Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
303 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 303 conjugacy classes of subgroups — too many to draw. Only its 152 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. C5×#4004 | C2 | direct (N × H) |
| 11. C2×#4004 | C5 | direct (N × H) |
| 16. C2×C5×Dic5 | C8 | semidirect |
| 27. #4004 | C2×C5 | direct (N × H) |
| 35. C5×Dic5 | C2×C8 | semidirect |
| 54. C2×C52 | C4⋊C8 | semidirect |
| 73. C2×Dic5 | C5×C8 | semidirect |
| 84. C52 | C2×C4⋊C8 | semidirect |
| 105. Dic5 | C2×C5×C8 | semidirect |
| 119. C2×C5 | C5×C4⋊C8 | semidirect |
| 120. C2×C5 | #4004 | direct (N × H) |
| 138. C5 | C2×C5×C4⋊C8 | semidirect |
| 139. C5 | C2×#4004 | direct (N × H) |
| 149. C2 | C5×#4004 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#170 | 2 |
| C2×C4×C5×Dic5 | 2 |
| C5×#4004 | 2 |
| C2×#4004 | 5 |
| C2×C5×C4⋊C8 | 5 |