Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
440 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 440 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 | C22×C3×C5 | #127 |
| commutator, Frattini, cosocle | C42 | C23×C3×C5 |
| prime radical | C3×C5×#493 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×#498 | C2 | semidirect |
| 3. C3×C5×#492 | C2 | semidirect |
| 4. C3×C5×#486 | C2 | semidirect |
| 5. C3×C5×#322 | C2 | semidirect |
| 6. C5×#1715 | C3 | direct (N × H) |
| 16. C3×#1715 | C5 | direct (N × H) |
| 17. C5×#498 | C2×C3 | semidirect |
| 19. C5×#492 | C2×C3 | semidirect |
| 20. C5×#486 | C2×C3 | semidirect |
| 21. C5×#322 | C2×C3 | semidirect |
| 34. C3×#498 | C2×C5 | semidirect |
| 36. C3×#492 | C2×C5 | semidirect |
| 37. C3×#486 | C2×C5 | semidirect |
| 38. C3×#322 | C2×C5 | semidirect |
| 48. #1715 | C3×C5 | direct (N × H) |
| 60. C3×C5×C8 | SD16 | semidirect |
| 82. #498 | C2×C3×C5 | semidirect |
| 84. #492 | C2×C3×C5 | semidirect |
| 85. #486 | C2×C3×C5 | semidirect |
| 86. #322 | C2×C3×C5 | semidirect |
| 118. C5×C8 | C3×SD16 | semidirect |
| 143. C3×C8 | C5×SD16 | semidirect |
| 164. C3×C5 | #1715 | direct (N × H) |
| 188. C8 | C3×C5×SD16 | semidirect |
| 193. C5 | C3×#1715 | direct (N × H) |
| 202. C3 | C5×#1715 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#498 | 2 |
| C3×C5×#493 | 2 |
| C3×C5×#492 | 2 |
| C3×C5×#486 | 2 |
| C3×C5×#322 | 2 |
| C5×#1715 | 3 |
| C3×#1715 | 5 |