Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
240 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 56 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 | #353 |
| commutator | C42 | C2×C3×C4×C5 |
| Frattini, cosocle | #127 | C22×C3×C5 |
| prime radical | C3×C5×#493 | C2 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C22×C3×C5 ◁ C2×C3×C4×C5 ◁ C3×C5×#127 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C5×#353 | C2 | semidirect |
| 3. C5×#1408 | C3 | direct (N × H) |
| 5. C3×C5×#127 | C4 | semidirect |
| 8. C3×C4×C5×C8 | C4 | semidirect |
| 9. C3×#1408 | C5 | direct (N × H) |
| 11. C5×#353 | C2×C3 | semidirect |
| 21. C3×#353 | C2×C5 | semidirect |
| 23. C5×#127 | C3×C4 | semidirect |
| 26. C4×C5×C8 | C3×C4 | semidirect |
| 27. #1408 | C3×C5 | direct (N × H) |
| 39. C3×#127 | C4×C5 | semidirect |
| 42. C3×C4×C8 | C4×C5 | semidirect |
| 52. #353 | C2×C3×C5 | semidirect |
| 80. #127 | C3×C4×C5 | semidirect |
| 83. C4×C8 | C3×C4×C5 | semidirect |
| 114. C3×C5 | #1408 | direct (N × H) |
| 141. C5 | C3×#1408 | direct (N × H) |
| 150. C3 | C5×#1408 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#493 | 2 |
| C3×C5×#353 | 2 |
| C5×#1408 | 3 |
| C3×#1408 | 5 |