Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
786 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C23×A4 |
| commutator, cosocle | C2×Q8 | C23×C3×C5 |
| Frattini | C22 | C23×C5×A4 |
| Fitting | C5×#3498 | C3 |
| hypercenter | C5×C4⋊Q8 | A4 |
| hypocenter | Q8 | C2×C3×C5×D4 |
| LCS | G ▷ C2×Q8 ▷ Q8 | |
| UCS | C1 ◁ C22×C5 ◁ C5×C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#994 | C2 | semidirect |
| 2. C5×C4⋊(#41⋊C3) | C2 | semidirect |
| 3. C4×C5×#41⋊C3 | C2 | semidirect |
| 4. C5×#3498 | C3 | semidirect |
| 7. C2×C5×#41⋊C3 | C22 | semidirect |
| 9. C4×C5×SL(2,𝔽3) | C22 | semidirect |
| 10. C4⋊#994 | C5 | direct (N × H) |
| 20. C5×#41⋊C3 | D4 | semidirect |
| 24. C2×#994 | C2×C5 | semidirect |
| 25. C4⋊(#41⋊C3) | C2×C5 | semidirect |
| 26. C4×#41⋊C3 | C2×C5 | semidirect |
| 48. #3498 | C3×C5 | semidirect |
| 53. C5×SL(2,𝔽3) | C2×D4 | semidirect |
| 56. C2×#41⋊C3 | C22×C5 | semidirect |
| 58. C4×SL(2,𝔽3) | C22×C5 | semidirect |
| 102. #41⋊C3 | C5×D4 | semidirect |
| 158. SL(2,𝔽3) | C2×C5×D4 | semidirect |
| 170. C4×C5 | #994 | semidirect |
| 237. C5 | C4⋊#994 | direct (N × H) |
| 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 |
| C5×C4⋊(#41⋊C3) | 2 |
| C4×C5×#41⋊C3 | 2 |
| C5×#3498 | 3 |
| C3×C5×C4⋊Q8 | 4 |
| C4⋊#994 | 5 |