Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
696 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 200 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. C2×C5×#681 | C2 | semidirect |
| 3. C22×C5×#168 | C2 | semidirect |
| 4. C2×#87769 | C2 | semidirect |
| 5. #11716935 | C2 | direct (N × H) |
| 6. C2×#87767 | C2 | semidirect |
| 14. C5×#681 | C22 | semidirect |
| 18. C2×C5×#168 | C22 | semidirect |
| 19. #87769 | C22 | semidirect |
| 20. #87767 | C22 | semidirect |
| 43. C2×#681 | D5 | semidirect |
| 44. C22×#168 | D5 | semidirect |
| 86. #681 | C2×D5 | semidirect |
| 90. C2×#168 | C2×D5 | semidirect |
| 97. C2×C52 | #131 | semidirect |
| 148. C52 | C2×#131 | semidirect |
| 195. C2×C5 | #4047 | semidirect |
| 196. C2×C5 | #4053 | semidirect |
| 218. C5 | C2×#4047 | semidirect |
| 219. C5 | C2×#4053 | semidirect |
| 231. C2 | #11716935 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87900 | 2 |
| C2×C5×#681 | 2 |
| C22×C5×#168 | 2 |
| C2×#87769 | 2 |
| #11716935 | 2 |
| C2×#87767 | 2 |
| C2×#4053 | 5 |
| C2×#4047 | 5 |