Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D5×A4 |
| commutator, socle, cosocle | C24×C5 | C23×C3 |
| Fitting | C22×C42×C5 | C2×C3 |
| hypercenter | C42 | D5×A4 |
| hypocenter | C22×C5 | C3×#127 |
| LCS | G ▷ C24×C5 ▷ C22×C5 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×A4×D20 | C2 | semidirect |
| 2. C42×C5×A4 | C2 | semidirect |
| 3. C22×#4020 | C3 | semidirect |
| 9. C23×D20 | C2×C3 | semidirect |
| 10. C22×C42×C5 | C2×C3 | semidirect |
| 17. C4×C5×A4 | D4 | semidirect |
| 20. C42×A4 | D5 | semidirect |
| 34. #4020 | A4 | direct (N × H) |
| 53. C22×C4×C5 | C3×D4 | semidirect |
| 63. C2×D20 | C2×A4 | semidirect |
| 66. C42×C5 | C2×A4 | semidirect |
| 71. C22×C42 | C3×D5 | semidirect |
| 74. C5×A4 | #127 | semidirect |
| 79. C4×A4 | D20 | semidirect |
| 128. C22×C5 | C3×#127 | semidirect |
| 137. C4×C5 | D4×A4 | semidirect |
| 156. C22×C4 | C3×D20 | semidirect |
| 159. C42 | D5×A4 | semidirect |
| 163. A4 | #4020 | direct (N × H) |
| 194. C5 | A4×#127 | semidirect |
| 205. C22 | C3×#4020 | semidirect |
| 208. C4 | A4×D20 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×A4×D20 | 2 |
| C42×C5×A4 | 2 |
| C22×#4020 | 3 |
| C3×#4020 | 4 |
| A4×#127 | 5 |