Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1072 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 250 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 |
|---|---|---|
| 3. C2×C4⋊#1044 | C2 | direct (N × H) |
| 7. C22×C4×C52 | C4 | semidirect |
| 8. C22×#1039 | C4 | semidirect |
| 9. C2×C4×C5⋊D5 | C4 | semidirect |
| 11. C4⋊#1044 | C22 | direct (N × H) |
| 20. C2×C4×C52 | C2×C4 | semidirect |
| 21. C2×#1039 | C2×C4 | semidirect |
| 22. C4×C5⋊D5 | C2×C4 | semidirect |
| 28. C22×C52 | C4⋊C4 | semidirect |
| 30. C2×C5⋊D5 | C4⋊C4 | semidirect |
| 36. C4×C52 | C22×C4 | semidirect |
| 37. #1039 | C22×C4 | semidirect |
| 43. C22×C4×C5 | AGL(1,𝔽5) | semidirect |
| 52. C2×C52 | C2×C4⋊C4 | semidirect |
| 54. C5⋊D5 | C2×C4⋊C4 | semidirect |
| 70. C2×C4×C5 | C2×AGL(1,𝔽5) | semidirect |
| 80. C52 | C22×C4⋊C4 | semidirect |
| 83. C22×C5 | C4⋊AGL(1,𝔽5) | semidirect |
| 97. C4×C5 | C22×AGL(1,𝔽5) | semidirect |
| 106. C22×C4 | #1044 | semidirect |
| 110. C2×C5 | C2×C4⋊AGL(1,𝔽5) | semidirect |
| 128. C2×C4 | C2×#1044 | semidirect |
| 130. C5 | C22×C4⋊AGL(1,𝔽5) | semidirect |
| 136. C22 | C4⋊#1044 | direct (N × H) |
| 140. C4 | C22×#1044 | semidirect |
| 144. C2 | C2×C4⋊#1044 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1044 | 2 |
| C22×C4×C5⋊D5 | 2 |
| C2×C4⋊#1044 | 2 |
| C22×C4⋊AGL(1,𝔽5) | 5 |