Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
380 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 124 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. #11746750 | C2 | semidirect |
| 4. C3×C8×#170 | C2 | semidirect |
| 5. #11746487 | C2 | semidirect |
| 23. C8×#170 | D3 | semidirect |
| 181. C3×C5 | #1453 | semidirect |
| 210. C5 | #68048 | semidirect |
| 219. C3 | #10604736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751795 | 2 |
| Dic5×ΓL(1,𝔽25) | 2 |
| #11746750 | 2 |
| C3×C8×#170 | 2 |
| #11746487 | 2 |
| #10604736 | 3 |
| #68048 | 5 |