Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
267 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 267 conjugacy classes of subgroups — too many to draw. Only its 120 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×C4⋊#170 | C2 | semidirect |
| 11. #65681 | C5 | direct (N × H) |
| 26. C4⋊#170 | C2×C5 | semidirect |
| 32. C4×C52 | M16 | semidirect |
| 78. C52 | #423 | semidirect |
| 92. C4×C5 | C5×M16 | semidirect |
| 93. C4×C5 | #700 | semidirect |
| 123. C5 | C5×#423 | semidirect |
| 124. C5 | #65681 | direct (N × H) |
| 131. C4 | C5×#700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#700 | 2 |
| C42×C5×D5 | 2 |
| C5×C4⋊#170 | 2 |
| #65681 | 5 |
| C5×#423 | 5 |