Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
920 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 920 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. C22×#6036 | C2 | semidirect |
| 3. C2×C5×#683 | C2 | semidirect |
| 4. C2×#87779 | C2 | semidirect |
| 5. C2×#87779 | C2 | semidirect |
| 6. #11717016 | C2 | direct (N × H) |
| 15. C2×#6036 | C22 | semidirect |
| 16. C5×#683 | C22 | semidirect |
| 17. #87779 | C22 | semidirect |
| 18. #87779 | C22 | semidirect |
| 42. C2×#683 | D5 | semidirect |
| 76. #683 | C2×D5 | semidirect |
| 78. C2×C52 | #123 | semidirect |
| 120. C52 | C2×#123 | semidirect |
| 163. C2×C5 | #4040 | semidirect |
| 187. C5 | C2×#4040 | semidirect |
| 202. C2 | #11717016 | 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 |
| C22×#6036 | 2 |
| C2×C5×#683 | 2 |
| C2×#87779 | 2 |
| #11717016 | 2 |
| C2×#4040 | 5 |