Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
752 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 182 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×C22⋊Dic5 | C2 | semidirect |
| 3. C2×C5×C4⋊Dic5 | C2 | semidirect |
| 4. C2×C4×C5×Dic5 | C2 | semidirect |
| 8. C2×C52×D4 | C4 | semidirect |
| 16. #65510 | C5 | direct (N × H) |
| 31. C2×C5×Dic5 | D4 | semidirect |
| 38. C2×C22⋊Dic5 | C2×C5 | semidirect |
| 39. C2×C4⋊Dic5 | C2×C5 | semidirect |
| 40. C2×C4×Dic5 | C2×C5 | semidirect |
| 51. C4×C52 | C22⋊C4 | semidirect |
| 64. C2×C5×D4 | Dic5 | semidirect |
| 65. C2×C5×D4 | C4×C5 | semidirect |
| 125. C2×Dic5 | C5×D4 | semidirect |
| 130. C52 | #390 | semidirect |
| 164. C4×C5 | C22⋊Dic5 | semidirect |
| 165. C4×C5 | C5×C22⋊C4 | semidirect |
| 171. C2×D4 | C5×Dic5 | semidirect |
| 212. C5 | #65510 | direct (N × H) |
| 213. C5 | C5×#390 | semidirect |
| 226. C4 | C5×C22⋊Dic5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D4 | 2 |
| C2×C5×C22⋊Dic5 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C2×C4×C5×Dic5 | 2 |
| C5×#390 | 5 |
| #65510 | 5 |