Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
2790 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 2790 conjugacy classes of subgroups — too many to draw. Only its 351 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D5×A4 |
| commutator, cosocle, hypocenter | C5×Q8 | C24×C3 |
| Frattini | C2 | C23×D5×A4 |
| Fitting | C23×C5×Q8 | C2×C3 |
| socle | C24×C5 | C2×A4 |
| LCS | G ▷ C5×Q8 | |
| UCS | C1 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C5×SL(2,𝔽3) | C2 | semidirect |
| 2. C22×C5⋊(#41⋊C3) | C2 | direct (N × H) |
| 3. C23×#713 | C3 | semidirect |
| 5. C22×C5×SL(2,𝔽3) | C22 | semidirect |
| 6. C2×C5⋊(#41⋊C3) | C22 | direct (N × H) |
| 10. C22×#713 | C2×C3 | semidirect |
| 15. C2×C5×SL(2,𝔽3) | C23 | semidirect |
| 16. C5⋊(#41⋊C3) | C23 | direct (N × H) |
| 18. C23×SL(2,𝔽3) | D5 | semidirect |
| 26. C2×#713 | C22×C3 | semidirect |
| 35. C5×SL(2,𝔽3) | C24 | semidirect |
| 38. C22×SL(2,𝔽3) | C2×D5 | semidirect |
| 50. #713 | C23×C3 | semidirect |
| 66. C2×SL(2,𝔽3) | C22×D5 | semidirect |
| 67. C23×C5 | #41⋊C3 | semidirect |
| 98. SL(2,𝔽3) | C23×D5 | semidirect |
| 99. C22×C5 | C2×#41⋊C3 | semidirect |
| 126. C2×C5 | C22×#41⋊C3 | semidirect |
| 131. C23 | C5⋊(#41⋊C3) | direct (N × H) |
| 145. C5 | C23×#41⋊C3 | semidirect |
| 148. C22 | C2×C5⋊(#41⋊C3) | direct (N × H) |
| 155. C2 | C22×C5⋊(#41⋊C3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×SL(2,𝔽3) | 2 |
| C22×C5⋊(#41⋊C3) | 2 |
| C23×#713 | 3 |
| C23×C3×Dic5 | 4 |
| C23×#41⋊C3 | 5 |