Finite Group DatabasebetaFinite Group DatabasebetaOrder 800.
158 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 52 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×C5×Dic10 | C2 | semidirect |
| 3. C2×#6029 | C2 | semidirect |
| 4. #87772 | C2 | direct (N × H) |
| 11. C5×Dic10 | C22 | semidirect |
| 12. #6029 | C22 | semidirect |
| 24. C2×Dic10 | D5 | semidirect |
| 30. C2×C52 | SD16 | semidirect |
| 47. Dic10 | C2×D5 | semidirect |
| 52. C52 | C2×SD16 | semidirect |
| 75. C2×C5 | #687 | semidirect |
| 76. C2×C5 | #688 | semidirect |
| 89. C5 | C2×#687 | semidirect |
| 90. C5 | C2×#688 | semidirect |
| 98. C2 | #87772 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D20 | 2 |
| C2×C5×Dic10 | 2 |
| C2×#6029 | 2 |
| #87772 | 2 |
| C2×#688 | 5 |
| C2×#687 | 5 |