Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
500 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 96 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×#5070 | C2 | semidirect |
| 3. #11747094 | C2 | semidirect |
| 4. #11746886 | C2 | semidirect |
| 5. #11746365 | C2 | semidirect |
| 6. #11745841 | C2 | semidirect |
| 7. #11745835 | C2 | semidirect |
| 60. #5070 | D5 | semidirect |
| 321. C3×C5 | #1641 | semidirect |
| 376. C5 | #71920 | semidirect |
| 393. C3 | #10602000 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66052 | 2 |
| C5×#5070 | 2 |
| #11747094 | 2 |
| #11746886 | 2 |
| #11746365 | 2 |
| #11745841 | 2 |
| #11745835 | 2 |
| #10602000 | 3 |
| #71920 | 5 |