Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1618 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 1618 conjugacy classes of subgroups — too many to draw. Only its 382 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C59×#376 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C59×#496 | C2 | semidirect |
| 2. C2×C59×#495 | C2 | semidirect |
| 3. C2×C59×#493 | C2 | semidirect |
| 4. C59×#2657 | C2 | semidirect |
| 5. C59×#1726 | C2 | semidirect |
| 37. #97×C59 | D4 | semidirect |
| 38. C4×C8×C59 | D4 | semidirect |
| 79. #33308 | C59 | direct (N × H) |
| 89. C2×#496 | C2×C59 | semidirect |
| 90. C2×#495 | C2×C59 | semidirect |
| 91. C2×#493 | C2×C59 | semidirect |
| 92. #2657 | C2×C59 | semidirect |
| 93. #1726 | C2×C59 | semidirect |
| 110. C59 | #33308 | direct (N × H) |
| 129. #97 | D4×C59 | semidirect |
| 130. C4×C8 | D4×C59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C59×#496 | 2 |
| C2×C59×#495 | 2 |
| C2×C59×#493 | 2 |
| C59×#2657 | 2 |
| C59×#1726 | 2 |
| #33308 | 59 |