Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
392 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 392 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 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C3×C5 |
| prime radical | C3×C5×#493 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ C3×C4×C5×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C5×SD32 | C2 | semidirect |
| 2. C3×C5×#494 | C2 | semidirect |
| 4. C3×C4×C5×C16 | C2 | semidirect |
| 5. C5×#2248 | C3 | direct (N × H) |
| 15. C3×#2248 | C5 | direct (N × H) |
| 16. C2×C5×SD32 | C2×C3 | semidirect |
| 17. C5×#494 | C2×C3 | semidirect |
| 19. C4×C5×C16 | C2×C3 | semidirect |
| 31. C3×C5×C16 | D4 | semidirect |
| 32. C2×C3×SD32 | C2×C5 | semidirect |
| 33. C3×#494 | C2×C5 | semidirect |
| 35. C3×C4×C16 | C2×C5 | semidirect |
| 45. #2248 | C3×C5 | direct (N × H) |
| 77. C5×C16 | C3×D4 | semidirect |
| 78. C2×SD32 | C2×C3×C5 | semidirect |
| 79. #494 | C2×C3×C5 | semidirect |
| 81. C4×C16 | C2×C3×C5 | semidirect |
| 86. C3×C4×C5 | SD32 | semidirect |
| 100. C3×C16 | C5×D4 | semidirect |
| 139. C4×C5 | C3×SD32 | semidirect |
| 153. C16 | C3×C5×D4 | semidirect |
| 154. C3×C5 | #2248 | direct (N × H) |
| 159. C3×C4 | C5×SD32 | semidirect |
| 179. C5 | C3×#2248 | direct (N × H) |
| 184. C4 | C3×C5×SD32 | semidirect |
| 187. C3 | C5×#2248 | 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×SD32 | 2 |
| C3×C5×#494 | 2 |
| C3×C5×#493 | 2 |
| C3×C4×C5×C16 | 2 |
| C5×#2248 | 3 |
| C3×#2248 | 5 |