Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
267 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 267 conjugacy classes of subgroups — too many to draw. Only its 109 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. C4⋊#6032 | C2 | semidirect |
| 32. C4×C52 | M16 | semidirect |
| 78. C52 | #423 | semidirect |
| 91. C4×C5 | #681 | semidirect |
| 93. C4×C5 | #700 | semidirect |
| 123. C5 | #65213 | semidirect |
| 124. C5 | #65681 | semidirect |
| 131. C4 | #87849 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87849 | 2 |
| C42×C5×D5 | 2 |
| C4⋊#6032 | 2 |
| #65681 | 5 |
| #65213 | 5 |