Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
444 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C3×C4×C5 | #127 |
| commutator, Frattini, cosocle | C22×C4 | C23×C3×C5 |
| socle | C2×C3×C5 | #399 |
| prime radical | C24×C3×C5 | Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C4×C5 ◁ C22×C3×C4×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×#430 | C2 | semidirect |
| 3. C3×C5×#338 | C2 | semidirect |
| 4. C5×#2091 | C3 | direct (N × H) |
| 10. C3×#2091 | C5 | direct (N × H) |
| 11. C5×#430 | C2×C3 | semidirect |
| 13. C5×#338 | C2×C3 | semidirect |
| 23. C3×#430 | C2×C5 | semidirect |
| 25. C3×#338 | C2×C5 | semidirect |
| 31. #2091 | C3×C5 | direct (N × H) |
| 56. #430 | C2×C3×C5 | semidirect |
| 58. #338 | C2×C3×C5 | semidirect |
| 121. C3×C5 | #2091 | direct (N × H) |
| 146. C5 | C3×#2091 | direct (N × H) |
| 155. C3 | C5×#2091 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#430 | 2 |
| C3×C5×#407 | 2 |
| C3×C5×#338 | 2 |
| C5×#2091 | 3 |
| C3×#2091 | 5 |