23. C5×#803 | C22 | semidirect |
| 24. C3×#3935 | C22 | semidirect |
| 25. C3×#3935 | C22 | semidirect |
| 33. #64760 | D3 | semidirect |
| 66. #5055 | D5 | semidirect |
| 89. #3935 | C2×D3 | semidirect |
| 90. #3935 | C2×D3 | semidirect |
| 130. #869 | C2×D5 | semidirect |
| 137. #803 | C2×D5 | semidirect |
| 347. C3×C5 | #1659 | semidirect |
| 405. C5 | #68352 | semidirect |
| 424. C3 | #10602037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756442 | 2 |
| C5×#5055 | 2 |
| #11747097 | 2 |
| #11746914 | 2 |
| C3×#64760 | 2 |
| #11745848 | 2 |
| #10602037 | 3 |
| #68352 | 5 |