Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
624 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 180 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×C4×C5×Dic5 | C2 | semidirect |
| 5. #11716620 | C2 | semidirect |
| 13. C2×C4×C5×D5 | C4 | semidirect |
| 16. #87778 | C4 | direct (N × H) |
| 30. C2×#1039 | C2×C4 | semidirect |
| 36. C2×C5×Dic5 | C2×C4 | semidirect |
| 46. C2×C4×Dic5 | D5 | semidirect |
| 58. C2×C5×D5 | C42 | semidirect |
| 59. C4×C52 | C22⋊C4 | semidirect |
| 80. C2×C4×D5 | Dic5 | semidirect |
| 137. C2×Dic5 | C4×D5 | semidirect |
| 145. C52 | C4×C22⋊C4 | semidirect |
| 170. C2×D5 | C4×Dic5 | semidirect |
| 174. C4×C5 | #685 | semidirect |
| 175. C4×C5 | C22⋊Dic5 | semidirect |
| 229. C5 | C4×#685 | semidirect |
| 230. C5 | C4×C22⋊Dic5 | semidirect |
| 244. C4 | #87778 | 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×C4×C5×Dic5 | 2 |
| C2×#87778 | 2 |
| #11716620 | 2 |
| C4×C22⋊Dic5 | 5 |
| C4×#685 | 5 |