Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
294 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 140 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×#3992 | C2 | semidirect |
| 5. C5×C8×AGL(1,𝔽5) | C2 | semidirect |
| 8. C5×#704 | C4 | semidirect |
| 12. C5×#700 | C4 | semidirect |
| 14. C52×M16 | C4 | semidirect |
| 15. C5×#681 | C4 | semidirect |
| 16. C5×#676 | C4 | semidirect |
| 18. M16×AGL(1,𝔽5) | C5 | direct (N × H) |
| 30. C5×#170 | C2×C4 | semidirect |
| 31. C52×C8 | C2×C4 | semidirect |
| 32. C5×#168 | C2×C4 | semidirect |
| 39. #3992 | C2×C5 | semidirect |
| 40. C8×AGL(1,𝔽5) | C2×C5 | semidirect |
| 48. C5×AGL(1,𝔽5) | M16 | direct (N × H) |
| 57. #704 | C4×C5 | semidirect |
| 61. #700 | C4×C5 | semidirect |
| 68. C5×M16 | C4×C5 | semidirect |
| 69. C5×M16 | AGL(1,𝔽5) | direct (N × H) |
| 75. #681 | C4×C5 | semidirect |
| 76. #676 | C4×C5 | semidirect |
| 104. #170 | C2×C4×C5 | semidirect |
| 108. C5×C8 | C2×C4×C5 | semidirect |
| 109. C5×C8 | C2×AGL(1,𝔽5) | semidirect |
| 110. #168 | C2×C4×C5 | semidirect |
| 116. C52 | C4×M16 | semidirect |
| 127. AGL(1,𝔽5) | C5×M16 | direct (N × H) |
| 146. M16 | C5×AGL(1,𝔽5) | direct (N × H) |
| 174. C8 | C2×C5×AGL(1,𝔽5) | semidirect |
| 176. C5 | C4×C5×M16 | semidirect |
| 177. C5 | M16×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 |
|---|---|
| C2×C4×C5×AGL(1,𝔽5) | 2 |
| C5×D5⋊M16 | 2 |
| C5×D5×M16 | 2 |
| C5×#3992 | 2 |
| C5×C8×AGL(1,𝔽5) | 2 |
| M16×AGL(1,𝔽5) | 5 |
| C4×C5×M16 | 5 |