Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
576 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 160 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. C2×#87812 | C2 | semidirect |
| 4. C2×C5×#689 | C2 | semidirect |
| 5. D5×#689 | C2 | direct (N × H) |
| 6. C2×#87776 | C2 | semidirect |
| 7. C2×#87775 | C2 | semidirect |
| 22. #87812 | C22 | semidirect |
| 24. C5×#689 | C22 | semidirect |
| 26. #87776 | C22 | semidirect |
| 27. #87775 | C22 | semidirect |
| 66. C2×#689 | D5 | direct (N × H) |
| 72. C2×C5×D5 | Q16 | semidirect |
| 117. #689 | C2×D5 | direct (N × H) |
| 126. C2×C52 | C2×Q16 | semidirect |
| 128. C5×D5 | C2×Q16 | semidirect |
| 191. C52 | C22×Q16 | semidirect |
| 197. C2×D5 | #689 | direct (N × H) |
| 240. C2×C5 | D5×Q16 | semidirect |
| 241. C2×C5 | C2×#689 | semidirect |
| 244. D5 | C2×#689 | direct (N × H) |
| 269. C5 | C2×D5×Q16 | semidirect |
| 270. C5 | C22×#689 | semidirect |
| 282. C2 | D5×#689 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×D5 | 2 |
| C2×D5×Dic10 | 2 |
| C2×#87812 | 2 |
| C2×C5×#689 | 2 |
| D5×#689 | 2 |
| C2×#87776 | 2 |
| C2×#87775 | 2 |
| C2×D5×#168 | 2 |
| C22×#689 | 5 |
| C2×D5×Q16 | 5 |