Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
380 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 380 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×#127 | C22 |
| 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×#487 | C2 | semidirect |
| 5. C3×C5×C82 | C2 | semidirect |
| 6. C5×#1708 | C3 | direct (N × H) |
| 16. C3×#1708 | C5 | direct (N × H) |
| 17. C5×#498 | C2×C3 | semidirect |
| 19. C5×#487 | C2×C3 | semidirect |
| 21. C5×C82 | C2×C3 | semidirect |
| 33. C3×#498 | C2×C5 | semidirect |
| 35. C3×#487 | C2×C5 | semidirect |
| 37. C3×C82 | C2×C5 | semidirect |
| 47. #1708 | C3×C5 | direct (N × H) |
| 79. #498 | C2×C3×C5 | semidirect |
| 81. #487 | C2×C3×C5 | semidirect |
| 83. C82 | C2×C3×C5 | semidirect |
| 154. C3×C5 | #1708 | direct (N × H) |
| 179. C5 | C3×#1708 | direct (N × H) |
| 187. C3 | C5×#1708 | 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×#492 | 2 |
| C3×C5×#487 | 2 |
| C3×C5×#486 | 2 |
| C3×C5×C82 | 2 |
| C5×#1708 | 3 |
| C3×#1708 | 5 |