Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
163 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 163 conjugacy classes of subgroups — too many to draw. Only its 43 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 |
|---|---|---|
| 2. C2×AGL(1,𝔽25) | C2 | semidirect |
| 3. C2×#10597167 | C2 | semidirect |
| 4. AΓL(1,𝔽25) | C2 | direct (N × H) |
| 11. AGL(1,𝔽25) | C22 | semidirect |
| 12. #10597167 | C22 | semidirect |
| 15. C2×#6053 | D3 | semidirect |
| 30. #6053 | C2×D3 | semidirect |
| 31. C2×C52⋊C3 | M16 | semidirect |
| 32. (C5⋊D5)⋊C3 | M16 | semidirect |
| 44. C52⋊C3 | C2×M16 | semidirect |
| 45. C2×C52 | ΓL(1,𝔽25) | semidirect |
| 46. C5⋊D5 | ΓL(1,𝔽25) | semidirect |
| 59. C52 | C2×ΓL(1,𝔽25) | semidirect |
| 114. C2 | AΓL(1,𝔽25) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64480⋊C2 | 2 |
| C2×AGL(1,𝔽25) | 2 |
| C2×#10597167 | 2 |
| AΓL(1,𝔽25) | 2 |
| C2×#6053⋊C2 | 3 |
| C2×ΓL(1,𝔽25) | 25 |