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×D5⋊#168 | C2 | semidirect |
| 3. C2×C5×#700 | C2 | semidirect |
| 4. C2×#87829 | C2 | semidirect |
| 5. C2×#87827 | C2 | semidirect |
| 6. #11717332 | C2 | direct (N × H) |
| 16. D5⋊#168 | C22 | semidirect |
| 18. C5×#700 | C22 | semidirect |
| 19. #87829 | C22 | semidirect |
| 20. #87827 | C22 | semidirect |
| 42. C2×#700 | D5 | semidirect |
| 78. #700 | C2×D5 | semidirect |
| 89. C2×C52 | #131 | semidirect |
| 132. C52 | C2×#131 | semidirect |
| 172. C2×C5 | #4053 | semidirect |
| 173. C2×C5 | #4133 | semidirect |
| 196. C5 | C2×#4053 | semidirect |
| 197. C5 | C2×#4133 | semidirect |
| 209. C2 | #11717332 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87874 | 2 |
| C2×D5⋊#168 | 2 |
| C2×C5×#700 | 2 |
| C2×#87829 | 2 |
| C2×#87827 | 2 |
| #11717332 | 2 |
| C2×#4133 | 5 |
| C2×#4053 | 5 |