Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
428 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 226 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. C3×C5×C82 | C2 | semidirect |
| 3. C5×#4455 | C2 | semidirect |
| 10. #68050 | C5 | direct (N × H) |
| 13. C5×C82 | D3 | semidirect |
| 21. C3×C82 | C2×C5 | semidirect |
| 22. #4455 | C2×C5 | semidirect |
| 33. C3×C5×C8 | M16 | semidirect |
| 48. C82 | C5×D3 | semidirect |
| 64. C5×C8 | ΓL(1,𝔽25) | semidirect |
| 76. C3×C8 | C5×M16 | semidirect |
| 88. C3×C5 | #1455 | semidirect |
| 100. C8 | C5×ΓL(1,𝔽25) | semidirect |
| 103. C5 | #68050 | direct (N × H) |
| 108. C3 | C5×#1455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×ΓL(1,𝔽25) | 2 |
| C3×C5×C82 | 2 |
| C5×#4455 | 2 |
| C5×#1455 | 3 |
| #68050 | 5 |