Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
640 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 180 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 |
| 4. #11717337 | C2 | semidirect |
| 5. AGL(1,𝔽5)×D20 | C2 | semidirect |
| 6. C4×D5×AGL(1,𝔽5) | C2 | semidirect |
| 7. #11717323 | C2 | semidirect |
| 10. #87904 | C4 | semidirect |
| 11. C5×#713 | C4 | semidirect |
| 15. #87874 | C4 | semidirect |
| 16. #87871 | C4 | semidirect |
| 33. C52×Q8 | C2×C4 | semidirect |
| 34. C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 35. C4×C5⋊D5 | C2×C4 | semidirect |
| 36. C5×D20 | C2×C4 | semidirect |
| 37. C4×C5×D5 | C2×C4 | semidirect |
| 39. C5×Dic10 | C2×C4 | semidirect |
| 40. #6038 | C2×C4 | semidirect |
| 41. #6036 | C2×C4 | semidirect |
| 42. D5×Dic5 | C2×C4 | semidirect |
| 47. Q8×AGL(1,𝔽5) | D5 | semidirect |
| 64. #1042 | #41 | semidirect |
| 66. C5×AGL(1,𝔽5) | #41 | semidirect |
| 80. #713 | AGL(1,𝔽5) | direct (N × H) |
| 120. C5×Q8 | C4×D5 | semidirect |
| 121. C5×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 136. D20 | C2×AGL(1,𝔽5) | semidirect |
| 146. C4×D5 | C2×AGL(1,𝔽5) | semidirect |
| 148. Dic10 | C4×D5 | semidirect |
| 156. C52 | C4×#41 | semidirect |
| 171. AGL(1,𝔽5) | #713 | direct (N × H) |
| 216. Q8 | D5×AGL(1,𝔽5) | semidirect |
| 233. C5 | C4×#713 | semidirect |
| 234. C5 | #41×AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#713 | 2 |
| Q8×#1042 | 2 |
| C5×Q8×AGL(1,𝔽5) | 2 |
| #11717337 | 2 |
| AGL(1,𝔽5)×D20 | 2 |
| C4×D5×AGL(1,𝔽5) | 2 |
| #11717323 | 2 |
| #41×AGL(1,𝔽5) | 5 |
| C4×#713 | 5 |