Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
304 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 128 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. C3×C5×#499 | C2 | semidirect |
| 3. C3×C5×#357 | C2 | semidirect |
| 4. C3×C5×#346 | C2 | semidirect |
| 5. C5×#2244 | C3 | direct (N × H) |
| 14. C3×#2244 | C5 | direct (N × H) |
| 15. C5×#499 | C2×C3 | semidirect |
| 17. C5×#357 | C2×C3 | semidirect |
| 18. C5×#346 | C2×C3 | semidirect |
| 29. C3×#499 | C2×C5 | semidirect |
| 31. C3×#357 | C2×C5 | semidirect |
| 32. C3×#346 | C2×C5 | semidirect |
| 41. #2244 | C3×C5 | direct (N × H) |
| 69. #499 | C2×C3×C5 | semidirect |
| 71. #357 | C2×C3×C5 | semidirect |
| 72. #346 | C2×C3×C5 | semidirect |
| 136. C3×C5 | #2244 | direct (N × H) |
| 159. C5 | C3×#2244 | direct (N × H) |
| 167. C3 | C5×#2244 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#499 | 2 |
| C3×C5×#493 | 2 |
| C3×C5×#357 | 2 |
| C3×C5×#346 | 2 |
| C5×#2244 | 3 |
| C3×#2244 | 5 |