Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
768 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 192 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×C5×Dic10 | C2 | semidirect |
| 3. C2×C4×#1039 | C2 | semidirect |
| 4. C2×#87778 | C2 | semidirect |
| 5. #11716981 | C2 | direct (N × H) |
| 13. C2×C5×Dic10 | C22 | semidirect |
| 14. C4×#1039 | C22 | semidirect |
| 15. #87778 | C22 | semidirect |
| 33. C22×Dic10 | D5 | semidirect |
| 67. C2×Dic10 | C2×D5 | semidirect |
| 74. C2×C52 | #124 | semidirect |
| 112. C52 | C2×#124 | semidirect |
| 150. C2×C5 | #4082 | semidirect |
| 151. C2×C5 | #4093 | semidirect |
| 170. C5 | C2×#4082 | semidirect |
| 171. C5 | C2×#4093 | semidirect |
| 182. C2 | #11716981 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D20 | 2 |
| C22×C5×Dic10 | 2 |
| C2×C4×#1039 | 2 |
| C2×#87778 | 2 |
| #11716981 | 2 |
| C2×#4093 | 5 |
| C2×#4082 | 5 |