Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
2802 conjugacy classes of subgroups; only the 759 normal subgroups are shown.
This group has 2802 conjugacy classes of subgroups — too many to draw. Only its 759 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 |
|---|---|---|
| 3. C42×#1044 | C2 | semidirect |
| 4. C42×#1043 | C2 | semidirect |
| 5. C4×#87830 | C2 | semidirect |
| 11. C4×D5⋊AGL(1,𝔽5) | C4 | direct (N × H) |
| 13. C42×C5×D5 | C4 | semidirect |
| 15. C4×D5×Dic5 | C4 | semidirect |
| 26. C4×#1044 | C2×C4 | semidirect |
| 27. C4×#1043 | C2×C4 | semidirect |
| 28. #87830 | C2×C4 | semidirect |
| 29. C42×C52 | C2×C4 | semidirect |
| 30. C4×#1039 | C2×C4 | semidirect |
| 31. C4×C5×Dic5 | C2×C4 | semidirect |
| 32. Dic52 | C2×C4 | semidirect |
| 44. D5⋊AGL(1,𝔽5) | C42 | direct (N × H) |
| 49. C4×C5×D5 | C42 | semidirect |
| 51. D5×Dic5 | C42 | semidirect |
| 65. C42×D5 | AGL(1,𝔽5) | semidirect |
| 71. #1044 | C2×C42 | semidirect |
| 72. #1043 | C2×C42 | semidirect |
| 73. C4×C52 | C2×C42 | semidirect |
| 74. #1039 | C2×C42 | semidirect |
| 75. C5×Dic5 | C2×C42 | semidirect |
| 95. C42×C5 | C2×AGL(1,𝔽5) | semidirect |
| 99. C4×Dic5 | C2×AGL(1,𝔽5) | semidirect |
| 107. C5×D5 | C43 | semidirect |
| 129. C4×D5 | C4×AGL(1,𝔽5) | semidirect |
| 140. C52 | C2×C43 | semidirect |
| 153. C4×C5 | C2×C4×AGL(1,𝔽5) | semidirect |
| 156. Dic5 | C2×C4×AGL(1,𝔽5) | semidirect |
| 172. C42 | D5⋊AGL(1,𝔽5) | direct (N × H) |
| 178. D5 | C42×AGL(1,𝔽5) | semidirect |
| 193. C5 | C2×C42×AGL(1,𝔽5) | semidirect |
| 202. C4 | C4×D5⋊AGL(1,𝔽5) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D5⋊AGL(1,𝔽5) | 2 |
| C42×D52 | 2 |
| C42×#1044 | 2 |
| C42×#1043 | 2 |
| C4×#87830 | 2 |
| C2×C42×AGL(1,𝔽5) | 5 |