Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
896 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 896 conjugacy classes of subgroups — too many to draw. Only its 176 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 |
|---|---|---|
| 3. C5×#3963 | C2 | semidirect |
| 4. #11716620 | C2 | semidirect |
| 9. C2×C4×C5⋊D5 | C4 | semidirect |
| 13. C2×#6036 | C4 | semidirect |
| 22. C2×C4×C52 | C2×C4 | semidirect |
| 24. C2×#1039 | C2×C4 | semidirect |
| 28. C2×C5×Dic5 | C2×C4 | semidirect |
| 35. #3963 | D5 | semidirect |
| 70. C5⋊D5 | #95 | semidirect |
| 89. C2×C4×C5 | C4×D5 | semidirect |
| 96. C2×Dic5 | C4×D5 | semidirect |
| 104. C52 | C2×#95 | semidirect |
| 166. C2×C4 | #6036 | semidirect |
| 168. C5 | D5×#95 | 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 |
| C22×#6036 | 2 |
| C5×#3963 | 2 |
| #11716620 | 2 |
| D5×#95 | 5 |