Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
400 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 400 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 |
| prime radical | C52×#41 | C22 |
| 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. C2×C52×Q16 | C2 | semidirect |
| 4. C52×#108 | C2 | semidirect |
| 5. C52×#101 | C2 | semidirect |
| 17. C5×#473 | C5 | direct (N × H) |
| 31. C2×C5×Q16 | C2×C5 | semidirect |
| 33. C5×#108 | C2×C5 | semidirect |
| 34. C5×#101 | C2×C5 | semidirect |
| 52. #473 | C52 | direct (N × H) |
| 69. C2×Q16 | C2×C52 | semidirect |
| 71. #108 | C2×C52 | semidirect |
| 72. #101 | C2×C52 | semidirect |
| 73. C52 | #473 | direct (N × H) |
| 106. C5 | C5×#473 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#137 | 2 |
| C2×C52×Q16 | 2 |
| C52×#131 | 2 |
| C52×#108 | 2 |
| C52×#101 | 2 |
| C5×#473 | 5 |