Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
392 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 392 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, socle | C2×C3×C5 | #396 |
| commutator, Frattini, cosocle | C22×C4 | C23×C3×C5 |
| prime radical | C23×C3×C5 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C22×C3×C4×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C5×#2070 | C3 | direct (N × H) |
| 10. C3×#2070 | C5 | direct (N × H) |
| 32. #2070 | C3×C5 | direct (N × H) |
| 112. C3×C5 | #2070 | direct (N × H) |
| 130. C5 | C3×#2070 | direct (N × H) |
| 136. C3 | C5×#2070 | 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 |
| C2×C3×C5×#101 | 2 |
| C3×C5×#338 | 2 |
| C5×#2070 | 3 |
| C3×#2070 | 5 |