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 |
|---|---|---|
| 2. C5×#5398 | C2 | semidirect |
| 3. C5×A4×C16 | C2 | semidirect |
| 9. #73036 | C5 | direct (N × H) |
| 11. C22×C5×C16 | D3 | semidirect |
| 24. #5398 | C2×C5 | semidirect |
| 25. A4×C16 | C2×C5 | semidirect |
| 65. C5×C16 | S4 | semidirect |
| 67. C22×C16 | C5×D3 | semidirect |
| 74. C5×A4 | SD32 | semidirect |
| 123. C22×C5 | #800 | semidirect |
| 145. C16 | C5×S4 | semidirect |
| 148. A4 | C5×SD32 | semidirect |
| 172. C5 | #73036 | direct (N × H) |
| 178. C22 | C5×#800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5402 | 2 |
| C5×#5398 | 2 |
| C5×A4×C16 | 2 |
| C5×#2217 | 3 |
| C5×#800 | 4 |
| #73036 | 5 |