Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1934 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 1934 conjugacy classes of subgroups — too many to draw. Only its 184 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 |
|---|---|---|
| 2. C22×C5×SL(2,ℤ/4) | C2 | semidirect |
| 3. C5×#5432 | C2 | direct (N × H) |
| 6. C23×C5×A4 | C4 | semidirect |
| 10. C2×C5×SL(2,ℤ/4) | C22 | semidirect |
| 12. C2×#5432 | C5 | direct (N × H) |
| 24. C22×C5×A4 | C2×C4 | semidirect |
| 31. C22×SL(2,ℤ/4) | C2×C5 | semidirect |
| 32. #5432 | C2×C5 | direct (N × H) |
| 39. C25×C5 | Dic3 | semidirect |
| 62. C2×C5×A4 | C22⋊C4 | semidirect |
| 68. C23×A4 | C4×C5 | semidirect |
| 72. C2×SL(2,ℤ/4) | C22×C5 | semidirect |
| 103. C24×C5 | C2×Dic3 | semidirect |
| 136. C5×A4 | C2×C22⋊C4 | semidirect |
| 142. C22×A4 | C2×C4×C5 | semidirect |
| 192. C23×C5 | #217 | semidirect |
| 193. C23×C5 | SL(2,ℤ/4) | semidirect |
| 213. C25 | C5×Dic3 | semidirect |
| 239. C2×A4 | C5×C22⋊C4 | semidirect |
| 272. C22×C5 | C2×#217 | semidirect |
| 274. C22×C5 | C2×SL(2,ℤ/4) | semidirect |
| 308. C24 | C2×C5×Dic3 | semidirect |
| 335. A4 | C2×C5×C22⋊C4 | semidirect |
| 343. C2×C5 | #5432 | direct (N × H) |
| 390. C23 | C5×#217 | semidirect |
| 391. C23 | C5×SL(2,ℤ/4) | semidirect |
| 409. C5 | C2×#5432 | direct (N × H) |
| 438. C22 | C2×C5×#217 | semidirect |
| 440. C22 | C2×C5×SL(2,ℤ/4) | semidirect |
| 452. C2 | C5×#5432 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C5×A4 | 2 |
| C22×C5×SL(2,ℤ/4) | 2 |
| C5×#5432 | 2 |
| C2×C5×#379 | 3 |
| C2×C5×#217 | 4 |
| C2×#5432 | 5 |