Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
176 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 176 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 |
|---|---|---|
| 7. #73037 | C5 | direct (N × H) |
| 51. C5×A4 | Q32 | semidirect |
| 82. C22×C5 | Dic24 | semidirect |
| 99. A4 | C5×Q32 | semidirect |
| 115. C5 | #73037 | direct (N × H) |
| 118. C22 | C5×Dic24 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5398 | 2 |
| C5×A4×C16 | 2 |
| C5×#2216 | 3 |
| C5×Dic24 | 4 |
| #73037 | 5 |