Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
5088 conjugacy classes of subgroups; only the 1014 normal subgroups are shown.
This group has 5088 conjugacy classes of subgroups — too many to draw. Only its 1014 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | #1043 |
| commutator, hypocenter | C52 | C2×C43 |
| Frattini | C22 | C23×#1043 |
| Fitting | C2×C42×C52 | C4 |
| socle | C23×C52 | C22×C4 |
| prime radical | C23×C5⋊D5 | C23 |
| cosocle | C22×C5⋊D5 | C24 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C42×#1043 | C2 | direct (N × H) |
| 6. C2×C4×#1043 | C4 | direct (N × H) |
| 8. C2×C42×C52 | C4 | semidirect |
| 9. C2×C4×#1039 | C4 | semidirect |
| 10. C42×C5⋊D5 | C4 | semidirect |
| 21. C4×#1043 | C2×C4 | direct (N × H) |
| 22. C42×C52 | C2×C4 | semidirect |
| 23. C4×#1039 | C2×C4 | semidirect |
| 31. C2×#1043 | C42 | direct (N × H) |
| 33. C2×C4×C52 | C42 | semidirect |
| 35. C2×#1039 | C42 | semidirect |
| 37. C4×C5⋊D5 | C42 | semidirect |
| 43. C2×C42×C5 | AGL(1,𝔽5) | semidirect |
| 53. #1043 | C2×C42 | direct (N × H) |
| 54. C4×C52 | C2×C42 | semidirect |
| 55. #1039 | C2×C42 | semidirect |
| 65. C42×C5 | C2×AGL(1,𝔽5) | semidirect |
| 70. C2×C52 | C43 | semidirect |
| 72. C5⋊D5 | C43 | semidirect |
| 80. C2×C4×C5 | C4×AGL(1,𝔽5) | semidirect |
| 93. C2×C42 | #1043 | direct (N × H) |
| 94. C52 | C2×C43 | semidirect |
| 101. C4×C5 | C2×C4×AGL(1,𝔽5) | semidirect |
| 113. C42 | C2×#1043 | direct (N × H) |
| 114. C2×C5 | C42×AGL(1,𝔽5) | semidirect |
| 128. C2×C4 | C4×#1043 | direct (N × H) |
| 130. C5 | C2×C42×AGL(1,𝔽5) | semidirect |
| 138. C4 | C2×C4×#1043 | direct (N × H) |
| 141. C2 | C42×#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 |
| C2×C42×C5⋊D5 | 2 |
| C42×#1043 | 2 |
| C2×C42×AGL(1,𝔽5) | 5 |