Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
559 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 559 conjugacy classes of subgroups — too many to draw. Only its 178 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×#87853 | C2 | semidirect |
| 3. C22×C5×#170 | C2 | semidirect |
| 4. C2×#87829 | C2 | semidirect |
| 5. C2×#87828 | C2 | semidirect |
| 6. C2×#87827 | C2 | semidirect |
| 7. #11717343 | C2 | direct (N × H) |
| 8. C2×D5×#170 | C2 | semidirect |
| 18. #87853 | C22 | semidirect |
| 23. C2×C5×#170 | C22 | semidirect |
| 24. #87829 | C22 | semidirect |
| 25. #87828 | C22 | semidirect |
| 26. #87827 | C22 | semidirect |
| 27. D5×#170 | C22 | semidirect |
| 56. C22×#170 | D5 | semidirect |
| 105. C2×#170 | C2×D5 | semidirect |
| 120. C2×C52 | #131 | semidirect |
| 178. C52 | C2×#131 | semidirect |
| 234. C2×C5 | #4047 | semidirect |
| 235. C2×C5 | #4131 | semidirect |
| 264. C5 | C2×#4047 | semidirect |
| 265. C5 | C2×#4131 | semidirect |
| 281. C2 | #11717343 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87879 | 2 |
| C2×#87853 | 2 |
| C22×C5×#170 | 2 |
| C2×#87829 | 2 |
| C2×#87828 | 2 |
| C2×#87827 | 2 |
| #11717343 | 2 |
| C2×D5×#170 | 2 |
| C2×#4131 | 5 |
| C2×#4047 | 5 |