Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
408 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 112 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×#87804 | C2 | semidirect |
| 3. C2×C4×C5×Dic5 | C2 | semidirect |
| 4. #11716610 | C2 | direct (N × H) |
| 10. C5×#709 | C4 | semidirect |
| 12. C2×C5×D20 | C4 | semidirect |
| 14. C2×C5×Dic10 | C4 | semidirect |
| 16. #87804 | C22 | semidirect |
| 19. C4×C5×Dic5 | C22 | semidirect |
| 36. C5×D20 | C2×C4 | semidirect |
| 40. C5×Dic10 | C2×C4 | semidirect |
| 45. C2×C4×Dic5 | D5 | semidirect |
| 79. #709 | Dic5 | semidirect |
| 81. C2×D20 | Dic5 | semidirect |
| 83. C2×Dic10 | Dic5 | semidirect |
| 87. C4×Dic5 | C2×D5 | semidirect |
| 100. C2×C52 | #104 | semidirect |
| 143. D20 | C2×Dic5 | semidirect |
| 147. Dic10 | C2×Dic5 | semidirect |
| 155. C52 | C2×#104 | semidirect |
| 212. C2×C5 | #3937 | semidirect |
| 213. C2×C5 | #3969 | semidirect |
| 238. C5 | C2×#3937 | semidirect |
| 239. C5 | C2×#3969 | semidirect |
| 255. C2 | #11716610 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#709 | 2 |
| C2×#87804 | 2 |
| C2×C4×C5×Dic5 | 2 |
| #11716610 | 2 |
| C2×#3969 | 5 |
| C2×#3937 | 5 |