Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
752 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 194 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 | direct (N × H) |
| 7. C2×C52×Q8 | C4 | semidirect |
| 8. Q8×C5⋊D5 | C4 | semidirect |
| 11. C2×#6045 | C4 | semidirect |
| 17. C2×#1044 | Q8 | direct (N × H) |
| 20. C52×Q8 | C2×C4 | semidirect |
| 25. #6045 | C2×C4 | semidirect |
| 37. #1044 | C2×Q8 | direct (N × H) |
| 43. C2×C5×Q8 | AGL(1,𝔽5) | semidirect |
| 55. C2×C52 | C4×Q8 | semidirect |
| 57. C5⋊D5 | C4×Q8 | semidirect |
| 67. C5×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 82. C52 | C2×C4×Q8 | semidirect |
| 102. C2×Q8 | #1044 | direct (N × H) |
| 110. C2×C5 | Q8×AGL(1,𝔽5) | semidirect |
| 120. Q8 | C2×#1044 | direct (N × H) |
| 130. C5 | C2×Q8×AGL(1,𝔽5) | semidirect |
| 143. C2 | Q8×#1044 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C5⋊D5 | 2 |
| Q8×#1044 | 2 |
| C2×C4⋊#1044 | 2 |
| C2×C4×#1044 | 2 |
| C2×Q8×AGL(1,𝔽5) | 5 |