Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
352 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 22. #71226 | C5 | direct (N × H) |
| 81. C5×C3⋊C8 | Q16 | semidirect |
| 187. C3⋊C8 | C5×Q16 | semidirect |
| 213. C3×C5 | #1723 | semidirect |
| 242. C5 | #71226 | direct (N × H) |
| 251. C3 | C5×#1723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#487 | 2 |
| C5×#5080 | 2 |
| C5×#5079 | 2 |
| C5×#5078 | 2 |
| C5×#4699 | 2 |
| C5×#4454 | 2 |
| C5×#1723 | 3 |
| #71226 | 5 |