Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1606 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 1606 conjugacy classes of subgroups — too many to draw. Only its 169 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | C5⋊S4 |
| commutator, cosocle, hypocenter | C5×SL(2,𝔽3) | C24 |
| Frattini | C2 | C23×C5⋊S4 |
| Fitting | C22×C5×#41 | D3 |
| socle | C23×C5 | C2×S4 |
| LCS | G ▷ C5×SL(2,𝔽3) | |
| UCS | C1 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C5×#41⋊C3 | C2 | semidirect |
| 2. C2×#91955 | C2 | direct (N × H) |
| 3. C22×C5⋊GL(2,𝔽3) | C2 | semidirect |
| 4. C22×C5⋊#226 | C2 | semidirect |
| 7. C2×C5×#41⋊C3 | C22 | semidirect |
| 9. #91955 | C22 | direct (N × H) |
| 10. C2×C5⋊GL(2,𝔽3) | C22 | semidirect |
| 11. C2×C5⋊#226 | C22 | semidirect |
| 13. C22×C5×#41 | D3 | semidirect |
| 26. C5×#41⋊C3 | C23 | semidirect |
| 28. C5⋊GL(2,𝔽3) | C23 | semidirect |
| 29. C5⋊#226 | C23 | semidirect |
| 30. C22×#41⋊C3 | D5 | semidirect |
| 35. C2×C5×#41 | C2×D3 | semidirect |
| 65. C2×#41⋊C3 | C2×D5 | semidirect |
| 74. C5×#41 | C22×D3 | semidirect |
| 102. C22×#41 | D15 | semidirect |
| 120. #41⋊C3 | C22×D5 | semidirect |
| 151. C2×#41 | C2×D15 | semidirect |
| 182. C22×C5 | #985 | semidirect |
| 196. #41 | C22×D15 | semidirect |
| 229. C2×C5 | C2×#985 | semidirect |
| 259. C5 | C22×#985 | semidirect |
| 264. C22 | #91955 | direct (N × H) |
| 273. C2 | C2×#91955 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#41⋊C3 | 2 |
| C2×#91955 | 2 |
| C22×C5⋊GL(2,𝔽3) | 2 |
| C22×C5⋊#226 | 2 |
| C22×#4096 | 3 |
| C22×C4×D15 | 4 |
| C22×#985 | 5 |