Finite Group DatabasebetaFinite Group DatabasebetaOrder 800.
160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 3. C4⋊#1042 | C2 | semidirect |
| 4. C4×#1042 | C2 | semidirect |
| 7. C2×C4×C52 | C4 | semidirect |
| 8. C2×C5×Dic5 | C4 | semidirect |
| 9. C4×C5×D5 | C4 | semidirect |
| 10. C4×C5×D5 | C4 | semidirect |
| 45. C2×C4×C5 | Dic5 | semidirect |
| 46. C2×C4×C5 | AGL(1,𝔽5) | semidirect |
| 48. C2×Dic5 | Dic5 | semidirect |
| 49. C4×D5 | Dic5 | semidirect |
| 50. C4×D5 | Dic5 | semidirect |
| 54. C52 | #117 | semidirect |
| 97. C2×C4 | #1042 | semidirect |
| 99. C5 | #4072 | semidirect |
| 100. C5 | #4130 | 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 |
| C22⋊#1042 | 2 |
| C4⋊#1042 | 2 |
| C4×#1042 | 2 |
| #4130 | 5 |
| #4072 | 5 |