Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
880 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 880 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. C22×C5×Dic10 | C2 | semidirect |
| 3. C2×C5×C4⋊Dic5 | C2 | semidirect |
| 4. C2×#87780 | C2 | semidirect |
| 6. #11716990 | C2 | direct (N × H) |
| 15. C2×C5×Dic10 | C22 | semidirect |
| 16. C5×C4⋊Dic5 | C22 | semidirect |
| 17. #87780 | C22 | semidirect |
| 24. C22×C5⋊D5 | Q8 | semidirect |
| 40. C22×Dic10 | D5 | semidirect |
| 46. C2×C4⋊Dic5 | D5 | semidirect |
| 56. C2×C5⋊D5 | C2×Q8 | semidirect |
| 83. C2×Dic10 | C2×D5 | semidirect |
| 88. C4⋊Dic5 | C2×D5 | semidirect |
| 91. C2×C52 | C22⋊Q8 | semidirect |
| 142. C52 | C2×C22⋊Q8 | semidirect |
| 193. C2×C5 | #4043 | semidirect |
| 194. C2×C5 | #4092 | semidirect |
| 220. C5 | C2×#4043 | semidirect |
| 221. C5 | C2×#4092 | semidirect |
| 235. C2 | #11716990 | 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×C5×Dic10 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C2×#87780 | 2 |
| C2×#87779 | 2 |
| #11716990 | 2 |
| C2×#4092 | 5 |
| C2×#4043 | 5 |