Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
687 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 687 conjugacy classes of subgroups — too many to draw. Only its 194 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×C4×#1042 | C2 | semidirect |
| 3. C2×C4×C5×AGL(1,𝔽5) | C2 | semidirect |
| 4. C2×#87825 | C2 | semidirect |
| 6. #11717325 | C2 | direct (N × H) |
| 10. C2×C4×C5⋊D5 | C4 | semidirect |
| 11. C2×C4×C5×D5 | C4 | semidirect |
| 13. C2×#6036 | C4 | semidirect |
| 14. C2×D5×Dic5 | C4 | semidirect |
| 16. C4×D52 | C4 | semidirect |
| 18. C4×#1042 | C22 | semidirect |
| 19. C4×C5×AGL(1,𝔽5) | C22 | semidirect |
| 20. #87825 | C22 | semidirect |
| 36. C4×C5⋊D5 | C2×C4 | semidirect |
| 40. C4×C5×D5 | C2×C4 | semidirect |
| 42. #6036 | C2×C4 | semidirect |
| 44. D5×Dic5 | C2×C4 | semidirect |
| 52. C2×C4×AGL(1,𝔽5) | D5 | semidirect |
| 95. C2×C4×D5 | AGL(1,𝔽5) | semidirect |
| 100. C4×AGL(1,𝔽5) | C2×D5 | semidirect |
| 106. C2×C52 | #117 | semidirect |
| 110. C5×D5 | #117 | semidirect |
| 158. C4×D5 | C2×AGL(1,𝔽5) | semidirect |
| 166. C52 | C2×#117 | semidirect |
| 224. C2×C5 | #4018 | semidirect |
| 225. C2×C5 | #4130 | semidirect |
| 232. D5 | #4018 | semidirect |
| 257. C5 | C2×#4018 | semidirect |
| 258. C5 | C2×#4130 | semidirect |
| 279. C2 | #11717325 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D52 | 2 |
| C2×C4×#1042 | 2 |
| C2×C4×C5×AGL(1,𝔽5) | 2 |
| C2×#87825 | 2 |
| C2×(C2×AGL(1,𝔽5))⋊D5 | 2 |
| #11717325 | 2 |
| C2×#4130 | 5 |
| C2×#4018 | 5 |