Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
108 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C4 | A4×AGL(1,𝔽5) |
| commutator, hypocenter | C5×Q8 | C3×C16 |
| Fitting | C4×C5×Q8 | C3×C4 |
| socle | C22×C5 | C8×A4 |
| prime radical | C2×C5×SL(2,𝔽3) | C8 |
| cosocle | Q8×#168 | C2×C3 |
| LCS | G ▷ C5×Q8 | |
| UCS | C1 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q8×#674 | C3 | semidirect |
| 20. C5×SL(2,𝔽3) | C16 | semidirect |
| 31. #674 | SL(2,𝔽3) | direct (N × H) |
| 42. C5×Q8 | C3×C16 | semidirect |
| 58. SL(2,𝔽3) | #674 | direct (N × H) |
| 82. Q8 | C3×#674 | semidirect |
| 92. C5 | C16×SL(2,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| SL(2,𝔽3)×#168 | 2 |
| Q8×#674 | 3 |
| C2×C3×#674 | 4 |
| C16×SL(2,𝔽3) | 5 |