Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
336 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 174 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 |
|---|---|---|
| 3. C5×#3949 | C2 | direct (N × H) |
| 6. C2×C52×C8 | C4 | semidirect |
| 11. C2×#3949 | C5 | direct (N × H) |
| 19. C52×C8 | C2×C4 | semidirect |
| 26. #3949 | C2×C5 | direct (N × H) |
| 41. C2×C5×C8 | Dic5 | semidirect |
| 42. C2×C5×C8 | C4×C5 | semidirect |
| 50. C2×C52 | #106 | semidirect |
| 73. C5×C8 | C2×Dic5 | semidirect |
| 74. C5×C8 | C2×C4×C5 | semidirect |
| 78. C52 | C2×#106 | semidirect |
| 101. C2×C8 | C5×Dic5 | semidirect |
| 108. C2×C5 | #3949 | direct (N × H) |
| 109. C2×C5 | C5×#106 | semidirect |
| 121. C8 | C2×C5×Dic5 | semidirect |
| 123. C5 | C2×#3949 | direct (N × H) |
| 124. C5 | C2×C5×#106 | semidirect |
| 132. C2 | C5×#3949 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×C8 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C5×#3949 | 2 |
| C2×C5×#106 | 5 |
| C2×#3949 | 5 |