Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
492 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 130 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 |
|---|---|---|
| 5. C2×C3×C5×M16 | C4 | semidirect |
| 9. C5×C3⋊#95 | C4 | semidirect |
| 10. #67683 | C5 | direct (N × H) |
| 27. C2×C5×M16 | Dic3 | semidirect |
| 49. C2×C3×M16 | C4×C5 | semidirect |
| 53. C3⋊#95 | C4×C5 | semidirect |
| 105. C2×M16 | C5×Dic3 | semidirect |
| 151. C3×C5 | #1297 | semidirect |
| 186. C5 | #67683 | direct (N × H) |
| 198. C3 | C5×#1297 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#407 | 2 |
| C4×C5×#217 | 2 |
| C5×#1297 | 3 |
| #67683 | 5 |