Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1792 conjugacy classes of subgroups; only the 601 normal subgroups are shown.
This group has 1792 conjugacy classes of subgroups — too many to draw. Only its 601 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D15 |
| commutator, socle, cosocle | C22×C3×C5 | C25 |
| Fitting | C3×C5×#564 | C2 |
| prime radical | C22×D15 | C24 |
| hypercenter | #564 | D15 |
| hypocenter | C3×C5 | C2×#564 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ #564 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×#564 | C2 | semidirect |
| 3. #11756445 | C2 | semidirect |
| 12. C5×#564 | D3 | semidirect |
| 21. C3×#564 | D5 | semidirect |
| 48. #564 | D15 | direct (N × H) |
| 71. D15 | #564 | direct (N × H) |
| 86. C3×C5 | C2×#564 | semidirect |
| 99. C5 | D3×#564 | semidirect |
| 104. C3 | D5×#564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#564 | 2 |
| D15×#125 | 2 |
| #11756445 | 2 |
| D5×#564 | 3 |
| D3×#564 | 5 |