Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
192 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 26 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 | C22×C5 | #1020 |
| commutator, cosocle, hypocenter | Q8⋊SL(2,𝔽3) | C2×C5 |
| Frattini | C22 | C5×#1020 |
| Fitting | C5×Q82 | D3 |
| prime radical | C5×Q8⋊SL(2,𝔽3) | C2 |
| LCS | G ▷ Q8⋊SL(2,𝔽3) | |
| UCS | C1 ◁ C22×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #85553 | C5 | direct (N × H) |
| 64. C5×Q8 | #226 | semidirect |
| 118. Q8 | C5×#226 | semidirect |
| 127. C5 | #85553 | 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×#1633 | 3 |
| C2×C5×#226 | 4 |
| C5×#859 | 4 |
| #85553 | 5 |