Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
752 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 144 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×C4⋊Dic5 | C2 | semidirect |
| 3. C2×C4×C5×Dic5 | C2 | semidirect |
| 4. C2×#87779 | C2 | semidirect |
| 9. C2×C4⋊(C5⋊D5) | C4 | semidirect |
| 31. C2×C5×Dic5 | D4 | semidirect |
| 39. C2×C4⋊Dic5 | D5 | semidirect |
| 40. C2×C4×Dic5 | D5 | semidirect |
| 51. C4×C52 | C22⋊C4 | semidirect |
| 122. C2×Dic5 | D20 | semidirect |
| 130. C52 | #390 | semidirect |
| 164. C4×C5 | #685 | semidirect |
| 165. C4×C5 | #685 | semidirect |
| 212. C5 | #65228 | semidirect |
| 213. C5 | #65277 | semidirect |
| 226. C4 | #87779 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C5⋊D5) | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C2×C4×C5×Dic5 | 2 |
| C2×#87779 | 2 |
| #65277 | 5 |
| #65228 | 5 |