Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
568 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 568 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 |
| prime radical | C52×2−1+4 | C2 |
| 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 |
|---|---|---|
| 2. C52×#137 | C2 | semidirect |
| 3. C52×C4⋊Q8 | C2 | semidirect |
| 4. C52×#104 | C2 | semidirect |
| 5. C52×#101 | C2 | semidirect |
| 17. C5×#456 | C5 | direct (N × H) |
| 33. C5×#137 | C2×C5 | semidirect |
| 34. C5×C4⋊Q8 | C2×C5 | semidirect |
| 35. C5×#104 | C2×C5 | semidirect |
| 36. C5×#101 | C2×C5 | semidirect |
| 55. #456 | C52 | direct (N × H) |
| 74. #137 | C2×C52 | semidirect |
| 75. C4⋊Q8 | C2×C52 | semidirect |
| 76. #104 | C2×C52 | semidirect |
| 77. #101 | C2×C52 | semidirect |
| 78. C52 | #456 | direct (N × H) |
| 114. C5 | C5×#456 | 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×#137 | 2 |
| C52×C4⋊Q8 | 2 |
| C52×#104 | 2 |
| C52×#101 | 2 |
| C5×#456 | 5 |