Finite Group DatabasebetaFinite Group DatabasebetaOrder 20480.
77942 conjugacy classes of subgroups.
The subgroup lattice has 396 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C32 | C26×C5 |
| socle, prime radical | C26×C5 | C2×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×C4×C5×C64 | C2 | direct (N × H) |
| 9. C22×C4×C5×C64 | C22 | direct (N × H) |
| 10. C24×C5×C64 | C4 | direct (N × H) |
| 12. C24×C4×C64 | C5 | direct (N × H) |
| 25. C23×C5×C64 | C2×C4 | direct (N × H) |
| 27. C2×C4×C5×C64 | C23 | direct (N × H) |
| 29. C23×C4×C64 | C2×C5 | direct (N × H) |
| 36. C22×C4×C64 | C22×C5 | direct (N × H) |
| 37. C24×C64 | C4×C5 | direct (N × H) |
| 58. C22×C5×C64 | C22×C4 | direct (N × H) |
| 62. C4×C5×C64 | C24 | direct (N × H) |
| 90. C2×C5×C64 | C23×C4 | direct (N × H) |
| 104. C23×C64 | C2×C4×C5 | direct (N × H) |
| 108. C2×C4×C64 | C23×C5 | direct (N × H) |
| 110. C24×C4×C5 | C64 | direct (N × H) |
| 142. C5×C64 | C24×C4 | direct (N × H) |
| 162. C22×C64 | C22×C4×C5 | direct (N × H) |
| 166. C4×C64 | C24×C5 | direct (N × H) |
| 171. C23×C4×C5 | C2×C64 | direct (N × H) |
| 225. C2×C64 | C23×C4×C5 | direct (N × H) |
| 229. C24×C5 | C4×C64 | direct (N × H) |
| 234. C22×C4×C5 | C22×C64 | direct (N × H) |
| 254. C24×C4 | C5×C64 | direct (N × H) |
| 286. C64 | C24×C4×C5 | direct (N × H) |
| 287. C23×C5 | C2×C4×C64 | direct (N × H) |
| 292. C2×C4×C5 | C23×C64 | direct (N × H) |
| 306. C23×C4 | C2×C5×C64 | direct (N × H) |
| 334. C22×C5 | C22×C4×C64 | direct (N × H) |
| 337. C4×C5 | C24×C64 | direct (N × H) |
| 341. C24 | C4×C5×C64 | direct (N × H) |
| 346. C22×C4 | C22×C5×C64 | direct (N × H) |
| 366. C2×C5 | C23×C4×C64 | direct (N × H) |
| 368. C23 | C2×C4×C5×C64 | direct (N × H) |
| 372. C2×C4 | C23×C5×C64 | direct (N × H) |
| 383. C5 | C24×C4×C64 | direct (N × H) |
| 385. C22 | C22×C4×C5×C64 | direct (N × H) |
| 388. C4 | C24×C5×C64 | direct (N × H) |
| 393. C2 | C23×C4×C5×C64 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C4×C5×C32 | 2 |
| C23×C4×C5×C64 | 2 |
| C25×C5×C64 | 2 |
| C24×C4×C64 | 5 |