Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
543 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 543 conjugacy classes of subgroups — too many to draw. Only its 128 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×C5×C22⋊AGL(1,𝔽5) | C2 | semidirect |
| 3. C2×C5×C4⋊AGL(1,𝔽5) | C2 | semidirect |
| 4. C2×C4×C5×AGL(1,𝔽5) | C2 | semidirect |
| 8. C2×C52×D4 | C4 | semidirect |
| 9. C2×C5×C22⋊D5 | C4 | semidirect |
| 12. C2×C5×D20 | C4 | semidirect |
| 17. #65780 | C5 | direct (N × H) |
| 30. C2×C5×AGL(1,𝔽5) | D4 | semidirect |
| 40. C2×C22⋊AGL(1,𝔽5) | C2×C5 | semidirect |
| 41. C2×C4⋊AGL(1,𝔽5) | C2×C5 | semidirect |
| 42. C2×C4×AGL(1,𝔽5) | C2×C5 | semidirect |
| 60. C4×C52 | C22⋊C4 | semidirect |
| 61. C5×Dic5 | C22⋊C4 | semidirect |
| 71. C2×C5×D4 | C4×C5 | semidirect |
| 72. C2×C5×D4 | AGL(1,𝔽5) | semidirect |
| 76. C2×C22⋊D5 | C4×C5 | semidirect |
| 79. C2×D20 | C4×C5 | semidirect |
| 114. C2×AGL(1,𝔽5) | C5×D4 | semidirect |
| 140. C52 | #390 | semidirect |
| 174. C4×C5 | C5×C22⋊C4 | semidirect |
| 175. C4×C5 | C22⋊AGL(1,𝔽5) | semidirect |
| 176. Dic5 | C5×C22⋊C4 | semidirect |
| 182. C2×D4 | C5×AGL(1,𝔽5) | semidirect |
| 226. C5 | C5×#390 | semidirect |
| 227. C5 | #65780 | direct (N × H) |
| 243. C4 | C5×C22⋊AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×D5 | 2 |
| C2×C5×C22⋊AGL(1,𝔽5) | 2 |
| C2×C5×C4⋊AGL(1,𝔽5) | 2 |
| C2×C4×C5×AGL(1,𝔽5) | 2 |
| #65780 | 5 |
| C5×#390 | 5 |