Finite Group DatabasebetaFinite Group DatabasebetaOrder 20480.
4038 conjugacy classes of subgroups.
The subgroup lattice has 200 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C162 | C23×C5 |
| socle, prime radical | C23×C5 | C2×C162 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C5×C322 | C4 | direct (N × H) |
| 8. C4×C322 | C5 | direct (N × H) |
| 23. C322 | C4×C5 | direct (N × H) |
| 43. C4×C5×C32 | C32 | direct (N × H) |
| 99. C5×C32 | C4×C32 | direct (N × H) |
| 107. C4×C32 | C5×C32 | direct (N × H) |
| 163. C32 | C4×C5×C32 | direct (N × H) |
| 166. C4×C5 | C322 | direct (N × H) |
| 191. C5 | C4×C322 | direct (N × H) |
| 194. C4 | C5×C322 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×C16×C32 | 2 |
| C2×C5×C322 | 2 |
| C4×C322 | 5 |