Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
138 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 30 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×C41 | #1404 |
| commutator | #125 | C2×C4×C41 |
| Frattini, cosocle | #491 | C22×C41 |
| prime radical | C41×#562 | C4 |
| LCS | G ▷ #125 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C41 ◁ C22×C41 ◁ C2×C4×C41 ◁ C42×C41 ◁ C41×#491 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#1413 | C2 | semidirect |
| 3. C41×#1356 | C2 | semidirect |
| 55. #7525 | C41 | direct (N × H) |
| 66. #1413 | C2×C41 | semidirect |
| 67. #1356 | C2×C41 | semidirect |
| 78. C41 | #7525 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#1662 | 2 |
| C41×#1413 | 2 |
| C41×#1356 | 2 |
| #7525 | 41 |