Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
896 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 896 conjugacy classes of subgroups — too many to draw. Only its 232 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 |
| 3. C2×#87781 | C2 | semidirect |
| 5. #11716992 | C2 | direct (N × H) |
| 9. C2×C4×C5⋊D5 | C4 | semidirect |
| 12. C4×C5×Dic5 | C22 | semidirect |
| 13. #87781 | C22 | semidirect |
| 24. C4×C5⋊D5 | C2×C4 | semidirect |
| 32. C2×C4×Dic5 | D5 | semidirect |
| 58. C4×Dic5 | C2×D5 | semidirect |
| 60. C2×C52 | #117 | semidirect |
| 91. C52 | C2×#117 | semidirect |
| 122. C2×C5 | #4018 | semidirect |
| 139. C5 | C2×#4018 | semidirect |
| 150. C2 | #11716992 | 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×#87781 | 2 |
| C2×#87779 | 2 |
| #11716992 | 2 |
| C2×#4018 | 5 |