Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
514 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C23×C5 | C22⋊A4 |
| commutator, cosocle, hypocenter | Q82 | C2×C3×C5 |
| Frattini | C22 | C2×C5×C22⋊A4 |
| Fitting | C2×C5×Q82 | C3 |
| LCS | G ▷ Q82 | |
| UCS | C1 ◁ C23×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×Q8⋊SL(2,𝔽3) | C2 | direct (N × H) |
| 2. C2×C5×Q82 | C3 | semidirect |
| 5. C2×Q8⋊SL(2,𝔽3) | C5 | direct (N × H) |
| 8. C5×Q82 | C2×C3 | semidirect |
| 15. Q8⋊SL(2,𝔽3) | C2×C5 | direct (N × H) |
| 30. C2×Q82 | C3×C5 | semidirect |
| 43. C2×C5×Q8 | SL(2,𝔽3) | semidirect |
| 56. Q82 | C2×C3×C5 | semidirect |
| 74. C5×Q8 | C2×SL(2,𝔽3) | semidirect |
| 117. C2×Q8 | C5×SL(2,𝔽3) | semidirect |
| 132. C2×C5 | Q8⋊SL(2,𝔽3) | direct (N × H) |
| 143. Q8 | C2×C5×SL(2,𝔽3) | semidirect |
| 154. C5 | C2×Q8⋊SL(2,𝔽3) | direct (N × H) |
| 164. C2 | C5×Q8⋊SL(2,𝔽3) | 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 |
| C2×C5×Q82 | 3 |
| C22×C5×SL(2,𝔽3) | 4 |
| C2×Q8⋊SL(2,𝔽3) | 5 |