Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
326 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 24. A4⋊Dic5 | C8 | semidirect |
| 102. C5×A4 | C4⋊C8 | semidirect |
| 186. C22×C5 | Dic3⋊C8 | semidirect |
| 229. A4 | #4004 | semidirect |
| 276. C5 | SL(2,ℤ/4)⋊C8 | semidirect |
| 287. C22 | #91177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×A4×#170 | 2 |
| C2×A4⋊#170 | 2 |
| Dic5×SL(2,ℤ/4) | 2 |
| #10604230 | 3 |
| #91177 | 4 |
| SL(2,ℤ/4)⋊C8 | 5 |