Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
224 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 224 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×A4×D8 | C2 | semidirect |
| 2. C5×#5402 | C2 | semidirect |
| 3. C5×A4⋊C16 | C2 | semidirect |
| 9. #73133 | C5 | direct (N × H) |
| 10. C22×C5×D8 | D3 | semidirect |
| 23. A4×D8 | C2×C5 | semidirect |
| 24. #5402 | C2×C5 | semidirect |
| 25. A4⋊C16 | C2×C5 | semidirect |
| 63. C5×D8 | S4 | semidirect |
| 70. C22×D8 | C5×D3 | semidirect |
| 79. C5×A4 | D16 | semidirect |
| 140. C22×C5 | #826 | semidirect |
| 156. D8 | C5×S4 | semidirect |
| 166. A4 | C5×D16 | semidirect |
| 196. C5 | #73133 | direct (N × H) |
| 208. C22 | C5×#826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×A4×D8 | 2 |
| C5×#5402 | 2 |
| C5×A4⋊C16 | 2 |
| C5×#2184 | 3 |
| C5×#826 | 4 |
| #73133 | 5 |