Finite Group DatabasebetaFinite Group DatabasebetaOrder 800.
190 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 62 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×C4×C5×D5 | C2 | semidirect |
| 3. C52×C22⋊C4 | C2 | semidirect |
| 4. C5×C22⋊Dic5 | C2 | semidirect |
| 5. C5×#685 | C2 | semidirect |
| 6. C5×C4⋊Dic5 | C2 | semidirect |
| 7. C5×#683 | C2 | semidirect |
| 18. #4029 | C5 | direct (N × H) |
| 34. C2×C4×D5 | C2×C5 | semidirect |
| 40. C5×C22⋊C4 | D5 | semidirect |
| 41. C5×C22⋊C4 | C2×C5 | semidirect |
| 42. C22⋊Dic5 | C2×C5 | semidirect |
| 43. #685 | C2×C5 | semidirect |
| 44. C4⋊Dic5 | C2×C5 | semidirect |
| 45. #683 | C2×C5 | semidirect |
| 73. C52 | #123 | semidirect |
| 110. C22⋊C4 | C5×D5 | semidirect |
| 135. C5 | #4029 | direct (N × H) |
| 136. C5 | C5×#123 | 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 |
| C2×C4×C5×D5 | 2 |
| C52×C22⋊C4 | 2 |
| C5×C22⋊Dic5 | 2 |
| C5×#685 | 2 |
| C5×C4⋊Dic5 | 2 |
| C5×#683 | 2 |
| C5×#123 | 5 |
| #4029 | 5 |