Finite Group DatabasebetaFinite Group Databasebeta← C2×C5×Q8×AGL(1,𝔽5) #13107728
Order 1600.
615 conjugacy classes of subgroups; only the 312 normal subgroups are shown.
This group has 615 conjugacy classes of subgroups — too many to draw. Only its 312 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. C5×Q8×AGL(1,𝔽5) | C2 | direct (N × H) |
| 7. C2×C52×Q8 | C4 | semidirect |
| 8. C5×Q8×D5 | C4 | semidirect |
| 11. C2×C5×Dic10 | C4 | semidirect |
| 14. C2×Q8×AGL(1,𝔽5) | C5 | direct (N × H) |
| 18. C2×C5×AGL(1,𝔽5) | Q8 | direct (N × H) |
| 21. C52×Q8 | C2×C4 | semidirect |
| 26. C5×Dic10 | C2×C4 | semidirect |
| 29. Q8×AGL(1,𝔽5) | C2×C5 | direct (N × H) |
| 41. C5×AGL(1,𝔽5) | C2×Q8 | direct (N × H) |
| 50. C2×C5×Q8 | C4×C5 | semidirect |
| 51. C2×C5×Q8 | AGL(1,𝔽5) | direct (N × H) |
| 55. Q8×D5 | C4×C5 | semidirect |
| 58. C2×Dic10 | C4×C5 | semidirect |
| 64. C2×C52 | C4×Q8 | semidirect |
| 66. C5×D5 | C4×Q8 | semidirect |
| 72. C2×AGL(1,𝔽5) | C5×Q8 | direct (N × H) |
| 77. C5×Q8 | C2×C4×C5 | semidirect |
| 78. C5×Q8 | C2×AGL(1,𝔽5) | direct (N × H) |
| 92. Dic10 | C2×C4×C5 | semidirect |
| 97. C52 | C2×C4×Q8 | semidirect |
| 110. AGL(1,𝔽5) | C2×C5×Q8 | direct (N × H) |
| 121. C2×Q8 | C5×AGL(1,𝔽5) | direct (N × H) |
| 132. C2×C5 | C4×C5×Q8 | semidirect |
| 133. C2×C5 | Q8×AGL(1,𝔽5) | direct (N × H) |
| 136. D5 | C4×C5×Q8 | semidirect |
| 141. Q8 | C2×C5×AGL(1,𝔽5) | direct (N × H) |
| 151. C5 | C2×C4×C5×Q8 | semidirect |
| 152. C5 | C2×Q8×AGL(1,𝔽5) | direct (N × H) |
| 165. C2 | C5×Q8×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×C5×Q8×D5 | 2 |
| C5×Q8×AGL(1,𝔽5) | 2 |
| C2×C5×C4⋊AGL(1,𝔽5) | 2 |
| C2×C4×C5×AGL(1,𝔽5) | 2 |
| C2×Q8×AGL(1,𝔽5) | 5 |
| C2×C4×C5×Q8 | 5 |