Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
504 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C5 | C22⋊A4 |
| commutator, cosocle, hypocenter | Q82 | C2×C3×C5 |
| Frattini | C22 | C2×C5×C22⋊A4 |
| Fitting | C5×#3483 | C3 |
| socle | C22×C5 | C2×C22⋊A4 |
| LCS | G ▷ Q82 | |
| UCS | C1 ◁ C2×C4×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×Q8⋊SL(2,𝔽3) | C2 | semidirect |
| 2. C5×#3483 | C3 | semidirect |
| 5. #85654 | C5 | direct (N × H) |
| 14. Q8⋊SL(2,𝔽3) | C2×C5 | semidirect |
| 29. #3483 | C3×C5 | semidirect |
| 67. C5×Q8 | #41⋊C3 | semidirect |
| 134. Q8 | C5×#41⋊C3 | semidirect |
| 148. C5 | #85654 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8⋊SL(2,𝔽3) | 2 |
| C5×#3483 | 3 |
| C2×C5×#41⋊C3 | 4 |
| C4×C5×SL(2,𝔽3) | 4 |
| #85654 | 5 |