Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
656 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 142 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×C5×C22⋊Dic5 | C2 | semidirect |
| 3. C5×#3966 | C2 | direct (N × H) |
| 4. C24×C52 | C4 | semidirect |
| 8. C2×C52×D4 | C4 | semidirect |
| 10. C22×C4×C52 | C4 | semidirect |
| 13. C5×C22⋊Dic5 | C22 | semidirect |
| 15. C2×#3966 | C5 | direct (N × H) |
| 22. C23×C52 | C2×C4 | semidirect |
| 30. C2×C4×C52 | C2×C4 | semidirect |
| 37. C2×C22⋊Dic5 | C2×C5 | semidirect |
| 39. #3966 | C2×C5 | direct (N × H) |
| 58. C24×C5 | Dic5 | semidirect |
| 59. C24×C5 | C4×C5 | semidirect |
| 70. C2×C5×D4 | Dic5 | semidirect |
| 71. C2×C5×D4 | C4×C5 | semidirect |
| 76. C22×C4×C5 | Dic5 | semidirect |
| 77. C22×C4×C5 | C4×C5 | semidirect |
| 82. C22⋊Dic5 | C22×C5 | semidirect |
| 89. C2×C52 | #99 | semidirect |
| 111. C23×C5 | C2×Dic5 | semidirect |
| 116. C23×C5 | C2×C4×C5 | semidirect |
| 136. C2×C4×C5 | C2×Dic5 | semidirect |
| 137. C2×C4×C5 | C2×C4×C5 | semidirect |
| 143. C52 | C2×#99 | semidirect |
| 191. C24 | C5×Dic5 | semidirect |
| 195. C2×D4 | C5×Dic5 | semidirect |
| 198. C22×C4 | C5×Dic5 | semidirect |
| 218. C2×C5 | #3966 | direct (N × H) |
| 219. C2×C5 | C5×#99 | semidirect |
| 228. C23 | C2×C5×Dic5 | semidirect |
| 238. C2×C4 | C2×C5×Dic5 | semidirect |
| 240. C5 | C2×#3966 | direct (N × H) |
| 241. C5 | C2×C5×#99 | semidirect |
| 263. C2 | C5×#3966 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D4 | 2 |
| C2×C5×C22⋊Dic5 | 2 |
| C5×#3966 | 2 |
| C2×C5×#99 | 5 |
| C2×#3966 | 5 |