Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
248 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 112 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 | #481 |
| commutator, Frattini, cosocle | C2×C8 | C23×C3×C5 |
| prime radical | C23×C3×C5 | SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C2×C3×C4×C5 ◁ C2×C3×C5×M16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C3×C5×#365 | C2 | semidirect |
| 4. C3×C5×#362 | C2 | semidirect |
| 6. C5×#2239 | C3 | direct (N × H) |
| 16. C3×#2239 | C5 | direct (N × H) |
| 19. C5×#365 | C2×C3 | semidirect |
| 20. C5×#362 | C2×C3 | semidirect |
| 37. C3×#365 | C2×C5 | semidirect |
| 38. C3×#362 | C2×C5 | semidirect |
| 49. #2239 | C3×C5 | direct (N × H) |
| 86. #365 | C2×C3×C5 | semidirect |
| 87. #362 | C2×C3×C5 | semidirect |
| 167. C3×C5 | #2239 | direct (N × H) |
| 194. C5 | C3×#2239 | direct (N × H) |
| 203. C3 | C5×#2239 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#470 | 2 |
| C3×C5×#430 | 2 |
| C3×C5×#365 | 2 |
| C3×C5×#362 | 2 |
| C3×C5×#349 | 2 |
| C5×#2239 | 3 |
| C3×#2239 | 5 |