Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
302 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 112 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×C79 | #120 |
| commutator | C2×C4 | C22×C4×C79 |
| Frattini, cosocle | C22×C4 | C23×C79 |
| prime radical | C2×#41×C79 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C22×C4×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #428×C79 | C2 | semidirect |
| 5. #384×C79 | C2 | semidirect |
| 6. #343×C79 | C2 | semidirect |
| 7. #339×C79 | C2 | semidirect |
| 23. #104×C79 | C4 | semidirect |
| 42. M16×C79 | C2×C4 | semidirect |
| 58. C42×C79 | C2×C4 | semidirect |
| 62. Q8×C79 | C4⋊C4 | semidirect |
| 66. D4×C79 | C4⋊C4 | semidirect |
| 112. #1859 | C79 | direct (N × H) |
| 113. C79 | #1859 | direct (N × H) |
| 115. #428 | C2×C79 | semidirect |
| 118. #384 | C2×C79 | semidirect |
| 119. #343 | C2×C79 | semidirect |
| 120. #339 | C2×C79 | semidirect |
| 136. #104 | C4×C79 | semidirect |
| 155. M16 | C2×C4×C79 | semidirect |
| 171. C42 | C2×C4×C79 | semidirect |
| 175. Q8 | C4⋊C4×C79 | semidirect |
| 179. D4 | C4⋊C4×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #520×C79 | 2 |
| #428×C79 | 2 |
| C2×#104×C79 | 2 |
| #417×C79 | 2 |
| #384×C79 | 2 |
| #343×C79 | 2 |
| #339×C79 | 2 |
| #1859 | 79 |