Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
378 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 52 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. C5×A4×M16 | C2 | semidirect |
| 3. C4×C5×SL(2,ℤ/4) | C2 | semidirect |
| 8. C5×C4⋊S4 | C4 | semidirect |
| 10. C5×A4⋊Q8 | C4 | semidirect |
| 13. #73117 | C5 | direct (N × H) |
| 14. C22×C5×M16 | D3 | semidirect |
| 31. A4×M16 | C2×C5 | semidirect |
| 32. C4×SL(2,ℤ/4) | C2×C5 | semidirect |
| 69. C4⋊S4 | C4×C5 | semidirect |
| 71. A4⋊Q8 | C4×C5 | semidirect |
| 96. C5×M16 | S4 | semidirect |
| 115. C22×M16 | C5×D3 | semidirect |
| 124. C5×A4 | #104 | semidirect |
| 220. C22×C5 | #825 | semidirect |
| 253. M16 | C5×S4 | semidirect |
| 275. A4 | C5×#104 | semidirect |
| 326. C5 | #73117 | direct (N × H) |
| 337. C22 | C5×#825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5912 | 2 |
| C5×A4×M16 | 2 |
| C4×C5×SL(2,ℤ/4) | 2 |
| C5×#1871 | 3 |
| C5×#825 | 4 |
| #73117 | 5 |