Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
752 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 272 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×C4⋊#1039 | C2 | semidirect |
| 3. C2×C5×C4⋊Dic5 | C2 | semidirect |
| 5. C2×Dic52 | C2 | semidirect |
| 6. #11716959 | C2 | direct (N × H) |
| 12. C2×C4×C5×D5 | C4 | semidirect |
| 14. C4⋊#1039 | C22 | semidirect |
| 15. C5×C4⋊Dic5 | C22 | semidirect |
| 17. Dic52 | C22 | semidirect |
| 33. C4×C5×D5 | C2×C4 | semidirect |
| 43. C2×C4⋊Dic5 | D5 | semidirect |
| 73. C2×C4×D5 | Dic5 | semidirect |
| 81. C4⋊Dic5 | C2×D5 | semidirect |
| 85. C2×C52 | #117 | semidirect |
| 122. C4×D5 | C2×Dic5 | semidirect |
| 129. C52 | C2×#117 | semidirect |
| 176. C2×C5 | #4038 | semidirect |
| 177. C2×C5 | #4072 | semidirect |
| 200. C5 | C2×#4038 | semidirect |
| 201. C5 | C2×#4072 | semidirect |
| 215. C2 | #11716959 | 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 |
| C2×C4⋊#1039 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C2×#87778 | 2 |
| C2×Dic52 | 2 |
| #11716959 | 2 |
| C2×#4072 | 5 |
| C2×#4038 | 5 |