Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
552 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 164 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. #11717037 | C2 | semidirect |
| 5. C4×#6039 | C2 | semidirect |
| 6. #11716991 | C2 | semidirect |
| 20. C2×C4×C52 | Q8 | semidirect |
| 74. C2×C4×C5 | Dic10 | semidirect |
| 91. C52 | #533 | semidirect |
| 131. C2×C4 | #6039 | semidirect |
| 135. C5 | #65851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1039 | 2 |
| C5×#4072 | 2 |
| #11717100 | 2 |
| #11717037 | 2 |
| C4×#6039 | 2 |
| #11716991 | 2 |
| #65851 | 5 |