Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
254 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 1. C5×Q8×AGL(1,𝔽5) | C2 | semidirect |
| 4. C5×#4009 | C2 | semidirect |
| 6. C5×#3993 | C2 | semidirect |
| 7. C5×C8×AGL(1,𝔽5) | C2 | semidirect |
| 18. C52×SD16 | C4 | semidirect |
| 19. C5×#688 | C4 | semidirect |
| 20. C5×#687 | C4 | semidirect |
| 21. C5×#677 | C4 | semidirect |
| 23. SD16×AGL(1,𝔽5) | C5 | direct (N × H) |
| 31. C52×Q8 | C2×C4 | semidirect |
| 38. C5×Dic10 | C2×C4 | semidirect |
| 40. C52×C8 | C2×C4 | semidirect |
| 41. C5×#168 | C2×C4 | semidirect |
| 42. Q8×AGL(1,𝔽5) | C2×C5 | semidirect |
| 48. #4009 | C2×C5 | semidirect |
| 50. #3993 | C2×C5 | semidirect |
| 51. C8×AGL(1,𝔽5) | C2×C5 | semidirect |
| 64. C5×AGL(1,𝔽5) | SD16 | direct (N × H) |
| 86. C5×SD16 | C4×C5 | semidirect |
| 87. C5×SD16 | AGL(1,𝔽5) | direct (N × H) |
| 96. #688 | C4×C5 | semidirect |
| 97. #687 | C4×C5 | semidirect |
| 98. #677 | C4×C5 | semidirect |
| 116. C5×Q8 | C2×C4×C5 | semidirect |
| 117. C5×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 135. Dic10 | C2×C4×C5 | semidirect |
| 140. C5×C8 | C2×C4×C5 | semidirect |
| 141. C5×C8 | C2×AGL(1,𝔽5) | semidirect |
| 142. #168 | C2×C4×C5 | semidirect |
| 150. C52 | C4×SD16 | semidirect |
| 165. AGL(1,𝔽5) | C5×SD16 | direct (N × H) |
| 186. SD16 | C5×AGL(1,𝔽5) | direct (N × H) |
| 210. Q8 | C2×C5×AGL(1,𝔽5) | semidirect |
| 223. C8 | C2×C5×AGL(1,𝔽5) | semidirect |
| 225. C5 | C4×C5×SD16 | semidirect |
| 226. C5 | SD16×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 |
|---|---|
| C5×Q8×AGL(1,𝔽5) | 2 |
| C5×D4×AGL(1,𝔽5) | 2 |
| C5×D5×SD16 | 2 |
| C5×#4009 | 2 |
| C5×#4007 | 2 |
| C5×#3993 | 2 |
| C5×C8×AGL(1,𝔽5) | 2 |
| SD16×AGL(1,𝔽5) | 5 |
| C4×C5×SD16 | 5 |