Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
664 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 170 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×#4926 | C2 | semidirect |
| 3. C5×#4544 | C2 | semidirect |
| 12. C5×C4⋊(C3⋊C8) | C22 | semidirect |
| 14. #71760 | C5 | direct (N × H) |
| 32. #4926 | C2×C5 | semidirect |
| 33. #4544 | C2×C5 | semidirect |
| 66. C4⋊(C3⋊C8) | C22×C5 | semidirect |
| 173. C3×C5 | #1555 | semidirect |
| 207. C5 | #71760 | direct (N × H) |
| 218. C3 | C5×#1555 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×#127 | 2 |
| C5×#4926 | 2 |
| C5×#4544 | 2 |
| C5×#1555 | 3 |
| #71760 | 5 |