Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
615 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 615 conjugacy classes of subgroups — too many to draw. Only its 194 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. Q8×#1042 | C2 | semidirect |
| 3. C5×Q8×AGL(1,𝔽5) | C2 | semidirect |
| 6. #1042⋊Q8 | C2 | semidirect |
| 7. AGL(1,𝔽5)×Dic10 | C2 | semidirect |
| 10. Q8×C5⋊D5 | C4 | semidirect |
| 11. C5×Q8×D5 | C4 | semidirect |
| 14. #87872 | C4 | semidirect |
| 15. D5×Dic10 | C4 | semidirect |
| 32. D5×AGL(1,𝔽5) | Q8 | direct (N × H) |
| 33. C52×Q8 | C2×C4 | semidirect |
| 35. #6045 | C2×C4 | semidirect |
| 38. C5×Dic10 | C2×C4 | semidirect |
| 39. C5×Dic10 | C2×C4 | semidirect |
| 40. #6039 | C2×C4 | semidirect |
| 49. Q8×AGL(1,𝔽5) | D5 | direct (N × H) |
| 64. #1042 | C2×Q8 | semidirect |
| 66. C5×AGL(1,𝔽5) | C2×Q8 | semidirect |
| 82. Q8×D5 | AGL(1,𝔽5) | direct (N × H) |
| 106. C5⋊D5 | C4×Q8 | semidirect |
| 107. C5×D5 | C4×Q8 | semidirect |
| 121. C5×Q8 | C4×D5 | semidirect |
| 122. C5×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 147. Dic10 | C4×D5 | semidirect |
| 148. Dic10 | C2×AGL(1,𝔽5) | semidirect |
| 156. C52 | C2×C4×Q8 | semidirect |
| 171. AGL(1,𝔽5) | Q8×D5 | direct (N × H) |
| 211. D5 | Q8×AGL(1,𝔽5) | direct (N × H) |
| 219. Q8 | D5×AGL(1,𝔽5) | direct (N × H) |
| 233. C5 | C4×Q8×D5 | semidirect |
| 234. C5 | C2×Q8×AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D52 | 2 |
| Q8×#1042 | 2 |
| C5×Q8×AGL(1,𝔽5) | 2 |
| D5×C4⋊AGL(1,𝔽5) | 2 |
| C4×D5×AGL(1,𝔽5) | 2 |
| #1042⋊Q8 | 2 |
| AGL(1,𝔽5)×Dic10 | 2 |
| C2×Q8×AGL(1,𝔽5) | 5 |
| C4×Q8×D5 | 5 |