Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
407 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 407 conjugacy classes of subgroups — too many to draw. Only its 100 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. C5×#4130 | C2 | semidirect |
| 3. C5×D5⋊M16 | C2 | semidirect |
| 4. C5×#4007 | C2 | semidirect |
| 6. C2×C52×D4 | C4 | semidirect |
| 10. C5×D4×D5 | C4 | semidirect |
| 12. C2×C5×D20 | C4 | semidirect |
| 16. C5×C4⋊AGL(1,𝔽5) | C22 | semidirect |
| 19. C5×D5⋊C8 | C22 | semidirect |
| 20. #65767 | C5 | direct (N × H) |
| 44. #4130 | C2×C5 | semidirect |
| 45. D5⋊M16 | C2×C5 | semidirect |
| 48. #4007 | C2×C5 | semidirect |
| 74. C2×C5×D4 | C4×C5 | semidirect |
| 75. C2×C5×D4 | AGL(1,𝔽5) | semidirect |
| 80. D4×D5 | C4×C5 | semidirect |
| 82. C2×D20 | C4×C5 | semidirect |
| 86. C4⋊AGL(1,𝔽5) | C22×C5 | semidirect |
| 89. D5⋊C8 | C22×C5 | semidirect |
| 151. C52 | #418 | semidirect |
| 194. C2×D4 | C5×AGL(1,𝔽5) | semidirect |
| 238. C5 | C5×#418 | semidirect |
| 239. C5 | #65767 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×D5 | 2 |
| C5×#4130 | 2 |
| C5×D5⋊M16 | 2 |
| C5×#4007 | 2 |
| #65767 | 5 |
| C5×#418 | 5 |