Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
240 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 50 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×#4545 | C2 | semidirect |
| 5. C3×C5×#127 | C4 | semidirect |
| 7. C3×C4×C5×C8 | C4 | semidirect |
| 9. #67792 | C5 | direct (N × H) |
| 21. #4545 | C2×C5 | semidirect |
| 23. C5×#127 | Dic3 | semidirect |
| 26. C4×C5×C8 | Dic3 | semidirect |
| 39. C3×#127 | C4×C5 | semidirect |
| 41. C3×C4×C8 | C4×C5 | semidirect |
| 80. #127 | C5×Dic3 | semidirect |
| 83. C4×C8 | C5×Dic3 | semidirect |
| 114. C3×C5 | #1408 | semidirect |
| 141. C5 | #67792 | direct (N × H) |
| 150. C3 | C5×#1408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#493 | 2 |
| C5×#4545 | 2 |
| C5×#1408 | 3 |
| #67792 | 5 |