Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
343 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 343 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 4. C5×#4009 | C2 | direct (N × H) |
| 6. C2×C52×Q8 | C4 | semidirect |
| 9. C5×Q8×D5 | C4 | semidirect |
| 14. C2×C5×Dic10 | C4 | semidirect |
| 20. C2×#4009 | C5 | direct (N × H) |
| 26. C52×Q8 | C2×C4 | semidirect |
| 40. C5×Dic10 | C2×C4 | semidirect |
| 48. #4009 | C2×C5 | direct (N × H) |
| 70. C2×C5×Q8 | C4×C5 | semidirect |
| 71. C2×C5×Q8 | AGL(1,𝔽5) | semidirect |
| 77. Q8×D5 | C4×C5 | semidirect |
| 82. C2×Dic10 | C4×C5 | semidirect |
| 94. C2×C52 | #103 | semidirect |
| 96. C5×D5 | #103 | semidirect |
| 111. C5×Q8 | C2×C4×C5 | semidirect |
| 112. C5×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 140. Dic10 | C2×C4×C5 | semidirect |
| 147. C52 | C2×#103 | semidirect |
| 182. C2×Q8 | C5×AGL(1,𝔽5) | semidirect |
| 196. C2×C5 | C5×#103 | semidirect |
| 197. C2×C5 | #4009 | direct (N × H) |
| 200. D5 | C5×#103 | semidirect |
| 209. Q8 | C2×C5×AGL(1,𝔽5) | semidirect |
| 224. C5 | C2×C5×#103 | semidirect |
| 225. C5 | C2×#4009 | direct (N × H) |
| 241. C2 | C5×#4009 | 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 |
| C2×C5×C4⋊AGL(1,𝔽5) | 2 |
| C2×C5×D5⋊C8 | 2 |
| C5×#4009 | 2 |
| C2×#4009 | 5 |
| C2×C5×#103 | 5 |