Finite Group DatabasebetaFinite Group DatabasebetaOrder 800.
138 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 38 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. C52×C22⋊C4 | C2 | semidirect |
| 3. C5×C22⋊Dic5 | C2 | semidirect |
| 5. C22×C5×D5 | C4 | semidirect |
| 10. C2×C5×Dic5 | C4 | semidirect |
| 12. #3938 | C5 | direct (N × H) |
| 26. C5×C22⋊C4 | D5 | semidirect |
| 27. C5×C22⋊C4 | C2×C5 | semidirect |
| 28. C22⋊Dic5 | C2×C5 | semidirect |
| 38. C22×D5 | C4×C5 | semidirect |
| 49. C2×Dic5 | C4×C5 | semidirect |
| 51. C52 | #99 | semidirect |
| 77. C22⋊C4 | C5×D5 | semidirect |
| 100. C5 | #3938 | direct (N × H) |
| 101. C5 | C5×#99 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C22⋊D5 | 2 |
| C52×C22⋊C4 | 2 |
| C5×C22⋊Dic5 | 2 |
| C5×#99 | 5 |
| #3938 | 5 |