Question: What kind of group does Birmingham City F.C. and English football league system have in common?

Context articles: Birmingham City F.C. Reserves and Academy
2004–05 Birmingham City F.C. season
History of Norwich City F.C.
Birmingham City F.C. league record by opponent
2007–08 Birmingham City F.C. season
2006–07 Birmingham City F.C. season
2015–16 Birmingham City F.C. season
Birmingham City F.C.
National League System
English football league system

Birmingham City F.C. Development Squad and Academy are the reserve team and the youth development system respectively of Birmingham City Football Club.
 The reserve team, established in 1879, played in the Premier Reserve League South in the 2009–10 season, but did not enter a league again until the 2012–13 season, when it was placed in the northern division of the newly formed Professional Development League 2, a predominantly under-21 league.
 The Academy, established in its current form in 1999, trains boys in age groups from under 9s through to under 18s.
The 2004–05 season was Birmingham City Football Club's 102nd season in the English football league system, their third season in the Premier League and their 53rd in the top tier of English football.
 It ran from 1 July 2004 to 30 June 2005.
 Under the management of former Birmingham City player Steve Bruce, the team finished in 12th place, two places lower than the season before.
 They reached the fourth round of the FA Cup and the third round of the League Cup.
 The top scorer for the season was England forward Emile Heskey with eleven goals in all competitions, of which ten were scored in the League.
The history of Norwich City F.C. stretches back to 1902.
 After a brief period in amateur football, Norwich City F.C. spent 15 years as a semi-professional team in the Southern League before admission to English Football League in 1920.
 For most of the next 50 years, Norwich City F.C. played in Division Three (South), then the joint lowest tier of the football league, a period that was distinguished by "a thrilling giant-killing sequence which took them to the FA Cup semi-finals" in 1959.
 Shortly afterwards, the club won its first major trophy, the 1962 League Cup.
 Norwich finally reached the pinnacle of the league structure in 1972, with their first promotion to the top tier.
Birmingham City Football Club, an English association football club based in the city of Birmingham, was founded in 1875 as Small Heath Alliance.
 For their first thirteen years, there was no league football, so matches were arranged on an occasional basis, supplemented by cup competitions organised at both local and national level.
 In 1888, Small Heath joined the Combination, a league set up to provide organised football for those clubs not invited to join the Football League which was to start the same year.
 However, the Combination was not well organised, and folded in April 1889 with many fixtures still outstanding.
 Small Heath were founder members of the Football Alliance in 1889, and three years later were elected to the newly formed Second Division of the Football League.
 They topped the table in their first season, though failed to win promotion via the test match system then in operation, but reached the top flight for the first time in 1894.
 Since that time, they have not fallen below the third tier of the English football league system, and were promoted to the Premier League for the first time for the 2002–03 season.
The 2007–08 season was Birmingham City Football Club's 105th season in the English football league system since their admission to the Football League in 1892, their fifth season in the Premier League, and their 55th season in the top tier of English football.
 Birmingham finished 19th in the 20-team league, so were relegated back to the Championship after just one season at the higher level.
The 2006–07 season was Birmingham City Football Club's 104th consecutive season played in the English football league system, their 46th in the second tier of English football, and their first season at that level under the name of the Football League Championship.
 Managed by Steve Bruce, Birmingham were promoted back to the Premier League after just one season in the Championship.
 They reached the fourth round of both the 2006–07 FA Cup and League Cup.
 The 2006–07 season also marked the 100th anniversary of the first match held at their St Andrew's stadium.
The 2015–16 season was Birmingham City Football Club' s 113th season in the English football league system and fifth consecutive season in the Football League Championship.
 It covered the period from 1 July 2015 to 30 June 2016.
 Their Championship record, of 63 points accrued via 16 wins, 15 draws and 15 losses resulting in a tenth-place finish, was exactly the same as in 2014–15.
 Tenth was the lowest position the team had occupied all season.
 The average attendance at league matches, of 17,602, was some 9% higher than in 2014–15.
 As with all clubs in the top two tiers of English football, Birmingham entered the 2015–16 FA Cup in the third round; they lost in that round at home to Premier League club AFC Bournemouth.
 In the League Cup, they progressed through two rounds before being eliminated by Aston Villa, also of the Premier League, in the third.
Birmingham City Football Club ( , locally ) is a professional association football club based in the city of Birmingham, England.
 Formed in 1875 as Small Heath Alliance, they became Small Heath in 1888, then Birmingham in 1905, finally becoming Birmingham City in 1943.
 The team compete in the EFL Championship, the second tier of the English football league system.
The National League System comprises the seven levels of the English football league system immediately below the level of the English Football League.
 It contains 86 league competitions and more than 1,600 clubs.
 It comes under the jurisdiction of The Football Association.
 The National League System has a hierarchical format with promotion and relegation between leagues at different levels.
 For details of leagues above and below the National League System, see the English football league system.
The English football league system, also known as the football pyramid, is a series of interconnected leagues for men's association football clubs in England, with six teams from Wales and one from Guernsey also competing.
 The system has a hierarchical format with promotion and relegation between leagues at different levels, allowing even the smallest club the theoretical possibility of ultimately rising to the very top of the system, although in practice it would take a team at the bottom levels at least two decades of consistently finishing at or near the top of each successive league to reach the top level, and even then additional restrictions, particularly in regard to stadium facilities, would then come into effect at the highest levels that could prevent a club from being allowed access to the top levels.
 There are more than 140 individual leagues, containing more than 480 divisions.