Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
164 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | D16 |
| commutator | C16 | C2×C3×C4×C5 |
| Frattini, cosocle | C2×C16 | C22×C3×C5 |
| prime radical | C2×C3×C5×D16 | C2 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C2×C3×C4×C5 ◁ C2×C3×C5×C8 ◁ C2×C3×C5×C16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×C5×C32 | C2 | semidirect |
| 3. C3×C5×#366 | C2 | semidirect |
| 4. C5×#1415 | C3 | direct (N × H) |
| 7. C3×C5×D16 | C4 | semidirect |
| 11. C3×#1415 | C5 | direct (N × H) |
| 13. C2×C5×C32 | C2×C3 | semidirect |
| 14. C5×#366 | C2×C3 | semidirect |
| 23. C2×C3×C32 | C2×C5 | semidirect |
| 24. C3×#366 | C2×C5 | semidirect |
| 27. C5×D16 | C3×C4 | semidirect |
| 31. #1415 | C3×C5 | direct (N × H) |
| 41. C3×D16 | C4×C5 | semidirect |
| 53. C2×C32 | C2×C3×C5 | semidirect |
| 54. #366 | C2×C3×C5 | semidirect |
| 78. D16 | C3×C4×C5 | semidirect |
| 107. C3×C5 | #1415 | direct (N × H) |
| 130. C5 | C3×#1415 | direct (N × H) |
| 138. C3 | C5×#1415 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×D16 | 2 |
| C2×C3×C5×C32 | 2 |
| C3×C5×#366 | 2 |
| C5×#1415 | 3 |
| C3×#1415 | 5 |