Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
800 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 208 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. C22×#6045 | C2 | semidirect |
| 3. C2×C5×C4⋊Dic5 | C2 | semidirect |
| 4. C2×#87780 | C2 | semidirect |
| 6. #11716975 | C2 | direct (N × H) |
| 11. C2×#6045 | C22 | semidirect |
| 16. C5×C4⋊Dic5 | C22 | semidirect |
| 17. #87780 | C22 | semidirect |
| 24. C22×C5×D5 | Q8 | semidirect |
| 45. C2×C4⋊Dic5 | D5 | semidirect |
| 56. C2×C5×D5 | C2×Q8 | semidirect |
| 87. C4⋊Dic5 | C2×D5 | semidirect |
| 90. C2×C52 | C22⋊Q8 | semidirect |
| 104. C22×D5 | Dic10 | semidirect |
| 137. C52 | C2×C22⋊Q8 | semidirect |
| 157. C2×D5 | C2×Dic10 | semidirect |
| 185. C2×C5 | #4043 | semidirect |
| 186. C2×C5 | #4070 | semidirect |
| 210. C5 | C2×#4043 | semidirect |
| 211. C5 | C2×#4070 | semidirect |
| 225. C2 | #11716975 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6045 | 2 |
| C22×C4×C5×D5 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C2×#87780 | 2 |
| C2×#87778 | 2 |
| #11716975 | 2 |
| C2×#4070 | 5 |
| C2×#4043 | 5 |