Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
896 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 896 conjugacy classes of subgroups — too many to draw. Only its 162 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. #11716899 | C2 | direct (N × H) |
| 7. C22×#1044 | C4 | semidirect |
| 9. C22×C4×C52 | C4 | semidirect |
| 10. C22×#1039 | C4 | semidirect |
| 12. C2×C4×C5⋊D5 | C4 | semidirect |
| 25. C2×#1044 | C2×C4 | semidirect |
| 27. C2×C4×C52 | C2×C4 | semidirect |
| 29. C2×#1039 | C2×C4 | semidirect |
| 59. C22×C4×C5 | AGL(1,𝔽5) | semidirect |
| 69. C2×C52 | #95 | semidirect |
| 73. C5⋊D5 | #95 | semidirect |
| 97. C2×C4×C5 | C2×AGL(1,𝔽5) | semidirect |
| 109. C52 | C2×#95 | semidirect |
| 150. C22×C4 | #1044 | semidirect |
| 155. C2×C5 | (C2×AGL(1,𝔽5))⋊C4 | semidirect |
| 181. C2×C4 | C2×#1044 | semidirect |
| 183. C5 | C2×(C2×AGL(1,𝔽5))⋊C4 | semidirect |
| 203. C2 | #11716899 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1044 | 2 |
| C22×C4×C5⋊D5 | 2 |
| #11716899 | 2 |
| C2×(C2×AGL(1,𝔽5))⋊C4 | 5 |