Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
271 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 271 conjugacy classes of subgroups — too many to draw. Only its 120 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. C5×#3993 | C2 | direct (N × H) |
| 8. C2×C52×C8 | C4 | semidirect |
| 9. C2×C5×#168 | C4 | semidirect |
| 10. C5×C8×D5 | C4 | semidirect |
| 12. C2×#3993 | C5 | direct (N × H) |
| 23. C52×C8 | C2×C4 | semidirect |
| 24. C5×#168 | C2×C4 | semidirect |
| 29. #3993 | C2×C5 | direct (N × H) |
| 50. C2×C5×C8 | C4×C5 | semidirect |
| 51. C2×C5×C8 | AGL(1,𝔽5) | semidirect |
| 54. C2×#168 | C4×C5 | semidirect |
| 55. C8×D5 | C4×C5 | semidirect |
| 58. C2×C52 | #106 | semidirect |
| 60. C5×D5 | #106 | semidirect |
| 83. C5×C8 | C2×C4×C5 | semidirect |
| 84. C5×C8 | C2×AGL(1,𝔽5) | semidirect |
| 85. #168 | C2×C4×C5 | semidirect |
| 89. C52 | C2×#106 | semidirect |
| 116. C2×C8 | C5×AGL(1,𝔽5) | semidirect |
| 123. C2×C5 | C5×#106 | semidirect |
| 124. C2×C5 | #3993 | direct (N × H) |
| 127. D5 | C5×#106 | semidirect |
| 139. C8 | C2×C5×AGL(1,𝔽5) | semidirect |
| 141. C5 | C2×C5×#106 | semidirect |
| 142. C5 | C2×#3993 | direct (N × H) |
| 154. C2 | C5×#3993 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊AGL(1,𝔽5) | 2 |
| C2×C5×C8×D5 | 2 |
| C5×#3993 | 2 |
| C2×#3993 | 5 |
| C2×C5×#106 | 5 |