Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
296 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 8. #91227 | C4 | semidirect |
| 13. #91096 | C4 | semidirect |
| 14. C5×#812 | C4 | semidirect |
| 76. #812 | AGL(1,𝔽5) | semidirect |
| 192. C3×C5 | #1376 | semidirect |
| 224. C5 | #67658 | semidirect |
| 234. C3 | #10598670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5⋊#812 | 2 |
| C2×C3×C8×AGL(1,𝔽5) | 2 |
| D5×#812 | 2 |
| #10598670 | 3 |
| #67658 | 5 |