Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1072 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 272 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 |
|---|---|---|
| 3. C2×C5×C4⋊Dic5 | C2 | semidirect |
| 4. C2×#87781 | C2 | semidirect |
| 5. #11717018 | C2 | direct (N × H) |
| 9. C2×C4×C5⋊D5 | C4 | semidirect |
| 14. C5×C4⋊Dic5 | C22 | semidirect |
| 15. #87781 | C22 | semidirect |
| 22. C2×C4×C52 | C2×C4 | semidirect |
| 24. C2×#1039 | C2×C4 | semidirect |
| 26. C4×C5⋊D5 | C2×C4 | semidirect |
| 34. C2×C4⋊Dic5 | D5 | semidirect |
| 41. C2×C5⋊D5 | C4⋊C4 | semidirect |
| 45. C4×C52 | C22×C4 | semidirect |
| 46. #1039 | C22×C4 | semidirect |
| 63. C4⋊Dic5 | C2×D5 | semidirect |
| 66. C2×C52 | C2×C4⋊C4 | semidirect |
| 70. C5⋊D5 | C2×C4⋊C4 | semidirect |
| 85. C2×C4×C5 | C4×D5 | semidirect |
| 101. C52 | C22×C4⋊C4 | semidirect |
| 120. C4×C5 | C2×C4×D5 | semidirect |
| 138. C2×C5 | D5×C4⋊C4 | semidirect |
| 155. C2×C4 | #6036 | semidirect |
| 158. C5 | C2×D5×C4⋊C4 | semidirect |
| 169. C4 | C2×#6036 | semidirect |
| 171. C2 | #11717018 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5⋊D5 | 2 |
| C22×#6036 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C2×#87781 | 2 |
| #11717018 | 2 |
| C2×D5×C4⋊C4 | 5 |