Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
174 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C16 | S4 |
| commutator, hypocenter | SL(2,𝔽3) | C2×C5×C8 |
| Frattini | C8 | C2×C5×S4 |
| Fitting | C5×#504 | D3 |
| socle | C2×C5 | C8×S4 |
| prime radical | C5×#985 | C4 |
| cosocle | #131⋊C3 | C22×C5 |
| LCS | G ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C5×C16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#504⋊C3 | C2 | semidirect |
| 3. C5×#4628 | C2 | semidirect |
| 9. #73038 | C5 | direct (N × H) |
| 11. C5×#504 | D3 | semidirect |
| 24. #504⋊C3 | C2×C5 | semidirect |
| 25. #4628 | C2×C5 | semidirect |
| 66. #504 | C5×D3 | semidirect |
| 158. C5 | #73038 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5404 | 2 |
| C5×#504⋊C3 | 2 |
| C5×#4628 | 2 |
| C5×#2170 | 3 |
| C5×D3×C16 | 4 |
| #73038 | 5 |