Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
6338 conjugacy classes of subgroups; only the 1291 normal subgroups are shown.
This group has 6338 conjugacy classes of subgroups — too many to draw. Only its 1291 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C22×#87832 | C2 | direct (N × H) |
| 10. C23×C5×Dic5 | C4 | semidirect |
| 11. C22×#6036 | C4 | semidirect |
| 13. C2×#87832 | C22 | direct (N × H) |
| 24. C22×C5×Dic5 | C2×C4 | semidirect |
| 25. C2×#6036 | C2×C4 | semidirect |
| 27. #87832 | C23 | direct (N × H) |
| 33. C23×C52 | C4⋊C4 | semidirect |
| 35. C22×C5⋊D5 | C4⋊C4 | semidirect |
| 44. C2×C5×Dic5 | C22×C4 | semidirect |
| 45. #6036 | C22×C4 | semidirect |
| 56. C23×Dic5 | AGL(1,𝔽5) | semidirect |
| 61. C22×C52 | C2×C4⋊C4 | semidirect |
| 63. C2×C5⋊D5 | C2×C4⋊C4 | semidirect |
| 70. C5×Dic5 | C23×C4 | semidirect |
| 88. C22×Dic5 | C2×AGL(1,𝔽5) | semidirect |
| 96. C2×C52 | C22×C4⋊C4 | semidirect |
| 98. C5⋊D5 | C22×C4⋊C4 | semidirect |
| 103. C23×C5 | C4⋊AGL(1,𝔽5) | semidirect |
| 122. C2×Dic5 | C22×AGL(1,𝔽5) | semidirect |
| 134. C52 | C23×C4⋊C4 | semidirect |
| 137. C22×C5 | C2×C4⋊AGL(1,𝔽5) | semidirect |
| 153. Dic5 | C23×AGL(1,𝔽5) | semidirect |
| 169. C2×C5 | C22×C4⋊AGL(1,𝔽5) | semidirect |
| 182. C23 | #87832 | direct (N × H) |
| 192. C5 | C23×C4⋊AGL(1,𝔽5) | semidirect |
| 198. C22 | C2×#87832 | direct (N × H) |
| 206. C2 | C22×#87832 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#1044 | 2 |
| C24×#1043 | 2 |
| C23×#6036 | 2 |
| C22×#87832 | 2 |
| C23×C4⋊AGL(1,𝔽5) | 5 |