Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
584 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 132 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. C22×C5×#125 | C3 | semidirect |
| 9. A4×#125 | C5 | direct (N × H) |
| 36. C5×#125 | A4 | direct (N × H) |
| 46. C22×#125 | C3×C5 | semidirect |
| 89. C5×A4 | #125 | direct (N × H) |
| 132. #125 | C5×A4 | direct (N × H) |
| 156. C22×C5 | C3×#125 | semidirect |
| 191. A4 | C5×#125 | direct (N × H) |
| 225. C5 | A4×#125 | direct (N × H) |
| 233. C22 | C3×C5×#125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×A4×C4⋊C4 | 2 |
| C42×C5×A4 | 2 |
| C22×C5×#125 | 3 |
| C3×C5×#125 | 4 |
| A4×#125 | 5 |