Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
350 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 94 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. C52×#498 | C2 | semidirect |
| 4. C5×#64707 | C2 | semidirect |
| 5. C5×#64683 | C2 | semidirect |
| 16. #10602143 | C5 | direct (N × H) |
| 25. C5×Dic20 | Q8 | semidirect |
| 26. C5×D40 | Q8 | semidirect |
| 32. C5×#498 | D5 | semidirect |
| 33. C5×#498 | C2×C5 | semidirect |
| 40. #64707 | C2×C5 | semidirect |
| 41. #64683 | C2×C5 | semidirect |
| 112. Dic20 | C5×Q8 | semidirect |
| 113. D40 | C5×Q8 | semidirect |
| 119. #498 | C5×D5 | semidirect |
| 170. C52 | #2230 | semidirect |
| 226. C5 | #10602143 | direct (N × H) |
| 227. C5 | C5×#2230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#498 | 2 |
| C5×#64989 | 2 |
| C5×#64708 | 2 |
| C5×#64707 | 2 |
| C5×#64683 | 2 |
| C5×#2230 | 5 |
| #10602143 | 5 |