Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
694 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 2. #11756726 | C2 | direct (N × H) |
| 3. C2×#91886 | C2 | semidirect |
| 5. C2×C5×#41⋊C3 | C4 | semidirect |
| 7. D5×#41⋊C3 | C4 | semidirect |
| 10. C2×C5⋊(#41⋊C3) | C4 | semidirect |
| 11. #91886 | C22 | semidirect |
| 22. C5×#41⋊C3 | C2×C4 | semidirect |
| 23. C2×C5×SL(2,𝔽3) | C2×C4 | semidirect |
| 25. D5×SL(2,𝔽3) | C2×C4 | semidirect |
| 27. C5⋊(#41⋊C3) | C2×C4 | semidirect |
| 32. C2×C5×#41 | Dic3 | semidirect |
| 35. D5×#41 | Dic3 | semidirect |
| 37. C2×#713 | Dic3 | semidirect |
| 63. C5×SL(2,𝔽3) | C22×C4 | semidirect |
| 67. C2×#41⋊C3 | AGL(1,𝔽5) | semidirect |
| 76. C5×#41 | C2×Dic3 | semidirect |
| 83. #713 | C2×Dic3 | semidirect |
| 134. #41⋊C3 | C2×AGL(1,𝔽5) | semidirect |
| 137. C2×SL(2,𝔽3) | C2×AGL(1,𝔽5) | semidirect |
| 186. C2×#41 | ΓL(1,𝔽16) | semidirect |
| 215. SL(2,𝔽3) | C22×AGL(1,𝔽5) | semidirect |
| 245. #41 | C2×ΓL(1,𝔽16) | semidirect |
| 290. C2×C5 | #5426 | semidirect |
| 293. D5 | #5426 | semidirect |
| 341. C5 | C2×#5426 | semidirect |
| 367. C2 | #11756726 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×#41⋊C3 | 2 |
| #11756726 | 2 |
| C2×#91886 | 2 |
| C2×#65793 | 3 |
| C2×C4⋊ΓL(1,𝔽16) | 4 |
| C2×#5426 | 5 |