Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
282 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 98 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. C5×Q8×Dic5 | C2 | semidirect |
| 4. C52×#103 | C2 | semidirect |
| 6. C5×#3947 | C2 | semidirect |
| 7. C5×#3939 | C2 | semidirect |
| 13. C5×#688 | C4 | semidirect |
| 21. #65106 | C5 | direct (N × H) |
| 24. C52×Q8 | C2×C4 | semidirect |
| 35. C5×#168 | C2×C4 | semidirect |
| 39. Q8×Dic5 | C2×C5 | semidirect |
| 44. C5×#103 | D5 | semidirect |
| 45. C5×#103 | C2×C5 | semidirect |
| 49. #3947 | C2×C5 | semidirect |
| 50. #3939 | C2×C5 | semidirect |
| 82. #688 | C4×C5 | semidirect |
| 100. C5×Q8 | C4×D5 | semidirect |
| 101. C5×Q8 | C2×C4×C5 | semidirect |
| 127. #168 | C2×C4×C5 | semidirect |
| 132. #103 | C5×D5 | semidirect |
| 135. C52 | #440 | semidirect |
| 188. Q8 | C4×C5×D5 | semidirect |
| 201. C5 | #65106 | direct (N × H) |
| 202. C5 | C5×#440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×Dic5 | 2 |
| C2×C5×#688 | 2 |
| C5×#4039 | 2 |
| C52×#103 | 2 |
| C5×#3953 | 2 |
| C5×#3947 | 2 |
| C5×#3939 | 2 |
| C5×#440 | 5 |
| #65106 | 5 |