Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
533 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 533 conjugacy classes of subgroups — too many to draw. Only its 133 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×#1042 | C2 | semidirect |
| 5. #11716849 | C2 | semidirect |
| 8. C22×#1042 | C4 | semidirect |
| 13. C22⋊#1042 | C4 | semidirect |
| 15. C52×C22⋊C4 | C4 | semidirect |
| 16. C5×C22⋊Dic5 | C4 | semidirect |
| 17. C5×#685 | C4 | semidirect |
| 33. C2×#1042 | C2×C4 | semidirect |
| 35. C2×C4×C52 | C2×C4 | semidirect |
| 36. C2×C5×Dic5 | C2×C4 | semidirect |
| 50. C22×C52 | C42 | semidirect |
| 56. C2×C5×D5 | C42 | semidirect |
| 63. #1042 | C22⋊C4 | direct (N × H) |
| 85. C5×C22⋊C4 | Dic5 | semidirect |
| 86. C5×C22⋊C4 | AGL(1,𝔽5) | semidirect |
| 88. C22⋊Dic5 | Dic5 | semidirect |
| 89. #685 | Dic5 | semidirect |
| 126. C2×C4×C5 | C2×Dic5 | semidirect |
| 127. C2×C4×C5 | C2×AGL(1,𝔽5) | semidirect |
| 136. C2×Dic5 | C2×Dic5 | semidirect |
| 144. C52 | C4×C22⋊C4 | semidirect |
| 159. C22×C5 | C4×Dic5 | semidirect |
| 160. C22×C5 | C4×AGL(1,𝔽5) | semidirect |
| 167. C2×D5 | C4×Dic5 | semidirect |
| 193. C22⋊C4 | #1042 | direct (N × H) |
| 230. C2×C4 | C2×#1042 | semidirect |
| 232. C5 | C22⋊C4×Dic5 | semidirect |
| 233. C5 | C22⋊C4×AGL(1,𝔽5) | semidirect |
| 244. C22 | C4×#1042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1042 | 2 |
| C2×C22⋊#1042 | 2 |
| C2×C4×#1042 | 2 |
| C5×D5×C22⋊C4 | 2 |
| #11716849 | 2 |
| C22⋊C4×AGL(1,𝔽5) | 5 |
| C22⋊C4×Dic5 | 5 |