Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
204 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 204 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 |
|---|---|---|
| 1. C5×#5402 | C2 | semidirect |
| 2. C5×A4×C16 | C2 | semidirect |
| 7. #73035 | C5 | direct (N × H) |
| 9. C22×C5×C16 | D3 | semidirect |
| 17. #5402 | C2×C5 | semidirect |
| 18. A4×C16 | C2×C5 | semidirect |
| 46. C5×C16 | S4 | semidirect |
| 48. C22×C16 | C5×D3 | semidirect |
| 53. C5×A4 | D16 | semidirect |
| 90. C22×C5 | D48 | semidirect |
| 104. C16 | C5×S4 | semidirect |
| 107. A4 | C5×D16 | semidirect |
| 126. C5 | #73035 | direct (N × H) |
| 132. C22 | C5×D48 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5402 | 2 |
| C5×A4×C16 | 2 |
| C5×#2215 | 3 |
| C5×D48 | 4 |
| #73035 | 5 |