Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
520 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 4. C5×#5388 | C2 | semidirect |
| 5. C4×C5×#226 | C2 | semidirect |
| 8. C5×#984 | C4 | direct (N × H) |
| 14. C4×#984 | C5 | direct (N × H) |
| 29. C5×#226 | C2×C4 | semidirect |
| 37. #5388 | C2×C5 | semidirect |
| 38. C4×#226 | C2×C5 | semidirect |
| 77. #984 | C4×C5 | direct (N × H) |
| 136. #226 | C2×C4×C5 | semidirect |
| 216. C4×C5 | #984 | direct (N × H) |
| 288. C5 | C4×#984 | direct (N × H) |
| 301. C4 | C5×#984 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#984 | 2 |
| C4×C5×#41⋊C3 | 2 |
| C5×#5426 | 2 |
| C5×#5388 | 2 |
| C4×C5×#226 | 2 |
| C4×C5×#137 | 3 |
| C4×C5×Dic6 | 4 |
| C4×#984 | 5 |