Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
2670 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 2670 conjugacy classes of subgroups — too many to draw. Only its 271 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D5×A4 |
| commutator, cosocle, hypocenter | C5×Q8 | C24×C3 |
| Frattini | C2 | C23×D5×A4 |
| Fitting | C22×C5×#41 | C2×C3 |
| socle | C23×C5 | C22×A4 |
| hypercenter | C22×C4 | D5×A4 |
| LCS | G ▷ C5×Q8 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C5×#41⋊C3 | C2 | semidirect |
| 2. C2×C5⋊#994 | C2 | direct (N × H) |
| 3. C22×C5⋊(#41⋊C3) | C2 | semidirect |
| 4. C22×#4149 | C3 | semidirect |
| 6. C2×C5×#41⋊C3 | C22 | semidirect |
| 7. C22×C5×SL(2,𝔽3) | C22 | semidirect |
| 8. C5⋊#994 | C22 | direct (N × H) |
| 9. C2×C5⋊(#41⋊C3) | C22 | semidirect |
| 13. C2×#4149 | C2×C3 | semidirect |
| 21. C5×#41⋊C3 | C23 | semidirect |
| 22. C2×C5×SL(2,𝔽3) | C23 | semidirect |
| 23. C5⋊(#41⋊C3) | C23 | semidirect |
| 26. C22×#41⋊C3 | D5 | semidirect |
| 36. #4149 | C22×C3 | semidirect |
| 54. C5×SL(2,𝔽3) | C24 | semidirect |
| 58. C2×#41⋊C3 | C2×D5 | semidirect |
| 59. C22×SL(2,𝔽3) | C2×D5 | semidirect |
| 107. #41⋊C3 | C22×D5 | semidirect |
| 108. C2×SL(2,𝔽3) | C22×D5 | semidirect |
| 162. SL(2,𝔽3) | C23×D5 | semidirect |
| 165. C22×C5 | #994 | semidirect |
| 212. C2×C5 | C2×#994 | semidirect |
| 242. C5 | C22×#994 | semidirect |
| 248. C22 | C5⋊#994 | direct (N × H) |
| 257. C2 | C2×C5⋊#994 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#41⋊C3 | 2 |
| C2×C5⋊#994 | 2 |
| C22×C5⋊(#41⋊C3) | 2 |
| C22×#4149 | 3 |
| C22×C3×Dic10 | 4 |
| C22×#994 | 5 |