Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
256 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 256 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. #11746284 | C2 | semidirect |
| 3. C3×#64683 | C2 | semidirect |
| 5. #11745877 | C2 | semidirect |
| 21. #64683 | D3 | semidirect |
| 174. C3×C5 | #2165 | semidirect |
| 202. C5 | #69298 | semidirect |
| 211. C3 | #10600657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×ΓL(1,𝔽25) | 2 |
| #11746284 | 2 |
| C3×#64683 | 2 |
| #11745883 | 2 |
| #11745877 | 2 |
| #10600657 | 3 |
| #69298 | 5 |