Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
584 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 328 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C52 | C22⋊C4 |
| commutator | C22 | C22×C4×C52 |
| Frattini, cosocle | C2×C4 | C23×C52 |
| prime radical | C23×C52 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C52 ◁ C22×C4×C52 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C52×#101 | C2 | direct (N × H) |
| 13. C2×C5×#101 | C5 | direct (N × H) |
| 27. C5×#101 | C2×C5 | direct (N × H) |
| 44. C2×#101 | C52 | direct (N × H) |
| 47. C2×C52 | #101 | direct (N × H) |
| 62. #101 | C2×C52 | direct (N × H) |
| 63. C52 | C2×#101 | direct (N × H) |
| 82. C2×C5 | C5×#101 | direct (N × H) |
| 95. C5 | C2×C5×#101 | direct (N × H) |
| 105. C2 | C52×#101 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×Q8 | 2 |
| C2×C52×M16 | 2 |
| C52×#101 | 2 |
| C2×C5×#101 | 5 |