Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1032 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1032 conjugacy classes of subgroups — too many to draw. Only its 235 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 |
|---|---|---|
| 1. C2×Q8×C5⋊D5 | C2 | semidirect |
| 3. C2×C52×SD16 | C2 | semidirect |
| 4. C2×#87812 | C2 | semidirect |
| 5. C2×#87810 | C2 | semidirect |
| 6. #11717235 | C2 | direct (N × H) |
| 7. C2×#87802 | C2 | semidirect |
| 8. C2×#87799 | C2 | semidirect |
| 14. Q8×C5⋊D5 | C22 | semidirect |
| 22. C52×SD16 | C22 | semidirect |
| 24. #87812 | C22 | semidirect |
| 25. #87810 | C22 | semidirect |
| 27. #87802 | C22 | semidirect |
| 28. #87799 | C22 | semidirect |
| 55. C2×C5×SD16 | D5 | semidirect |
| 85. C5×SD16 | C2×D5 | semidirect |
| 94. C2×C52 | #137 | semidirect |
| 126. C2×SD16 | C5⋊D5 | semidirect |
| 128. C52 | C2×#137 | semidirect |
| 156. SD16 | C2×C5⋊D5 | semidirect |
| 161. C2×C5 | #4061 | semidirect |
| 187. C5 | C2×#4061 | semidirect |
| 201. C2 | #11717235 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C5⋊D5 | 2 |
| C2×#87902 | 2 |
| C2×C52×SD16 | 2 |
| C2×#87812 | 2 |
| C2×#87810 | 2 |
| #11717235 | 2 |
| C2×#87802 | 2 |
| C2×#87799 | 2 |
| C2×#4061 | 5 |