Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
720 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 3. M16×ΓL(1,𝔽16) | C2 | semidirect |
| 5. #11746770 | C2 | semidirect |
| 16. #91242 | C4 | semidirect |
| 19. C3×C5×#100 | C4 | semidirect |
| 20. C3×#3965 | C4 | semidirect |
| 21. C3×#3955 | C4 | semidirect |
| 42. #6762 | C2×C4 | semidirect |
| 48. C3×C5×M16 | C2×C4 | semidirect |
| 49. C3×#681 | C2×C4 | semidirect |
| 69. C5×#100 | Dic3 | semidirect |
| 70. #3965 | Dic3 | semidirect |
| 71. #3955 | Dic3 | semidirect |
| 110. C3×#100 | AGL(1,𝔽5) | semidirect |
| 134. C5×M16 | C2×Dic3 | semidirect |
| 135. #681 | C2×Dic3 | semidirect |
| 158. ΓL(1,𝔽16) | #100 | direct (N × H) |
| 176. C3×M16 | C2×AGL(1,𝔽5) | semidirect |
| 223. #100 | ΓL(1,𝔽16) | direct (N × H) |
| 294. M16 | C2×ΓL(1,𝔽16) | semidirect |
| 301. C3×C5 | C4×#100 | semidirect |
| 360. C5 | Dic3×#100 | semidirect |
| 379. C3 | AGL(1,𝔽5)×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×ΓL(1,𝔽16) | 2 |
| D5⋊#833 | 2 |
| M16×ΓL(1,𝔽16) | 2 |
| C3×D5×#100 | 2 |
| #11746770 | 2 |
| AGL(1,𝔽5)×#100 | 3 |
| Dic3×#100 | 5 |