Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1080 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #85647 |
| commutator, cosocle, hypocenter | C22×C42 | C2×C3×C5 |
| Frattini | C22 | C2×C5×C22⋊A4 |
| Fitting | C22×C5×#127 | C3 |
| socle | C24×C5 | C2×A4 |
| LCS | G ▷ C22×C42 | |
| UCS | C1 ◁ C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×C22⋊(C42⋊C3) | C2 | semidirect |
| 2. C22×C5×#127 | C3 | semidirect |
| 5. #85647 | C5 | direct (N × H) |
| 10. C22×C42×C5 | C2×C3 | semidirect |
| 13. C22⋊(C42⋊C3) | C2×C5 | semidirect |
| 25. C5×#127 | A4 | semidirect |
| 27. C22×#127 | C3×C5 | semidirect |
| 49. C42×C5 | C2×A4 | semidirect |
| 54. C22×C42 | C2×C3×C5 | semidirect |
| 89. #127 | C5×A4 | semidirect |
| 103. C22×C5 | #127⋊C3 | semidirect |
| 123. C42 | C2×C5×A4 | semidirect |
| 152. C5 | #85647 | direct (N × H) |
| 162. C22 | C5×#127⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C22⋊(C42⋊C3) | 2 |
| C22×C5×#127 | 3 |
| C2×C5×C22⋊A4 | 4 |
| C5×#127⋊C3 | 4 |
| #85647 | 5 |