Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
736 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 192 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×#6039 | C2 | semidirect |
| 3. C2×#87806 | C2 | semidirect |
| 4. C2×C5×#683 | C2 | semidirect |
| 5. C2×#87780 | C2 | semidirect |
| 8. #11716969 | C2 | direct (N × H) |
| 19. C2×#6039 | C22 | semidirect |
| 20. #87806 | C22 | semidirect |
| 21. C5×#683 | C22 | semidirect |
| 22. #87780 | C22 | semidirect |
| 30. C22×C5×D5 | Q8 | semidirect |
| 61. C2×#683 | D5 | semidirect |
| 70. C2×C5×D5 | C2×Q8 | semidirect |
| 112. #683 | C2×D5 | semidirect |
| 114. C2×C52 | C22⋊Q8 | semidirect |
| 128. C22×D5 | Dic10 | semidirect |
| 172. C52 | C2×C22⋊Q8 | semidirect |
| 192. C2×D5 | C2×Dic10 | semidirect |
| 229. C2×C5 | #4042 | semidirect |
| 230. C2×C5 | #4070 | semidirect |
| 258. C5 | C2×#4042 | semidirect |
| 259. C5 | C2×#4070 | semidirect |
| 275. C2 | #11716969 | 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×#6039 | 2 |
| C2×#87806 | 2 |
| C2×C5×#683 | 2 |
| C2×#87780 | 2 |
| C2×#87778 | 2 |
| #11716969 | 2 |
| C2×#4070 | 5 |
| C2×#4042 | 5 |