Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
240 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 78 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. C2×C52×Q16 | C2 | semidirect |
| 3. C5×#3960 | C2 | direct (N × H) |
| 4. C2×C5×#672 | C2 | semidirect |
| 8. C52×Q16 | C22 | semidirect |
| 12. C5×#672 | C22 | semidirect |
| 14. C2×#3960 | C5 | direct (N × H) |
| 25. C2×C5×Q16 | D5 | semidirect |
| 26. C2×C5×Q16 | C2×C5 | semidirect |
| 31. #3960 | C2×C5 | direct (N × H) |
| 32. C2×#672 | C2×C5 | semidirect |
| 48. C5×Q16 | C2×D5 | semidirect |
| 49. C5×Q16 | C22×C5 | semidirect |
| 58. #672 | C22×C5 | semidirect |
| 60. C2×C52 | SD32 | semidirect |
| 87. C2×Q16 | C5×D5 | semidirect |
| 91. C52 | C2×SD32 | semidirect |
| 111. Q16 | C2×C5×D5 | semidirect |
| 119. C2×C5 | #3960 | direct (N × H) |
| 120. C2×C5 | C5×SD32 | semidirect |
| 134. C5 | C2×#3960 | direct (N × H) |
| 135. C5 | C2×C5×SD32 | semidirect |
| 143. C2 | C5×#3960 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×Q16 | 2 |
| C2×C5×D40 | 2 |
| C5×#3960 | 2 |
| C2×C5×#672 | 2 |
| C2×C5×SD32 | 5 |
| C2×#3960 | 5 |