Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
447 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 447 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×C5×C22⋊AGL(1,𝔽5) | C2 | semidirect |
| 3. C5×#3999 | C2 | direct (N × H) |
| 4. C23×C5×D5 | C4 | semidirect |
| 7. C22×C4×C52 | C4 | semidirect |
| 10. C2×C5×D20 | C4 | semidirect |
| 13. C5×C22⋊AGL(1,𝔽5) | C22 | semidirect |
| 14. C2×#3999 | C5 | direct (N × H) |
| 22. C22×C5×D5 | C2×C4 | semidirect |
| 30. C2×C4×C52 | C2×C4 | semidirect |
| 35. C2×C22⋊AGL(1,𝔽5) | C2×C5 | semidirect |
| 37. #3999 | C2×C5 | direct (N × H) |
| 57. C23×D5 | C4×C5 | semidirect |
| 66. C22×C4×C5 | C4×C5 | semidirect |
| 67. C22×C4×C5 | AGL(1,𝔽5) | semidirect |
| 70. C2×D20 | C4×C5 | semidirect |
| 73. C22⋊AGL(1,𝔽5) | C22×C5 | semidirect |
| 79. C2×C52 | #99 | semidirect |
| 101. C22×D5 | C2×C4×C5 | semidirect |
| 118. C2×C4×C5 | C2×C4×C5 | semidirect |
| 119. C2×C4×C5 | C2×AGL(1,𝔽5) | semidirect |
| 125. C52 | C2×#99 | semidirect |
| 170. C22×C4 | C5×AGL(1,𝔽5) | semidirect |
| 184. C2×C5 | C5×#99 | semidirect |
| 185. C2×C5 | #3999 | direct (N × H) |
| 207. C2×C4 | C2×C5×AGL(1,𝔽5) | semidirect |
| 209. C5 | C2×C5×#99 | semidirect |
| 210. C5 | C2×#3999 | direct (N × H) |
| 232. C2 | C5×#3999 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D20 | 2 |
| C2×C5×C22⋊AGL(1,𝔽5) | 2 |
| C5×#3999 | 2 |
| C2×#3999 | 5 |
| C2×C5×#99 | 5 |