Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
312 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 312 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 |
|---|---|---|
| 4. C5×#4505 | C2 | semidirect |
| 5. C3×#64724 | C2 | semidirect |
| 6. #11745943 | C2 | semidirect |
| 7. #11745940 | C2 | semidirect |
| 14. #91082 | C4 | semidirect |
| 26. #64724 | D3 | semidirect |
| 42. C3×C5×C16 | C2×C4 | semidirect |
| 43. C3⋊#672 | C2×C4 | semidirect |
| 48. #4505 | D5 | semidirect |
| 102. C5×C16 | C4×D3 | semidirect |
| 135. C3×C16 | C4×D5 | semidirect |
| 204. C16 | #1200 | semidirect |
| 205. C3×C5 | #2159 | semidirect |
| 238. C5 | #69326 | semidirect |
| 250. C3 | #10600139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91082 | 2 |
| #11747690 | 2 |
| #11747636 | 2 |
| C5×#4505 | 2 |
| C3×#64724 | 2 |
| #11745943 | 2 |
| #11745940 | 2 |
| #10600139 | 3 |
| #69326 | 5 |