Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
432 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C52 | #121 |
| commutator, Frattini, cosocle | C2×C4 | C23×C52 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C52 ◁ C2×C4×C52 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C52×AGL(1,ℤ/8) | C2 | semidirect |
| 2. C2×C52×D8 | C2 | semidirect |
| 3. C52×#131 | C2 | semidirect |
| 4. C52×#108 | C2 | semidirect |
| 5. C52×#100 | C2 | semidirect |
| 17. C5×#472 | C5 | direct (N × H) |
| 30. C5×AGL(1,ℤ/8) | C2×C5 | semidirect |
| 31. C2×C5×D8 | C2×C5 | semidirect |
| 32. C5×#131 | C2×C5 | semidirect |
| 33. C5×#108 | C2×C5 | semidirect |
| 34. C5×#100 | C2×C5 | semidirect |
| 53. #472 | C52 | direct (N × H) |
| 70. AGL(1,ℤ/8) | C2×C52 | semidirect |
| 71. C2×D8 | C2×C52 | semidirect |
| 72. #131 | C2×C52 | semidirect |
| 73. #108 | C2×C52 | semidirect |
| 74. #100 | C2×C52 | semidirect |
| 75. C52 | #472 | direct (N × H) |
| 110. C5 | C5×#472 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×AGL(1,ℤ/8) | 2 |
| C2×C52×D8 | 2 |
| C52×#131 | 2 |
| C52×#108 | 2 |
| C52×#100 | 2 |
| C5×#472 | 5 |