Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
279 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 279 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 1. C5×D4×AGL(1,𝔽5) | C2 | semidirect |
| 3. C5×#4007 | C2 | semidirect |
| 4. C5×#3994 | C2 | semidirect |
| 5. C5×C8×AGL(1,𝔽5) | C2 | semidirect |
| 12. C52×D8 | C4 | semidirect |
| 13. C5×#686 | C4 | semidirect |
| 14. C5×D40 | C4 | semidirect |
| 16. D8×AGL(1,𝔽5) | C5 | direct (N × H) |
| 23. C52×D4 | C2×C4 | semidirect |
| 25. C5×D20 | C2×C4 | semidirect |
| 28. C52×C8 | C2×C4 | semidirect |
| 29. C5×#168 | C2×C4 | semidirect |
| 30. D4×AGL(1,𝔽5) | C2×C5 | semidirect |
| 34. #4007 | C2×C5 | semidirect |
| 35. #3994 | C2×C5 | semidirect |
| 36. C8×AGL(1,𝔽5) | C2×C5 | semidirect |
| 47. C5×AGL(1,𝔽5) | D8 | direct (N × H) |
| 61. C5×D8 | C4×C5 | semidirect |
| 62. C5×D8 | AGL(1,𝔽5) | direct (N × H) |
| 68. #686 | C4×C5 | semidirect |
| 69. D40 | C4×C5 | semidirect |
| 86. C5×D4 | C2×C4×C5 | semidirect |
| 87. C5×D4 | C2×AGL(1,𝔽5) | semidirect |
| 94. D20 | C2×C4×C5 | semidirect |
| 100. C5×C8 | C2×C4×C5 | semidirect |
| 101. C5×C8 | C2×AGL(1,𝔽5) | semidirect |
| 102. #168 | C2×C4×C5 | semidirect |
| 108. C52 | C4×D8 | semidirect |
| 122. AGL(1,𝔽5) | C5×D8 | direct (N × H) |
| 135. D8 | C5×AGL(1,𝔽5) | direct (N × H) |
| 156. D4 | C2×C5×AGL(1,𝔽5) | semidirect |
| 164. C8 | C2×C5×AGL(1,𝔽5) | semidirect |
| 166. C5 | C4×C5×D8 | semidirect |
| 167. C5 | D8×AGL(1,𝔽5) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×AGL(1,𝔽5) | 2 |
| C5×D5×D8 | 2 |
| C5×#4007 | 2 |
| C5×#3994 | 2 |
| C5×C8×AGL(1,𝔽5) | 2 |
| D8×AGL(1,𝔽5) | 5 |
| C4×C5×D8 | 5 |