Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
626 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 78 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. #11756724 | C2 | semidirect |
| 3. D5⋊GU(2,𝔽3) | C2 | semidirect |
| 4. #11756720 | C2 | semidirect |
| 6. C2×C5×#41⋊C3 | C4 | semidirect |
| 8. D5×#41⋊C3 | C4 | semidirect |
| 9. D5×#41⋊C3 | C4 | semidirect |
| 12. C2×D5×SL(2,𝔽3) | C4 | semidirect |
| 14. #91885 | C22 | semidirect |
| 27. C5×#41⋊C3 | C2×C4 | semidirect |
| 28. C2×C5×SL(2,𝔽3) | C2×C4 | semidirect |
| 33. D5×SL(2,𝔽3) | C2×C4 | semidirect |
| 34. C5⋊(#41⋊C3) | C2×C4 | semidirect |
| 88. C2×#41⋊C3 | AGL(1,𝔽5) | semidirect |
| 177. #41⋊C3 | C2×AGL(1,𝔽5) | semidirect |
| 180. C2×SL(2,𝔽3) | C2×AGL(1,𝔽5) | semidirect |
| 387. D5 | #5423 | semidirect |
| 446. C5 | C2×#5423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×#41⋊C3 | 2 |
| #11756724 | 2 |
| D5⋊GU(2,𝔽3) | 2 |
| #11756720 | 2 |
| D5⋊#421 | 3 |
| D5⋊#208 | 4 |
| C2×#5423 | 5 |