Finite Group DatabasebetaFinite Group DatabasebetaOrder 800.
174 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 66 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. C52×C4⋊C4 | C2 | semidirect |
| 6. C5×#683 | C2 | semidirect |
| 7. C5×#683 | C2 | semidirect |
| 18. #4042 | C5 | direct (N × H) |
| 22. C2×C5×D5 | Q8 | semidirect |
| 32. C2×Dic10 | C2×C5 | semidirect |
| 36. C5×C4⋊C4 | D5 | semidirect |
| 37. C5×C4⋊C4 | C2×C5 | semidirect |
| 42. #683 | C2×C5 | semidirect |
| 43. #683 | C2×C5 | semidirect |
| 70. C52 | C22⋊Q8 | semidirect |
| 79. C2×D5 | C5×Q8 | semidirect |
| 99. C4⋊C4 | C5×D5 | semidirect |
| 123. C5 | #4042 | direct (N × H) |
| 124. C5 | C5×C22⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×D5 | 2 |
| C2×C5×Dic10 | 2 |
| C52×C4⋊C4 | 2 |
| C5×#685 | 2 |
| C5×#683 | 2 |
| C5×C22⋊Q8 | 5 |
| #4042 | 5 |