Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
432 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 1. C52×#127 | C2 | semidirect |
| 2. C2×C5×#686 | C2 | semidirect |
| 3. C5×#4020 | C2 | semidirect |
| 4. C4×C5×#168 | C2 | semidirect |
| 13. #65362 | C5 | direct (N × H) |
| 22. C5×#168 | D4 | semidirect |
| 26. C5×#127 | D5 | semidirect |
| 27. C5×#127 | C2×C5 | semidirect |
| 28. C2×#686 | C2×C5 | semidirect |
| 29. #4020 | C2×C5 | semidirect |
| 31. C4×#168 | C2×C5 | semidirect |
| 37. C4×C52 | D8 | semidirect |
| 83. #168 | C5×D4 | semidirect |
| 86. #127 | C5×D5 | semidirect |
| 88. C52 | #493 | semidirect |
| 104. C4×C5 | #686 | semidirect |
| 105. C4×C5 | C5×D8 | semidirect |
| 136. C5 | #65362 | direct (N × H) |
| 137. C5 | C5×#493 | semidirect |
| 143. C4 | C5×#686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#127 | 2 |
| C2×C5×#686 | 2 |
| C5×#4020 | 2 |
| C4×C5×#168 | 2 |
| C5×#493 | 5 |
| #65362 | 5 |