Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
487 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 487 conjugacy classes of subgroups — too many to draw. Only its 104 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. C2×C5×C22⋊AGL(1,𝔽5) | C2 | semidirect |
| 3. C5×#4011 | C2 | direct (N × H) |
| 4. C24×C52 | C4 | semidirect |
| 9. C2×C5×C22⋊D5 | C4 | semidirect |
| 11. C22×C5×Dic5 | C4 | semidirect |
| 13. C5×C22⋊AGL(1,𝔽5) | C22 | semidirect |
| 14. C2×#4011 | C5 | direct (N × H) |
| 20. C23×C52 | C2×C4 | semidirect |
| 32. C2×C5×Dic5 | C2×C4 | semidirect |
| 35. C2×C22⋊AGL(1,𝔽5) | C2×C5 | semidirect |
| 37. #4011 | C2×C5 | direct (N × H) |
| 57. C24×C5 | C4×C5 | semidirect |
| 58. C24×C5 | AGL(1,𝔽5) | semidirect |
| 69. C2×C22⋊D5 | C4×C5 | semidirect |
| 71. C22×Dic5 | C4×C5 | semidirect |
| 73. C22⋊AGL(1,𝔽5) | C22×C5 | semidirect |
| 80. C2×C52 | #99 | semidirect |
| 101. C23×C5 | C2×C4×C5 | semidirect |
| 103. C23×C5 | C2×AGL(1,𝔽5) | semidirect |
| 122. C2×Dic5 | C2×C4×C5 | semidirect |
| 126. C52 | C2×#99 | semidirect |
| 168. C24 | C5×AGL(1,𝔽5) | semidirect |
| 190. C2×C5 | C5×#99 | semidirect |
| 191. C2×C5 | #4011 | direct (N × H) |
| 205. C23 | C2×C5×AGL(1,𝔽5) | semidirect |
| 214. C5 | C2×C5×#99 | semidirect |
| 215. C5 | C2×#4011 | direct (N × H) |
| 237. C2 | C5×#4011 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C22⋊D5 | 2 |
| C2×C5×C22⋊AGL(1,𝔽5) | 2 |
| C5×#4011 | 2 |
| C2×#4011 | 5 |
| C2×C5×#99 | 5 |