Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
436 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 60 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. C4×C5×SL(2,ℤ/4) | C2 | semidirect |
| 3. C5×#5409 | C2 | semidirect |
| 5. C5×Q8×A4 | C4 | semidirect |
| 7. C5×D4×A4 | C4 | semidirect |
| 13. #73150 | C5 | direct (N × H) |
| 31. C4×SL(2,ℤ/4) | C2×C5 | semidirect |
| 32. #5409 | C2×C5 | semidirect |
| 39. C22×C5×Q8 | Dic3 | semidirect |
| 41. C22×C5×D4 | Dic3 | semidirect |
| 69. Q8×A4 | C4×C5 | semidirect |
| 71. D4×A4 | C4×C5 | semidirect |
| 134. C5×A4 | #104 | semidirect |
| 160. C5×Q8 | SL(2,ℤ/4) | semidirect |
| 169. C5×D4 | SL(2,ℤ/4) | semidirect |
| 200. C22×Q8 | C5×Dic3 | semidirect |
| 202. C22×D4 | C5×Dic3 | semidirect |
| 245. C22×C5 | #837 | semidirect |
| 306. A4 | C5×#104 | semidirect |
| 330. Q8 | C5×SL(2,ℤ/4) | semidirect |
| 339. D4 | C5×SL(2,ℤ/4) | semidirect |
| 367. C5 | #73150 | direct (N × H) |
| 381. C22 | C5×#837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×A4×#41 | 2 |
| C4×C5×SL(2,ℤ/4) | 2 |
| C5×#5409 | 2 |
| C5×#1789 | 3 |
| C5×#837 | 4 |
| #73150 | 5 |