Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 432 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.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C5 | C22⋊A4 |
| commutator, cosocle, hypocenter | #543 | C2×C3×C5 |
| Frattini | C22 | C2×C5×C22⋊A4 |
| Fitting | C5×#3458 | C3 |
| socle | C22×C5 | C2×C22⋊A4 |
| prime radical | C5×#543⋊C3 | C2 |
| LCS | G ▷ #543 | |
| UCS | C1 ◁ C2×C4×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#3458 | C3 | semidirect |
| 5. #3458⋊C3 | C5 | direct (N × H) |
| 23. C4×C5×Q8 | A4 | semidirect |
| 30. #3458 | C3×C5 | semidirect |
| 45. C22×C4×C5 | SL(2,𝔽3) | semidirect |
| 89. C4×Q8 | C5×A4 | semidirect |
| 120. C22×C4 | C5×SL(2,𝔽3) | semidirect |
| 155. C5 | #3458⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#543⋊C3 | 2 |
| C5×#3458 | 3 |
| C2×C4×C5×A4 | 4 |
| C4×C5×SL(2,𝔽3) | 4 |
| #3458⋊C3 | 5 |