Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
3040 conjugacy classes of subgroups; only the 646 normal subgroups are shown.
This group has 3040 conjugacy classes of subgroups — too many to draw. Only its 646 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×C8 | #1043 |
| commutator, hypocenter | C52 | C22×C4×C8 |
| Frattini | C4 | C23×#1043 |
| Fitting | C22×C52×C8 | C4 |
| socle | C23×C52 | C42 |
| prime radical | C23×C5⋊D5 | C2×C4 |
| cosocle | C4×C5⋊D5 | C24 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×C8×#1043 | C2 | direct (N × H) |
| 7. C22×#6033 | C4 | semidirect |
| 10. C2×#87855 | C4 | semidirect |
| 12. C22×C52×C8 | C4 | semidirect |
| 13. C22×#6029 | C4 | semidirect |
| 14. C2×C8×C5⋊D5 | C4 | semidirect |
| 16. C8×#1043 | C22 | direct (N × H) |
| 19. C22×#1043 | C8 | direct (N × H) |
| 27. C2×#6033 | C2×C4 | semidirect |
| 30. #87855 | C2×C4 | semidirect |
| 32. C2×C52×C8 | C2×C4 | semidirect |
| 33. C2×#6029 | C2×C4 | semidirect |
| 34. C8×C5⋊D5 | C2×C4 | semidirect |
| 44. C2×#1043 | C2×C8 | direct (N × H) |
| 55. #6033 | C22×C4 | semidirect |
| 56. C52×C8 | C22×C4 | semidirect |
| 57. #6029 | C22×C4 | semidirect |
| 65. C22×C5×C8 | AGL(1,𝔽5) | semidirect |
| 71. C22×C52 | C4×C8 | semidirect |
| 73. C2×C5⋊D5 | C4×C8 | semidirect |
| 77. #1043 | C22×C8 | direct (N × H) |
| 96. C2×C5×C8 | C2×AGL(1,𝔽5) | semidirect |
| 104. C2×C52 | C2×C4×C8 | semidirect |
| 106. C5⋊D5 | C2×C4×C8 | semidirect |
| 124. C5×C8 | C22×AGL(1,𝔽5) | semidirect |
| 134. C22×C8 | #1043 | direct (N × H) |
| 138. C52 | C22×C4×C8 | semidirect |
| 139. C22×C5 | C8×AGL(1,𝔽5) | semidirect |
| 165. C2×C8 | C2×#1043 | direct (N × H) |
| 168. C2×C5 | C2×C8×AGL(1,𝔽5) | semidirect |
| 189. C8 | C22×#1043 | direct (N × H) |
| 190. C5 | C22×C8×AGL(1,𝔽5) | semidirect |
| 195. C22 | C8×#1043 | direct (N × H) |
| 204. C2 | C2×C8×#1043 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#1043 | 2 |
| C22×#87855 | 2 |
| C22×C8×C5⋊D5 | 2 |
| C2×C8×#1043 | 2 |
| C22×C8×AGL(1,𝔽5) | 5 |