Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
256 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 3. C5×#4511 | C2 | semidirect |
| 4. C3×#64732 | C2 | semidirect |
| 5. #11745932 | C2 | semidirect |
| 7. #11745876 | C2 | semidirect |
| 26. #64732 | D3 | semidirect |
| 49. #4511 | D5 | semidirect |
| 198. C3×C5 | #2165 | semidirect |
| 226. C5 | #69088 | semidirect |
| 235. C3 | #10600091 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11747599 | 2 |
| #11746335 | 2 |
| C5×#4511 | 2 |
| C3×#64732 | 2 |
| #11745932 | 2 |
| #11745884 | 2 |
| #11745876 | 2 |
| #10600091 | 3 |
| #69088 | 5 |