Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
2096 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 2096 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 |
|---|---|---|
| 2. C23×#1044 | C2 | semidirect |
| 3. C2×C22⋊#1044 | C2 | direct (N × H) |
| 4. C24×C52 | C4 | semidirect |
| 6. C23×C5⋊D5 | C4 | semidirect |
| 7. C23×C5⋊D5 | C4 | semidirect |
| 11. C22×#1044 | C22 | semidirect |
| 12. C22⋊#1044 | C22 | direct (N × H) |
| 16. C23×C52 | C2×C4 | semidirect |
| 21. C22×C5⋊D5 | C2×C4 | semidirect |
| 22. C22×C5⋊D5 | C2×C4 | semidirect |
| 27. C2×#1044 | C23 | semidirect |
| 33. C22×C52 | C22⋊C4 | semidirect |
| 35. C22×C52 | C22×C4 | semidirect |
| 39. C2×C5⋊D5 | C22⋊C4 | semidirect |
| 41. C2×C5⋊D5 | C22×C4 | semidirect |
| 46. C24×C5 | AGL(1,𝔽5) | semidirect |
| 62. C2×C52 | C2×C22⋊C4 | semidirect |
| 65. C5⋊D5 | C2×C22⋊C4 | semidirect |
| 72. C23×C5 | C2×AGL(1,𝔽5) | semidirect |
| 96. C52 | C22×C22⋊C4 | semidirect |
| 102. C22×C5 | C22⋊AGL(1,𝔽5) | semidirect |
| 104. C22×C5 | C22×AGL(1,𝔽5) | semidirect |
| 127. C24 | #1044 | semidirect |
| 135. C2×C5 | C2×C22⋊AGL(1,𝔽5) | semidirect |
| 154. C23 | C2×#1044 | semidirect |
| 158. C5 | C22×C22⋊AGL(1,𝔽5) | semidirect |
| 168. C22 | C22⋊#1044 | direct (N × H) |
| 170. C22 | C22×#1044 | semidirect |
| 176. C2 | C2×C22⋊#1044 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C5⋊D5 | 2 |
| C23×#1044 | 2 |
| C2×C22⋊#1044 | 2 |
| C22×C22⋊AGL(1,𝔽5) | 5 |