Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
190 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 36 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 |
|---|---|---|
| 9. #73136 | C5 | direct (N × H) |
| 75. C5×A4 | Q32 | semidirect |
| 121. C22×C5 | #829 | semidirect |
| 148. A4 | C5×Q32 | semidirect |
| 171. C5 | #73136 | direct (N × H) |
| 174. C22 | C5×#829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×A4×Q16 | 2 |
| C5×#5398 | 2 |
| C5×A4⋊C16 | 2 |
| C5×#2188 | 3 |
| C5×#829 | 4 |
| #73136 | 5 |