Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
752 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 168 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×C4×C5×Dic5 | C2 | semidirect |
| 4. #11716620 | C2 | semidirect |
| 9. C2×C4×C5⋊D5 | C4 | semidirect |
| 12. #87779 | C4 | direct (N × H) |
| 26. C2×C5×Dic5 | C2×C4 | semidirect |
| 31. C2×C4×Dic5 | D5 | semidirect |
| 40. C2×C5⋊D5 | C42 | semidirect |
| 41. C4×C52 | C22⋊C4 | semidirect |
| 92. C2×Dic5 | C4×D5 | semidirect |
| 99. C52 | C4×C22⋊C4 | semidirect |
| 120. C4×C5 | #685 | semidirect |
| 157. C5 | C4×#685 | semidirect |
| 168. C4 | #87779 | direct (N × H) |
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×C4×C5×Dic5 | 2 |
| C2×#87779 | 2 |
| #11716620 | 2 |
| C4×#685 | 5 |