Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
616 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 100 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. #11751171 | C2 | semidirect |
| 3. #11747062 | C2 | semidirect |
| 4. #11746889 | C2 | semidirect |
| 5. C5×#4544 | C2 | semidirect |
| 6. #11745834 | C2 | semidirect |
| 7. #11745834 | C2 | semidirect |
| 12. #91758 | C22 | semidirect |
| 20. C4×C3⋊#168 | C22 | semidirect |
| 21. C5×C4⋊(C3⋊C8) | C22 | semidirect |
| 22. C5×C4⋊(C3⋊C8) | C22 | semidirect |
| 65. #4544 | D5 | semidirect |
| 110. C3×D20 | SD16 | semidirect |
| 132. C4⋊(C3⋊C8) | C2×D5 | semidirect |
| 133. C4⋊(C3⋊C8) | C2×D5 | semidirect |
| 237. D20 | #214 | semidirect |
| 348. C3×C5 | #1639 | semidirect |
| 412. C5 | #71908 | semidirect |
| 432. C3 | #10599185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66051 | 2 |
| #11751171 | 2 |
| #11747062 | 2 |
| #11746889 | 2 |
| C5×#4544 | 2 |
| #11745834 | 2 |
| #10599185 | 3 |
| #71908 | 5 |