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×#3950 | C2 | direct (N × H) |
| 6. C2×C52×C8 | C4 | semidirect |
| 11. C2×#3950 | C5 | direct (N × H) |
| 19. C52×C8 | C2×C4 | semidirect |
| 26. #3950 | C2×C5 | direct (N × H) |
| 42. C2×C5×C8 | Dic5 | semidirect |
| 43. C2×C5×C8 | C4×C5 | semidirect |
| 51. C2×C52 | #107 | semidirect |
| 75. C5×C8 | C2×Dic5 | semidirect |
| 76. C5×C8 | C2×C4×C5 | semidirect |
| 80. C52 | C2×#107 | semidirect |
| 106. C2×C8 | C5×Dic5 | semidirect |
| 114. C2×C5 | #3950 | direct (N × H) |
| 115. C2×C5 | C5×#107 | semidirect |
| 129. C8 | C2×C5×Dic5 | semidirect |
| 131. C5 | C2×#3950 | direct (N × H) |
| 132. C5 | C2×C5×#107 | semidirect |
| 141. C2 | C5×#3950 | 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×#3950 | 2 |
| C2×C5×#107 | 5 |
| C2×#3950 | 5 |