Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
620 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 106 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. C5×#5510 | C2 | semidirect |
| 2. C3×C5×#394 | C2 | semidirect |
| 3. C5×#5217 | C2 | semidirect |
| 4. C5×#4528 | C2 | semidirect |
| 5. C5×#4451 | C2 | semidirect |
| 20. #69703 | C5 | direct (N × H) |
| 23. C5×#394 | D3 | semidirect |
| 50. #5510 | C2×C5 | semidirect |
| 51. C3×#394 | C2×C5 | semidirect |
| 52. #5217 | C2×C5 | semidirect |
| 53. #4528 | C2×C5 | semidirect |
| 54. #4451 | C2×C5 | semidirect |
| 88. C2×C3×C4×C5 | D8 | semidirect |
| 138. #394 | C5×D3 | semidirect |
| 212. C2×C4×C5 | #213 | semidirect |
| 254. C2×C3×C4 | C5×D8 | semidirect |
| 309. C3×C5 | #1598 | semidirect |
| 364. C2×C4 | C5×#213 | semidirect |
| 374. C5 | #69703 | direct (N × H) |
| 395. C3 | C5×#1598 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5510 | 2 |
| C3×C5×#394 | 2 |
| C5×#5217 | 2 |
| C5×#4528 | 2 |
| C5×#4451 | 2 |
| C5×#1598 | 3 |
| #69703 | 5 |