Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
207 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 207 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 14. #65788 | C5 | direct (N × H) |
| 24. C5×#170 | Q8 | semidirect |
| 80. #170 | C5×Q8 | semidirect |
| 89. C52 | #446 | semidirect |
| 134. C5 | C5×#446 | semidirect |
| 135. C5 | #65788 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×Dic5 | 2 |
| C5×#4004 | 2 |
| C5×#4002 | 2 |
| C5×C4⋊#170 | 2 |
| C4×C5×#170 | 2 |
| #65788 | 5 |
| C5×#446 | 5 |