Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1948 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 1948 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×C5×A4 | C2 | semidirect |
| 2. C2×C5×D4×A4 | C2 | semidirect |
| 3. C5×A4×C22⋊C4 | C2 | semidirect |
| 4. C22×C5×#120 | C3 | semidirect |
| 7. C23×C5×A4 | C22 | semidirect |
| 9. C2×C4×C5×A4 | C22 | semidirect |
| 11. A4×#120 | C5 | direct (N × H) |
| 12. C26×C5 | C2×C3 | semidirect |
| 13. C23×C5×D4 | C2×C3 | semidirect |
| 18. C22×C5×C22⋊C4 | C2×C3 | semidirect |
| 23. C22×C5×A4 | D4 | semidirect |
| 28. C24×A4 | C2×C5 | semidirect |
| 29. C2×D4×A4 | C2×C5 | semidirect |
| 30. A4×C22⋊C4 | C2×C5 | semidirect |
| 36. C25×C5 | C22×C3 | semidirect |
| 43. C23×C4×C5 | C22×C3 | semidirect |
| 50. C5×#120 | A4 | direct (N × H) |
| 54. C22×#120 | C3×C5 | semidirect |
| 65. C23×A4 | C22×C5 | semidirect |
| 67. C2×C4×A4 | C22×C5 | semidirect |
| 89. C24×C5 | C3×D4 | semidirect |
| 90. C24×C5 | C2×A4 | semidirect |
| 104. C2×C5×D4 | C2×A4 | semidirect |
| 112. C5×C22⋊C4 | C2×A4 | semidirect |
| 113. C26 | C2×C3×C5 | semidirect |
| 114. C23×D4 | C2×C3×C5 | semidirect |
| 119. C22×C22⋊C4 | C2×C3×C5 | semidirect |
| 125. C5×A4 | #120 | direct (N × H) |
| 131. C22×A4 | C5×D4 | semidirect |
| 170. C23×C5 | C22×A4 | semidirect |
| 181. C2×C4×C5 | C22×A4 | semidirect |
| 187. C25 | C22×C3×C5 | semidirect |
| 194. C23×C4 | C22×C3×C5 | semidirect |
| 201. #120 | C5×A4 | direct (N × H) |
| 238. C22×C5 | C3×#120 | semidirect |
| 239. C22×C5 | D4×A4 | semidirect |
| 263. C24 | C3×C5×D4 | semidirect |
| 264. C24 | C2×C5×A4 | semidirect |
| 278. C2×D4 | C2×C5×A4 | semidirect |
| 286. C22⋊C4 | C2×C5×A4 | semidirect |
| 293. A4 | C5×#120 | direct (N × H) |
| 336. C23 | C22×C5×A4 | semidirect |
| 347. C2×C4 | C22×C5×A4 | semidirect |
| 351. C5 | A4×#120 | direct (N × H) |
| 374. C22 | C3×C5×#120 | semidirect |
| 375. C22 | C5×D4×A4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C5×A4 | 2 |
| C2×C5×D4×A4 | 2 |
| C5×A4×C22⋊C4 | 2 |
| C22×C5×#120 | 3 |
| C3×C5×#120 | 4 |
| A4×#120 | 5 |