Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
444 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 184 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×C79 | D42 |
| commutator, Frattini, cosocle | C2×C4 | C24×C79 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C79 ◁ C2×C4×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #578×C79 | C2 | semidirect |
| 2. #494×C79 | C2 | semidirect |
| 3. #473×C79 | C2 | semidirect |
| 4. #456×C79 | C2 | semidirect |
| 5. #443×C79 | C2 | semidirect |
| 60. #3293 | C79 | direct (N × H) |
| 61. C79 | #3293 | direct (N × H) |
| 62. #578 | C2×C79 | semidirect |
| 63. #494 | C2×C79 | semidirect |
| 64. #473 | C2×C79 | semidirect |
| 65. #456 | C2×C79 | semidirect |
| 66. #443 | C2×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #578×C79 | 2 |
| #494×C79 | 2 |
| #473×C79 | 2 |
| #456×C79 | 2 |
| #443×C79 | 2 |
| #3293 | 79 |