Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
784 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 176 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. Q8×#1044 | C2 | semidirect |
| 3. D4×#1044 | C2 | semidirect |
| 4. #11717451 | C2 | semidirect |
| 5. C2×C4×#1044 | C2 | semidirect |
| 7. C52×#41 | C4 | semidirect |
| 8. #87904 | C4 | semidirect |
| 10. #87902 | C4 | semidirect |
| 12. #87900 | C4 | semidirect |
| 24. C52×Q8 | C2×C4 | semidirect |
| 25. C52×D4 | C2×C4 | semidirect |
| 26. C2×C4×C52 | C2×C4 | semidirect |
| 27. C22⋊(C5⋊D5) | C2×C4 | semidirect |
| 28. C2×#1039 | C2×C4 | semidirect |
| 29. C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 30. C4×C5⋊D5 | C2×C4 | semidirect |
| 31. C4×C5⋊D5 | C2×C4 | semidirect |
| 34. #6045 | C2×C4 | semidirect |
| 46. #1044 | #41 | direct (N × H) |
| 53. C5×#41 | AGL(1,𝔽5) | semidirect |
| 82. C5×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 84. C5×D4 | C2×AGL(1,𝔽5) | semidirect |
| 86. C2×C4×C5 | C2×AGL(1,𝔽5) | semidirect |
| 108. C52 | C4×#41 | semidirect |
| 130. #41 | #1044 | direct (N × H) |
| 150. Q8 | C2×#1044 | semidirect |
| 153. D4 | C2×#1044 | semidirect |
| 162. C2×C4 | C2×#1044 | semidirect |
| 164. C5 | #41×AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×C5⋊D5 | 2 |
| Q8×#1044 | 2 |
| D4×#1044 | 2 |
| #11717451 | 2 |
| C2×C4×#1044 | 2 |
| #41×AGL(1,𝔽5) | 5 |