Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
344 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 10. C5×#836 | C4 | semidirect |
| 11. #67644 | C5 | direct (N × H) |
| 62. #836 | C4×C5 | semidirect |
| 177. C3×C5 | #1394 | semidirect |
| 217. C5 | #67644 | direct (N × H) |
| 229. C3 | C5×#1394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#391 | 2 |
| C2×C5×#836 | 2 |
| C5×#1394 | 3 |
| #67644 | 5 |