Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1606 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 1606 conjugacy classes of subgroups — too many to draw. Only its 249 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | C5⋊S4 |
| commutator, cosocle, hypocenter | C5×SL(2,𝔽3) | C24 |
| Frattini | C2 | C23×C5⋊S4 |
| Fitting | C23×C5×Q8 | D3 |
| socle | C24×C5 | S4 |
| prime radical | C23×C5×SL(2,𝔽3) | C2 |
| LCS | G ▷ C5×SL(2,𝔽3) | |
| UCS | C1 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C5⋊#226 | C2 | direct (N × H) |
| 6. C2×C5⋊#226 | C22 | direct (N × H) |
| 16. C5⋊#226 | C23 | direct (N × H) |
| 60. C23×C5 | #226 | semidirect |
| 86. C22×C5 | C2×#226 | semidirect |
| 107. C2×C5 | C22×#226 | semidirect |
| 109. C23 | C5⋊#226 | direct (N × H) |
| 122. C5 | C23×#226 | semidirect |
| 123. C22 | C2×C5⋊#226 | direct (N × H) |
| 129. C2 | C22×C5⋊#226 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×SL(2,𝔽3) | 2 |
| C22×C5⋊#226 | 2 |
| C23×#689 | 3 |
| C23×Dic15 | 4 |
| C23×#226 | 5 |