Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
816 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 176 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. C22×D5×Dic5 | C2 | semidirect |
| 3. C2×C22⋊#1039 | C2 | semidirect |
| 4. C2×C5×C22⋊Dic5 | C2 | semidirect |
| 5. #11717087 | C2 | direct (N × H) |
| 6. C2×#87781 | C2 | semidirect |
| 7. C2×#87780 | C2 | semidirect |
| 8. C2×#87778 | C2 | semidirect |
| 19. C2×D5×Dic5 | C22 | semidirect |
| 20. C22⋊#1039 | C22 | semidirect |
| 21. C5×C22⋊Dic5 | C22 | semidirect |
| 22. #87781 | C22 | semidirect |
| 23. #87780 | C22 | semidirect |
| 24. #87778 | C22 | semidirect |
| 57. C2×C22⋊Dic5 | D5 | semidirect |
| 112. C22⋊Dic5 | C2×D5 | semidirect |
| 120. C2×C52 | #123 | semidirect |
| 184. C52 | C2×#123 | semidirect |
| 253. C2×C5 | #4029 | semidirect |
| 254. C2×C5 | #4081 | semidirect |
| 284. C5 | C2×#4029 | semidirect |
| 285. C5 | C2×#4081 | semidirect |
| 305. C2 | #11717087 | 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 |
| C22×D5×Dic5 | 2 |
| C2×C22⋊#1039 | 2 |
| C2×C5×C22⋊Dic5 | 2 |
| #11717087 | 2 |
| C2×#87781 | 2 |
| C2×#87780 | 2 |
| C2×#87778 | 2 |
| C2×#4081 | 5 |
| C2×#4029 | 5 |