Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
628 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 124 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×#5409 | C2 | semidirect |
| 3. C2×C5×A4⋊C8 | C2 | semidirect |
| 11. #85511 | C5 | direct (N × H) |
| 26. #5409 | C2×C5 | semidirect |
| 27. C2×A4⋊C8 | C2×C5 | semidirect |
| 101. C5×A4 | #131 | semidirect |
| 171. C22×C5 | #948 | semidirect |
| 210. A4 | C5×#131 | semidirect |
| 245. C5 | #85511 | direct (N × H) |
| 253. C22 | C5×#948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×A4×#41 | 2 |
| C5×#5409 | 2 |
| C2×C5×A4⋊C8 | 2 |
| C5×#2880 | 3 |
| C5×#948 | 4 |
| #85511 | 5 |