Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 122 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. C2×C5×#829 | C2 | semidirect |
| 4. C5×#4564 | C2 | semidirect |
| 18. #72064 | C5 | direct (N × H) |
| 43. C2×#829 | C2×C5 | semidirect |
| 45. #4564 | C2×C5 | semidirect |
| 111. C22×C3×C5 | Q32 | semidirect |
| 186. C22×C5 | #829 | semidirect |
| 212. C3×C5 | #2188 | semidirect |
| 215. C22×C3 | C5×Q32 | semidirect |
| 247. C5 | #72064 | direct (N × H) |
| 250. C22 | C5×#829 | semidirect |
| 258. C3 | C5×#2188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×Q16 | 2 |
| C2×C5×#829 | 2 |
| C5×#5116 | 2 |
| C5×#4564 | 2 |
| C5×#4549 | 2 |
| C5×#2188 | 3 |
| #72064 | 5 |