Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
672 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 136 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×C5×#689 | C2 | semidirect |
| 4. C2×C5×#688 | C2 | semidirect |
| 5. #11717069 | C2 | direct (N × H) |
| 6. C2×#87776 | C2 | semidirect |
| 7. C2×#87773 | C2 | semidirect |
| 8. C2×#87769 | C2 | semidirect |
| 11. Q8×C5⋊D5 | C22 | semidirect |
| 22. C5×#689 | C22 | semidirect |
| 23. C5×#688 | C22 | semidirect |
| 26. #87776 | C22 | semidirect |
| 27. #87773 | C22 | semidirect |
| 28. #87769 | C22 | semidirect |
| 62. C2×#689 | D5 | semidirect |
| 63. C2×#688 | D5 | semidirect |
| 120. #689 | C2×D5 | semidirect |
| 121. #688 | C2×D5 | semidirect |
| 130. C2×C52 | #137 | semidirect |
| 201. C52 | C2×#137 | semidirect |
| 255. C2×C5 | #4061 | semidirect |
| 256. C2×C5 | #4064 | semidirect |
| 287. C5 | C2×#4061 | semidirect |
| 288. C5 | C2×#4064 | semidirect |
| 302. C2 | #11717069 | 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×#87871 | 2 |
| C2×C5×#689 | 2 |
| C2×C5×#688 | 2 |
| #11717069 | 2 |
| C2×#87776 | 2 |
| C2×#87773 | 2 |
| C2×#87769 | 2 |
| C2×#4064 | 5 |
| C2×#4061 | 5 |