Finite Group Databasebeta

← C2×C3×D2145 #38788315

Subgroups — C2×C3×D2145 #38788315

Order 25740.

176 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D2145C212yesmaximal, direct product factor
2C2×C32×C5×C11×C13C211yesmaximal, characteristic, complemented
3C2×C3×D715—31nomaximal
4C2×D2145C311yesmaximal, characteristic, direct product factor
5C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
6C2×C3×D429—51nomaximal, Hall
7D2145C2×C312yesdirect product factor
8C3×D715—32no—
9C2×C3×C5×C11×C13—21no—
10C2×C3×C5×C11×C13D311yescharacteristic, complemented
11C2×C3×C5×C11×C13C2×C311yescharacteristic, complemented
12C2×D715—31noHall
13C3×D429—52no—
14C2×C32×C11×C13D511yescharacteristic, complemented
15C2×C3×D195—111nomaximal, Hall
16C3×C5×C11×C13—21no—
17C3×C5×C11×C13C2×D311yescharacteristic, complemented
18C3×C5×C11×C13C22×C311yescharacteristic, complemented
19C2×C3×D165—131nomaximal, Hall
20C2×D429—51no—
21C2×C3×D143—151no—
22C2×C5×C11×C13C3×D311yescharacteristic, complemented
23D715—32no—
24C32×C11×C13C2×D511yescharacteristic, complemented, Hall
25C2×C32×C5×C13D1111yescharacteristic, complemented
26C3×D195—112no—
27C2×C32×C5×C11D1311yescharacteristic, complemented
28C3×D165—132no—
29C2×C3×C11×C13—21no—
30C2×C3×C11×C13C3×D511yescharacteristic, complemented
31C2×C3×C11×C13D1511yescharacteristic, complemented
32D429—52no—
33C3×D143—152no—
34C2×D195—111no—
35C2×C3×D65—331no—
36C5×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
37C2×D165—131no—
38C2×C3×D55—391no—
39C32×C5×C13C2×D1111yescharacteristic, complemented, Hall
40C2×D143—151noHall
41C32×C5×C11C2×D1311yescharacteristic, complemented, Hall
42C2×C3×D39—551noHall
43C3×C11×C13—21no—
44C3×C11×C13C2×C3×D511yescharacteristic, complemented
45C3×C11×C13C2×D1511yescharacteristic, complemented
46C2×C3×D33—651noHall
47C2×C3×C5×C13—21no—
48C2×C3×C5×C13C3×D1111yescharacteristic, complemented
49C2×C3×C5×C13D3311yescharacteristic, complemented
50D195—112no—
51C3×D65—332no—
52C2×C3×C5×C11—21no—
53C2×C3×C5×C11C3×D1311yescharacteristic, complemented
54C2×C3×C5×C11D3911yescharacteristic, complemented
55D165—132no—
56C3×D55—392no—
57C2×C11×C13C3×D1511yescharacteristic, complemented
58D143—152no—
59C2×D65—331noHall
60C2×C32×C13D5511yescharacteristic, complemented
61C3×D39—552no—
62C2×D55—391noHall
63C2×C32×C11D6511yescharacteristic, complemented
64C3×D33—652no—
65C3×C5×C13—21no—
66C3×C5×C13C2×C3×D1111yescharacteristic, complemented
67C3×C5×C13C2×D3311yescharacteristic, complemented
68C2×C3×D15—1431noHall
69C3×C5×C11—21no—
70C3×C5×C11C2×C3×D1311yescharacteristic, complemented
71C3×C5×C11C2×D3911yescharacteristic, complemented
72C2×D39—551no—
73C2×C3×D13—1651no—
74C11×C13C2×C3×D1511yescharacteristic, complemented, Hall
75C2×D33—651no—
76C2×C3×D11—1951no—
77C2×C5×C13C3×D3311yescharacteristic, complemented
78D65—332no—
79C32×C13C2×D5511yescharacteristic, complemented, Hall
80C2×C5×C11C3×D3911yescharacteristic, complemented
81D55—392no—
82C32×C11C2×D6511yescharacteristic, complemented, Hall
83C2×C32×C5D14311yescharacteristic, complemented
84C3×D15—1432no—
85C2×C3×C13—21no—
86C2×C3×C13C3×D5511yescharacteristic, complemented
87C2×C3×C13D16511yescharacteristic, complemented
88D39—552no—
89C3×D13—1652no—
90C2×C3×C11—21no—
91C2×C3×C11C3×D6511yescharacteristic, complemented
92C2×C3×C11D19511yescharacteristic, complemented
93D33—652no—
94C3×D11—1952no—
95C5×C13C2×C3×D3311yescharacteristic, complemented, Hall
96C2×D15—1431no—
97C2×C3×D5—4291no—
98C5×C11C2×C3×D3911yescharacteristic, complemented, Hall
99C2×D13—1651noHall
100C32×C5C2×D14311yescharacteristic, complemented, Hall
101C2×D11—1951noHall
102C3×C13—21no—
103C3×C13C2×C3×D5511yescharacteristic, complemented
104C3×C13C2×D16511yescharacteristic, complemented
105C2×C3×D3—7151noHall
106C3×C11—21no—
107C3×C11C2×C3×D6511yescharacteristic, complemented
108C3×C11C2×D19511yescharacteristic, complemented
109C2×C3×C5—21no—
110C2×C3×C5C3×D14311yescharacteristic, complemented
111C2×C3×C5D42911yescharacteristic, complemented
112D15—1432no—
113C3×D5—4292no—
114C2×C13C3×D16511yescharacteristic, complemented
115D13—1652no—
116C2×C11C3×D19511yescharacteristic, complemented
117D11—1952no—
118C2×D5—4291noHall
119C2×C32D71511yescharacteristic, complemented
120C3×D3—7152no—
121C3×C5—21no—
122C3×C5C2×C3×D14311yescharacteristic, complemented
123C3×C5C2×D42911yescharacteristic, complemented
124C13C2×C3×D16511yescharacteristic, complemented, Sylow
125C22×C3—21451no—
126C2×D3—7151no—
127C11C2×C3×D19511yescharacteristic, complemented, Sylow
128C2×C5C3×D42911yescharacteristic, complemented
129D5—4292no—
130C32C2×D71511yescharacteristic, complemented, Sylow
131C2×C3—21no—
132C2×C3—21452no—
133C2×C3C3×D71511yescharacteristic, complemented
134C2×C3D214511yescharacteristic, direct product factor
135D3—7152no—
136C5C2×C3×D42911yescharacteristic, complemented, Sylow
137C22—21451noSylow
138C3—21no—
139C3C2×D214511yescharacteristic, direct product factor
140C3C2×C3×D71511yescharacteristic, complemented
141C2—21452no—
142C2C3×D214511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3D2145
commutator, cosocle, hypocenterC3×C5×C11×C13C22×C3
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C13C2
LCSG ▷ C3×C5×C11×C13
UCSC1 ◁ C2×C3

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×D2145C2direct (N × H)
2. C2×C32×C5×C11×C13C2semidirect
4. C2×D2145C3direct (N × H)
5. C32×C5×C11×C13C22semidirect
7. D2145C2×C3direct (N × H)
10. C2×C3×C5×C11×C13D3semidirect
11. C2×C3×C5×C11×C13C2×C3semidirect
14. C2×C32×C11×C13D5semidirect
17. C3×C5×C11×C13C2×D3semidirect
18. C3×C5×C11×C13C22×C3semidirect
22. C2×C5×C11×C13C3×D3semidirect
24. C32×C11×C13C2×D5semidirect
25. C2×C32×C5×C13D11semidirect
27. C2×C32×C5×C11D13semidirect
30. C2×C3×C11×C13C3×D5semidirect
31. C2×C3×C11×C13D15semidirect
36. C5×C11×C13C2×C3×D3semidirect
39. C32×C5×C13C2×D11semidirect
41. C32×C5×C11C2×D13semidirect
44. C3×C11×C13C2×C3×D5semidirect
45. C3×C11×C13C2×D15semidirect
48. C2×C3×C5×C13C3×D11semidirect
49. C2×C3×C5×C13D33semidirect
53. C2×C3×C5×C11C3×D13semidirect
54. C2×C3×C5×C11D39semidirect
57. C2×C11×C13C3×D15semidirect
60. C2×C32×C13D55semidirect
63. C2×C32×C11D65semidirect
66. C3×C5×C13C2×C3×D11semidirect
67. C3×C5×C13C2×D33semidirect
70. C3×C5×C11C2×C3×D13semidirect
71. C3×C5×C11C2×D39semidirect
74. C11×C13C2×C3×D15semidirect
77. C2×C5×C13C3×D33semidirect
79. C32×C13C2×D55semidirect
80. C2×C5×C11C3×D39semidirect
82. C32×C11C2×D65semidirect
83. C2×C32×C5D143semidirect
86. C2×C3×C13C3×D55semidirect
87. C2×C3×C13D165semidirect
91. C2×C3×C11C3×D65semidirect
92. C2×C3×C11D195semidirect
95. C5×C13C2×C3×D33semidirect
98. C5×C11C2×C3×D39semidirect
100. C32×C5C2×D143semidirect
103. C3×C13C2×C3×D55semidirect
104. C3×C13C2×D165semidirect
107. C3×C11C2×C3×D65semidirect
108. C3×C11C2×D195semidirect
110. C2×C3×C5C3×D143semidirect
111. C2×C3×C5D429semidirect
114. C2×C13C3×D165semidirect
116. C2×C11C3×D195semidirect
119. C2×C32D715semidirect
122. C3×C5C2×C3×D143semidirect
123. C3×C5C2×D429semidirect
124. C13C2×C3×D165semidirect
127. C11C2×C3×D195semidirect
128. C2×C5C3×D429semidirect
130. C32C2×D715semidirect
133. C2×C3C3×D715semidirect
134. C2×C3D2145direct (N × H)
136. C5C2×C3×D429semidirect
139. C3C2×D2145direct (N × H)
140. C3C2×C3×D715semidirect
142. C2C3×D2145direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×D21452
C2×C32×C5×C11×C132
C2×C3×D7153
C2×D21453
C2×C3×D4295
C2×C3×D19511
C2×C3×D16513