Finite Group DatabasebetaFinite Group DatabasebetaOrder 4800.
714 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 172 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. C22×AGL(1,𝔽25) | C2 | semidirect |
| 2. C22×#10597167 | C2 | semidirect |
| 4. C2×AΓL(1,𝔽25) | C2 | direct (N × H) |
| 11. C2×AGL(1,𝔽25) | C22 | semidirect |
| 12. C2×#10597167 | C22 | semidirect |
| 13. AΓL(1,𝔽25) | C22 | direct (N × H) |
| 16. C22×#6053 | D3 | semidirect |
| 27. AGL(1,𝔽25) | C23 | semidirect |
| 28. #10597167 | C23 | semidirect |
| 35. C2×#6053 | C2×D3 | semidirect |
| 37. C22×C52⋊C3 | M16 | semidirect |
| 38. C2×(C5⋊D5)⋊C3 | M16 | semidirect |
| 56. #6053 | C22×D3 | semidirect |
| 59. C2×C52⋊C3 | C2×M16 | semidirect |
| 60. (C5⋊D5)⋊C3 | C2×M16 | semidirect |
| 63. C22×C52 | ΓL(1,𝔽25) | semidirect |
| 64. C2×C5⋊D5 | ΓL(1,𝔽25) | semidirect |
| 81. C52⋊C3 | C22×M16 | semidirect |
| 83. C2×C52 | C2×ΓL(1,𝔽25) | semidirect |
| 84. C5⋊D5 | C2×ΓL(1,𝔽25) | semidirect |
| 109. C52 | C22×ΓL(1,𝔽25) | semidirect |
| 174. C22 | AΓL(1,𝔽25) | direct (N × H) |
| 182. C2 | 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 |
|---|---|
| C22×AGL(1,𝔽25) | 2 |
| C22×#10597167 | 2 |
| C22×#64480⋊C2 | 2 |
| C2×AΓL(1,𝔽25) | 2 |
| C22×#6053⋊C2 | 3 |
| C22×ΓL(1,𝔽25) | 25 |