Finite Group Databasebeta

← C3×C5×D3×D7×C29 #49141558

Subgroups — C3×C5×D3×D7×C29 #49141558

Order 36540.

176 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C32×C5×D7×C29C211yesmaximal, characteristic, complemented
2C3×C5×D3×C7×C29C211yesmaximal, characteristic, complemented
3C3×C5×C29×D21C211yesmaximal, characteristic, complemented
4C2×C3×C5×D7×C29—31nomaximal
5C5×D3×D7×C29C311yesmaximal, characteristic, direct product factor
6C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
7C3×D3×D7×C29C511yesmaximal, characteristic, direct product factor, Hall
8C5×C29×D21C2×C311yescharacteristic, complemented
9C5×D3×C7×C29C2×C311yescharacteristic, complemented
10C3×C5×D7×C29—21no—
11C3×C5×D7×C29—31no—
12C3×C5×D7×C29D311yescharacteristic, direct product factor
13C3×C5×D7×C29C2×C311yescharacteristic, complemented
14C2×C3×C5×C7×C29—31no—
15C2×C3×C5×D3×C29—71nomaximal, Hall
16C2×C5×D7×C29—31noHall
17C3×C29×D21C2×C511yescharacteristic, complemented
18C3×D3×C7×C29C2×C511yescharacteristic, complemented
19C32×D7×C29C2×C511yescharacteristic, complemented
20C3×C5×C7×C29—21no—
21C3×C5×C7×C29C2×D311yescharacteristic, complemented
22C3×C5×C7×C29C22×C311yescharacteristic, complemented
23C3×C5×D3×C29—71no—
24C3×C5×D3×C29D711yescharacteristic, direct product factor
25C2×C32×C5×C29—71no—
26C2×C3×D7×C29—31no—
27D3×D7×C29C3×C511yescharacteristic, direct product factor
28C5×D7×C29—31no—
29C5×D7×C29C3×D311yescharacteristic, direct product factor
30C2×C5×C7×C29—31no—
31C32×C7×C29C22×C511yescharacteristic, complemented, Hall
32C22×C3×C5×C29—211no—
33C2×C5×D3×C29—71no—
34C32×C5×C29C2×D711yescharacteristic, complemented, Hall
35C3×C5×D3×D7C2911yesmaximal, characteristic, direct product factor, Hall
36C2×C3×C7×C29—31no—
37C29×D21C2×C3×C511yescharacteristic, complemented
38D3×C7×C29C2×C3×C511yescharacteristic, complemented
39C3×D7×C29—21no—
40C3×D7×C29—31no—
41C3×D7×C29C5×D311yescharacteristic, direct product factor
42C3×D7×C29C2×C3×C511yescharacteristic, complemented
43C2×C3×D3×C29—71noHall
44C5×C7×C29C2×C3×D311yescharacteristic, complemented, Hall
45C2×C3×C5×C29—31no—
46C2×C3×C5×C29—71no—
47C2×C3×C5×C29—71no—
48C2×C3×C5×C29—141no—
49C2×C3×C5×C29—211no—
50C5×D3×C29—71no—
51C5×D3×C29C3×D711yescharacteristic, direct product factor
52C2×D7×C29—31noHall
53C3×C5×D21C2×C2911yescharacteristic, complemented
54C3×C5×D3×C7C2×C2911yescharacteristic, complemented
55C32×C5×D7C2×C2911yescharacteristic, complemented
56C3×C7×C29—21no—
57C3×C7×C29C2×C5×D311yescharacteristic, complemented
58C3×C7×C29C22×C3×C511yescharacteristic, complemented
59C22×C5×C29—211noHall
60C2×C32×C29—71no—
61C3×D3×C29—71no—
62C3×D3×C29C5×D711yescharacteristic, direct product factor
63C3×C5×C29—21no—
64C3×C5×C29D3×D711yescharacteristic, direct product factor
65C3×C5×C29C2×C3×D711yescharacteristic, complemented
66C2×C3×C5×D7—31no—
67C5×D3×D7C3×C2911yescharacteristic, direct product factor
68C2×C7×C29—31no—
69D7×C29—31no—
70D7×C29C3×C5×D311yescharacteristic, direct product factor
71C22×C3×C29—211no—
72C2×D3×C29—71no—
73C32×C5×C7C22×C2911yescharacteristic, complemented, Hall
74C2×C5×C29—31no—
75C2×C5×C29—71no—
76C2×C5×C29—211no—
77C32×C29C2×C5×D711yescharacteristic, complemented, Hall
78C3×D3×D7C5×C2911yescharacteristic, direct product factor, Hall
79C2×C3×C5×C7—31no—
80C5×D21C2×C3×C2911yescharacteristic, complemented
81C5×D3×C7C2×C3×C2911yescharacteristic, complemented
82C3×C5×D7—21no—
83C3×C5×D7—31no—
84C3×C5×D7D3×C2911yescharacteristic, direct product factor
85C3×C5×D7C2×C3×C2911yescharacteristic, complemented
86C7×C29C2×C3×C5×D311yescharacteristic, complemented, Hall
87C2×C3×C5×D3—71noHall
88C2×C3×C29—31no—
89C2×C3×C29—71no—
90C2×C3×C29—71no—
91C2×C3×C29—141no—
92C2×C3×C29—211no—
93D3×C29—71no—
94D3×C29C3×C5×D711yescharacteristic, direct product factor
95C5×C29C3×D3×D711yescharacteristic, direct product factor, Hall
96C2×C5×D7—31noHall
97C3×D21C2×C5×C2911yescharacteristic, complemented
98C3×D3×C7C2×C5×C2911yescharacteristic, complemented
99C32×D7C2×C5×C2911yescharacteristic, complemented
100C22×C29—211noHall
101C3×C5×C7—21no—
102C3×C5×C7C2×D3×C2911yescharacteristic, complemented
103C3×C5×C7C22×C3×C2911yescharacteristic, complemented
104C2×C32×C5—71no—
105C3×C5×D3—71no—
106C3×C5×D3D7×C2911yescharacteristic, direct product factor
107C3×C29—21no—
108C3×C29C5×D3×D711yescharacteristic, direct product factor
109C3×C29C2×C3×C5×D711yescharacteristic, complemented
110C2×C3×D7—31no—
111D3×D7C3×C5×C2911yescharacteristic, direct product factor
112C2×C5×C7—31no—
113C5×D7—31no—
114C5×D7C3×D3×C2911yescharacteristic, direct product factor
115C32×C7C22×C5×C2911yescharacteristic, complemented, Hall
116C22×C3×C5—211no—
117C2×C5×D3—71no—
118C2×C29—31no—
119C2×C29—71no—
120C2×C29—211no—
121C32×C5C2×D7×C2911yescharacteristic, complemented, Hall
122C2×C3×C7—31no—
123D21C2×C3×C5×C2911yescharacteristic, complemented
124C3×D7—21no—
125C3×D7—31no—
126C3×D7C5×D3×C2911yescharacteristic, direct product factor
127C3×D7C2×C3×C5×C2911yescharacteristic, complemented
128D3×C7C2×C3×C5×C2911yescharacteristic, complemented
129C2×C3×D3—71noHall
130C5×C7C2×C3×D3×C2911yescharacteristic, complemented, Hall
131C2×C3×C5—31no—
132C2×C3×C5—71no—
133C2×C3×C5—71no—
134C2×C3×C5—141no—
135C2×C3×C5—211no—
136C5×D3—71no—
137C5×D3C3×D7×C2911yescharacteristic, direct product factor
138C29C3×C5×D3×D711yescharacteristic, direct product factor, Sylow
139C2×D7—31noHall
140C3×C7—21no—
141C3×C7C2×C5×D3×C2911yescharacteristic, complemented
142C3×C7C22×C3×C5×C2911yescharacteristic, complemented
143C22×C5—211noHall
144C2×C32—71no—
145C3×D3—71no—
146C3×D3C5×D7×C2911yescharacteristic, direct product factor
147C3×C5—21no—
148C3×C5D3×D7×C2911yescharacteristic, direct product factor
149C3×C5C2×C3×D7×C2911yescharacteristic, complemented
150C2×C7—31no—
151D7—31no—
152D7C3×C5×D3×C2911yescharacteristic, direct product factor
153C22×C3—211no—
154C2×D3—71no—
155C2×C5—31no—
156C2×C5—71no—
157C2×C5—211no—
158C32C2×C5×D7×C2911yescharacteristic, complemented, Sylow
159C7C2×C3×C5×D3×C2911yescharacteristic, complemented, Sylow
160C2×C3—31no—
161C2×C3—71no—
162C2×C3—71no—
163C2×C3—141no—
164C2×C3—211no—
165D3—71no—
166D3C3×C5×D7×C2911yescharacteristic, direct product factor
167C5C3×D3×D7×C2911yescharacteristic, direct product factor, Sylow
168C22—211noSylow
169C3—21no—
170C3C5×D3×D7×C2911yescharacteristic, direct product factor
171C3C2×C3×C5×D7×C2911yescharacteristic, complemented
172C2—31no—
173C2—71no—
174C2—211no—
subgroupG/H
center, hypercenterC3×C5×C29D3×D7
commutator, cosocle, hypocenterC3×C7C22×C3×C5×C29
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C3×C7
UCSC1 ◁ C3×C5×C29

Complements

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

NH ≅ G/Ntype
1. C32×C5×D7×C29C2semidirect
2. C3×C5×D3×C7×C29C2semidirect
3. C3×C5×C29×D21C2semidirect
5. C5×D3×D7×C29C3direct (N × H)
6. C32×C5×C7×C29C22semidirect
7. C3×D3×D7×C29C5direct (N × H)
8. C5×C29×D21C2×C3semidirect
9. C5×D3×C7×C29C2×C3semidirect
12. C3×C5×D7×C29D3direct (N × H)
13. C3×C5×D7×C29C2×C3semidirect
17. C3×C29×D21C2×C5semidirect
18. C3×D3×C7×C29C2×C5semidirect
19. C32×D7×C29C2×C5semidirect
21. C3×C5×C7×C29C2×D3semidirect
22. C3×C5×C7×C29C22×C3semidirect
24. C3×C5×D3×C29D7direct (N × H)
27. D3×D7×C29C3×C5direct (N × H)
29. C5×D7×C29C3×D3direct (N × H)
31. C32×C7×C29C22×C5semidirect
34. C32×C5×C29C2×D7semidirect
35. C3×C5×D3×D7C29direct (N × H)
37. C29×D21C2×C3×C5semidirect
38. D3×C7×C29C2×C3×C5semidirect
41. C3×D7×C29C5×D3direct (N × H)
42. C3×D7×C29C2×C3×C5semidirect
44. C5×C7×C29C2×C3×D3semidirect
51. C5×D3×C29C3×D7direct (N × H)
53. C3×C5×D21C2×C29semidirect
54. C3×C5×D3×C7C2×C29semidirect
55. C32×C5×D7C2×C29semidirect
57. C3×C7×C29C2×C5×D3semidirect
58. C3×C7×C29C22×C3×C5semidirect
62. C3×D3×C29C5×D7direct (N × H)
64. C3×C5×C29D3×D7direct (N × H)
65. C3×C5×C29C2×C3×D7semidirect
67. C5×D3×D7C3×C29direct (N × H)
70. D7×C29C3×C5×D3direct (N × H)
73. C32×C5×C7C22×C29semidirect
77. C32×C29C2×C5×D7semidirect
78. C3×D3×D7C5×C29direct (N × H)
80. C5×D21C2×C3×C29semidirect
81. C5×D3×C7C2×C3×C29semidirect
84. C3×C5×D7D3×C29direct (N × H)
85. C3×C5×D7C2×C3×C29semidirect
86. C7×C29C2×C3×C5×D3semidirect
94. D3×C29C3×C5×D7direct (N × H)
95. C5×C29C3×D3×D7direct (N × H)
97. C3×D21C2×C5×C29semidirect
98. C3×D3×C7C2×C5×C29semidirect
99. C32×D7C2×C5×C29semidirect
102. C3×C5×C7C2×D3×C29semidirect
103. C3×C5×C7C22×C3×C29semidirect
106. C3×C5×D3D7×C29direct (N × H)
108. C3×C29C5×D3×D7direct (N × H)
109. C3×C29C2×C3×C5×D7semidirect
111. D3×D7C3×C5×C29direct (N × H)
114. C5×D7C3×D3×C29direct (N × H)
115. C32×C7C22×C5×C29semidirect
121. C32×C5C2×D7×C29semidirect
123. D21C2×C3×C5×C29semidirect
126. C3×D7C5×D3×C29direct (N × H)
127. C3×D7C2×C3×C5×C29semidirect
128. D3×C7C2×C3×C5×C29semidirect
130. C5×C7C2×C3×D3×C29semidirect
137. C5×D3C3×D7×C29direct (N × H)
138. C29C3×C5×D3×D7direct (N × H)
141. C3×C7C2×C5×D3×C29semidirect
142. C3×C7C22×C3×C5×C29semidirect
146. C3×D3C5×D7×C29direct (N × H)
148. C3×C5D3×D7×C29direct (N × H)
149. C3×C5C2×C3×D7×C29semidirect
152. D7C3×C5×D3×C29direct (N × H)
158. C32C2×C5×D7×C29semidirect
159. C7C2×C3×C5×D3×C29semidirect
166. D3C3×C5×D7×C29direct (N × H)
167. C5C3×D3×D7×C29direct (N × H)
170. C3C5×D3×D7×C29direct (N × H)
171. C3C2×C3×C5×D7×C29semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D7×C292
C3×C5×D3×C7×C292
C3×C5×C29×D212
C2×C3×C5×D7×C293
C5×D3×D7×C293
C3×D3×D7×C295
C2×C3×C5×D3×C297
C3×C5×D3×D729