Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
520 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 98 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. C2×#91082 | C2 | semidirect |
| 3. #11747690 | C2 | semidirect |
| 4. C5×#4509 | C2 | semidirect |
| 5. C3×#64729 | C2 | semidirect |
| 6. #11745893 | C2 | semidirect |
| 7. #11745891 | C2 | semidirect |
| 16. #91256 | C4 | semidirect |
| 17. C2×C3×C5×C16 | C22 | semidirect |
| 18. C2×C3⋊#672 | C22 | semidirect |
| 20. C5×#818 | C22 | semidirect |
| 21. C3×#3950 | C22 | semidirect |
| 29. #64729 | D3 | semidirect |
| 58. #4509 | D5 | semidirect |
| 68. C2×C5×C16 | C2×D3 | semidirect |
| 70. #3950 | C2×D3 | semidirect |
| 103. C2×C3×C16 | C2×D5 | semidirect |
| 105. #818 | C2×D5 | semidirect |
| 206. C2×C16 | D3×D5 | semidirect |
| 274. C3×C5 | #2140 | semidirect |
| 323. C5 | #69190 | semidirect |
| 340. C3 | #10599983 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91256 | 2 |
| C2×#91082 | 2 |
| #11747690 | 2 |
| C5×#4509 | 2 |
| C3×#64729 | 2 |
| #11745893 | 2 |
| #11745891 | 2 |
| #10599983 | 3 |
| #69190 | 5 |