Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
276 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5 | #857 |
| commutator, cosocle, hypocenter | #95⋊C3 | C22×C5 |
| Frattini | C23 | C2×C5×S4 |
| Fitting | C2×C5×#95 | D3 |
| socle | C24×C5 | S4 |
| prime radical | C2×C5×#95⋊C3 | C2 |
| LCS | G ▷ #95⋊C3 | |
| UCS | C1 ◁ C22×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#4621 | C2 | direct (N × H) |
| 6. C2×#4621 | C5 | direct (N × H) |
| 15. #4621 | C2×C5 | direct (N × H) |
| 152. C2×C5 | #4621 | direct (N × H) |
| 179. C5 | C2×#4621 | direct (N × H) |
| 199. C2 | C5×#4621 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#95⋊C3 | 2 |
| C5×#4621 | 2 |
| C2×C5×#328 | 3 |
| C2×C5×SL(2,ℤ/4) | 4 |
| C2×#4621 | 5 |