Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
560 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 254 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×#4016 | C2 | direct (N × H) |
| 12. C2×#4016 | C5 | direct (N × H) |
| 28. #4016 | C2×C5 | direct (N × H) |
| 51. C2×C52 | #125 | semidirect |
| 77. C52 | C2×#125 | semidirect |
| 104. C2×C5 | #4016 | direct (N × H) |
| 105. C2×C5 | C5×#125 | semidirect |
| 118. C5 | C2×#4016 | direct (N × H) |
| 119. C5 | C2×C5×#125 | semidirect |
| 126. C2 | C5×#4016 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×C52 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C2×C5×#683 | 2 |
| C5×#4016 | 2 |
| C2×C5×#125 | 5 |
| C2×#4016 | 5 |