Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
359 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 359 conjugacy classes of subgroups — too many to draw. Only its 104 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. C2×C4×C5×AGL(1,𝔽5) | C2 | semidirect |
| 3. C2×C5×#700 | C2 | semidirect |
| 4. C5×#4010 | C2 | direct (N × H) |
| 6. C2×C52×Q8 | C4 | semidirect |
| 9. C5×#713 | C4 | semidirect |
| 12. C2×C5×D20 | C4 | semidirect |
| 17. C4×C5×AGL(1,𝔽5) | C22 | semidirect |
| 19. C5×#700 | C22 | semidirect |
| 20. C2×#4010 | C5 | direct (N × H) |
| 27. C52×Q8 | C2×C4 | semidirect |
| 34. C5×D20 | C2×C4 | semidirect |
| 44. C2×C4×AGL(1,𝔽5) | C2×C5 | semidirect |
| 45. C2×#700 | C2×C5 | semidirect |
| 48. #4010 | C2×C5 | direct (N × H) |
| 68. C2×C5×Q8 | C4×C5 | semidirect |
| 69. C2×C5×Q8 | AGL(1,𝔽5) | semidirect |
| 77. #713 | C4×C5 | semidirect |
| 80. C2×D20 | C4×C5 | semidirect |
| 85. C4×AGL(1,𝔽5) | C22×C5 | semidirect |
| 87. #700 | C22×C5 | semidirect |
| 94. C2×C52 | #104 | semidirect |
| 109. C5×Q8 | C2×C4×C5 | semidirect |
| 110. C5×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 134. D20 | C2×C4×C5 | semidirect |
| 147. C52 | C2×#104 | semidirect |
| 180. C2×Q8 | C5×AGL(1,𝔽5) | semidirect |
| 196. C2×C5 | C5×#104 | semidirect |
| 197. C2×C5 | #4010 | direct (N × H) |
| 206. Q8 | C2×C5×AGL(1,𝔽5) | semidirect |
| 224. C5 | C2×C5×#104 | semidirect |
| 225. C5 | C2×#4010 | direct (N × H) |
| 241. C2 | C5×#4010 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#713 | 2 |
| C2×C4×C5×AGL(1,𝔽5) | 2 |
| C2×C5×#700 | 2 |
| C5×#4010 | 2 |
| C2×#4010 | 5 |
| C2×C5×#104 | 5 |