Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
300 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 300 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 |
|---|---|---|
| 6. AGL(1,𝔽5)×Q32 | C3 | direct (N × H) |
| 13. C3×C5×Q32 | C4 | semidirect |
| 14. C3×#3961 | C4 | semidirect |
| 15. C3×Dic40 | C4 | semidirect |
| 47. C5×Q32 | C3×C4 | semidirect |
| 48. #3961 | C3×C4 | semidirect |
| 49. Dic40 | C3×C4 | semidirect |
| 67. C3×Q32 | AGL(1,𝔽5) | direct (N × H) |
| 94. C3×AGL(1,𝔽5) | Q32 | direct (N × H) |
| 127. Q32 | C3×AGL(1,𝔽5) | direct (N × H) |
| 150. AGL(1,𝔽5) | C3×Q32 | direct (N × H) |
| 168. C3×C5 | C4×Q32 | semidirect |
| 194. C5 | C3×C4×Q32 | semidirect |
| 203. C3 | AGL(1,𝔽5)×Q32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q16×AGL(1,𝔽5) | 2 |
| C3×D5×Q32 | 2 |
| C3×#64908 | 2 |
| C3×#64849 | 2 |
| C3×C16×AGL(1,𝔽5) | 2 |
| AGL(1,𝔽5)×Q32 | 3 |
| C3×C4×Q32 | 5 |