Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
600 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C5⋊(#126⋊C3) |
| commutator, cosocle, hypocenter | C42×C5 | C23×C3 |
| Frattini | C22 | C22×D5×A4 |
| Fitting | C22×C42×C5 | C2×C3 |
| socle | C24×C5 | C2×A4 |
| LCS | G ▷ C42×C5 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C5×C42⋊C3 | C2 | semidirect |
| 2. C2×C5⋊(#126⋊C3) | C2 | direct (N × H) |
| 3. C22×#4022 | C3 | semidirect |
| 5. C2×C5×C42⋊C3 | C22 | semidirect |
| 6. C5⋊(#126⋊C3) | C22 | direct (N × H) |
| 8. C22×C42×C5 | C2×C3 | semidirect |
| 12. C2×#4022 | C2×C3 | semidirect |
| 15. C5×C42⋊C3 | C23 | semidirect |
| 17. C22×C42⋊C3 | D5 | semidirect |
| 22. C2×C42×C5 | C22×C3 | semidirect |
| 29. #4022 | C22×C3 | semidirect |
| 36. C2×C42⋊C3 | C2×D5 | semidirect |
| 50. C42×C5 | C23×C3 | semidirect |
| 59. C22×C42 | C3×D5 | semidirect |
| 65. C42⋊C3 | C22×D5 | semidirect |
| 95. C2×C42 | C2×C3×D5 | semidirect |
| 105. C22×C5 | #126⋊C3 | semidirect |
| 130. C42 | C22×C3×D5 | semidirect |
| 137. C2×C5 | C2×#126⋊C3 | semidirect |
| 159. C5 | C22×#126⋊C3 | semidirect |
| 167. C22 | C5⋊(#126⋊C3) | direct (N × H) |
| 176. C2 | C2×C5⋊(#126⋊C3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C42⋊C3 | 2 |
| C2×C5⋊(#126⋊C3) | 2 |
| C22×#4022 | 3 |
| C22×D5×A4 | 4 |
| C22×#126⋊C3 | 5 |