Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
863 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 863 conjugacy classes of subgroups — too many to draw. Only its 290 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 |
|---|---|---|
| 4. C2×#87825 | C2 | direct (N × H) |
| 10. C22×#1039 | C4 | semidirect |
| 11. C22×C5×Dic5 | C4 | semidirect |
| 12. C2×D5×Dic5 | C4 | semidirect |
| 14. #87825 | C22 | direct (N × H) |
| 26. C2×#1039 | C2×C4 | semidirect |
| 27. C2×C5×Dic5 | C2×C4 | semidirect |
| 28. D5×Dic5 | C2×C4 | semidirect |
| 38. C22×C52 | C4⋊C4 | semidirect |
| 40. C2×C5×D5 | C4⋊C4 | semidirect |
| 47. #1039 | C22×C4 | semidirect |
| 48. C5×Dic5 | C22×C4 | semidirect |
| 65. C22×Dic5 | AGL(1,𝔽5) | semidirect |
| 71. C2×C52 | C2×C4⋊C4 | semidirect |
| 73. C5×D5 | C2×C4⋊C4 | semidirect |
| 101. C2×Dic5 | C2×AGL(1,𝔽5) | semidirect |
| 108. C52 | C22×C4⋊C4 | semidirect |
| 116. C22×C5 | #683 | semidirect |
| 117. C22×C5 | C4⋊AGL(1,𝔽5) | semidirect |
| 120. C2×D5 | #683 | semidirect |
| 133. Dic5 | C22×AGL(1,𝔽5) | semidirect |
| 149. C2×C5 | C2×#683 | semidirect |
| 150. C2×C5 | C2×C4⋊AGL(1,𝔽5) | semidirect |
| 153. D5 | C2×#683 | semidirect |
| 170. C5 | C22×#683 | semidirect |
| 171. C5 | C22×C4⋊AGL(1,𝔽5) | semidirect |
| 177. C22 | #87825 | direct (N × H) |
| 186. C2 | C2×#87825 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1042 | 2 |
| C23×C5×AGL(1,𝔽5) | 2 |
| C22×D5×Dic5 | 2 |
| C2×#87825 | 2 |
| C22×C4⋊AGL(1,𝔽5) | 5 |
| C22×#683 | 5 |