Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
786 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D5×A4 |
| commutator, cosocle | C2×C5×Q8 | C23×C3 |
| Fitting | C4×C5×#41 | C2×C3 |
| socle | C22×C5 | C23×A4 |
| hypercenter | C42 | D5×A4 |
| hypocenter | C5×Q8 | C2×C3×D4 |
| LCS | G ▷ C2×C5×Q8 ▷ C5×Q8 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5⋊#994 | C2 | semidirect |
| 2. C4×C5×#41⋊C3 | C2 | semidirect |
| 3. C4⋊(C5⋊(#41⋊C3)) | C2 | semidirect |
| 4. #10617747 | C3 | semidirect |
| 7. C2×C5⋊(#41⋊C3) | C22 | semidirect |
| 9. C4×C5×SL(2,𝔽3) | C22 | semidirect |
| 19. C5×#41⋊C3 | D4 | semidirect |
| 26. C4×#41⋊C3 | D5 | semidirect |
| 53. C5×SL(2,𝔽3) | C2×D4 | semidirect |
| 58. C4×SL(2,𝔽3) | C2×D5 | semidirect |
| 102. #41⋊C3 | D20 | semidirect |
| 158. SL(2,𝔽3) | C2×D20 | semidirect |
| 169. C4×C5 | #994 | semidirect |
| 237. C5 | C4⋊#994 | semidirect |
| 249. C4 | C5⋊#994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5⋊#994 | 2 |
| C4×C5×#41⋊C3 | 2 |
| C4⋊(C5⋊(#41⋊C3)) | 2 |
| #10617747 | 3 |
| C3×#4015 | 4 |
| C4⋊#994 | 5 |