Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
216 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 216 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 | #124 | C22×C3×C5 |
| prime radical | C3×C5×#496 | C2 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C22×C3×C5 ◁ C2×C3×C4×C5 ◁ C3×C5×#124 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C5×#355 | C2 | semidirect |
| 3. C3×C5×#354 | C2 | semidirect |
| 4. C5×#1406 | C3 | direct (N × H) |
| 7. C3×C5×#127 | C4 | semidirect |
| 11. C3×C5×#97 | C4 | semidirect |
| 12. C3×#1406 | C5 | direct (N × H) |
| 14. C5×#355 | C2×C3 | semidirect |
| 15. C5×#354 | C2×C3 | semidirect |
| 28. C3×#355 | C2×C5 | semidirect |
| 29. C3×#354 | C2×C5 | semidirect |
| 32. C5×#127 | C3×C4 | semidirect |
| 36. C5×#97 | C3×C4 | semidirect |
| 37. #1406 | C3×C5 | direct (N × H) |
| 53. C3×#127 | C4×C5 | semidirect |
| 57. C3×#97 | C4×C5 | semidirect |
| 70. #355 | C2×C3×C5 | semidirect |
| 71. #354 | C2×C3×C5 | semidirect |
| 107. #127 | C3×C4×C5 | semidirect |
| 111. #97 | C3×C4×C5 | semidirect |
| 149. C3×C5 | #1406 | direct (N × H) |
| 180. C5 | C3×#1406 | direct (N × H) |
| 190. C3 | C5×#1406 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#496 | 2 |
| C3×C5×#355 | 2 |
| C3×C5×#354 | 2 |
| C5×#1406 | 3 |
| C3×#1406 | 5 |