Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
472 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 1. C22×C52×Q8 | C2 | semidirect |
| 2. C2×C5×#688 | C2 | semidirect |
| 4. C5×#3967 | C2 | semidirect |
| 5. C5×C22⋊#168 | C2 | semidirect |
| 18. #65516 | C5 | direct (N × H) |
| 23. C52×Q8 | D4 | semidirect |
| 34. C22×C5×Q8 | D5 | semidirect |
| 35. C22×C5×Q8 | C2×C5 | semidirect |
| 38. C2×#688 | C2×C5 | semidirect |
| 42. #3967 | C2×C5 | semidirect |
| 43. C22⋊#168 | C2×C5 | semidirect |
| 46. C22×C52 | SD16 | semidirect |
| 100. C5×Q8 | C22⋊D5 | semidirect |
| 101. C5×Q8 | C5×D4 | semidirect |
| 125. C22×Q8 | C5×D5 | semidirect |
| 130. C52 | #448 | semidirect |
| 142. C22×C5 | #688 | semidirect |
| 143. C22×C5 | C5×SD16 | semidirect |
| 189. Q8 | C5×C22⋊D5 | semidirect |
| 200. C5 | #65516 | direct (N × H) |
| 201. C5 | C5×#448 | semidirect |
| 207. C22 | C5×#688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×Q8 | 2 |
| C2×C5×#688 | 2 |
| C5×#4076 | 2 |
| C5×#3967 | 2 |
| C5×C22⋊#168 | 2 |
| C5×#448 | 5 |
| #65516 | 5 |