Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
584 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 216 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 | #120 |
| 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. C52×2−1+4 | C2 | semidirect |
| 2. C52×AGL(1,ℤ/8) | C2 | semidirect |
| 3. C52×#124 | C2 | semidirect |
| 4. C52×#104 | C2 | semidirect |
| 5. C52×#101 | C2 | semidirect |
| 17. C5×#454 | C5 | direct (N × H) |
| 32. C5×2−1+4 | C2×C5 | semidirect |
| 33. C5×AGL(1,ℤ/8) | C2×C5 | semidirect |
| 34. C5×#124 | C2×C5 | semidirect |
| 35. C5×#104 | C2×C5 | semidirect |
| 36. C5×#101 | C2×C5 | semidirect |
| 56. #454 | C52 | direct (N × H) |
| 75. 2−1+4 | C2×C52 | semidirect |
| 76. AGL(1,ℤ/8) | C2×C52 | semidirect |
| 77. #124 | C2×C52 | semidirect |
| 78. #104 | C2×C52 | semidirect |
| 79. #101 | C2×C52 | semidirect |
| 80. C52 | #454 | direct (N × H) |
| 118. C5 | C5×#454 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×2−1+4 | 2 |
| C52×AGL(1,ℤ/8) | 2 |
| C52×#124 | 2 |
| C52×#104 | 2 |
| C52×#101 | 2 |
| C5×#454 | 5 |