Finite Group Databasebeta

← C3×D3×C29×D35 #49141586

Subgroups — C3×D3×C29×D35 #49141586

Order 36540.

176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 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×C29×D35C211yesmaximal, characteristic, complemented
2C3×C5×D3×C7×C29C211yesmaximal, characteristic, complemented
3C3×C29×D105C211yesmaximal, characteristic, complemented
4C2×C3×C29×D35—31nomaximal
5D3×C29×D35C311yesmaximal, characteristic, direct product factor
6C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
7C3×D3×D7×C29—51nomaximal, Hall
8C29×D105C2×C311yescharacteristic, complemented
9C5×D3×C7×C29C2×C311yescharacteristic, complemented
10C3×C29×D35—21no—
11C3×C29×D35—31no—
12C3×C29×D35D311yescharacteristic, direct product factor
13C3×C29×D35C2×C311yescharacteristic, complemented
14C2×C3×C5×C7×C29—31no—
15C3×D3×D5×C29—71nomaximal, Hall
16C2×C29×D35—31noHall
17C3×C29×D21—51no—
18C3×D3×C7×C29D511yescharacteristic, complemented
19C32×D7×C29—51no—
20C3×C5×C7×C29—21no—
21C3×C5×C7×C29C2×D311yescharacteristic, complemented
22C3×C5×C7×C29C22×C311yescharacteristic, complemented
23C3×C29×D15—71no—
24C3×C5×D3×C29D711yescharacteristic, complemented
25C32×D5×C29—71no—
26C2×C3×D7×C29—151no—
27D3×D7×C29—51no—
28C29×D35—31no—
29C29×D35C3×D311yescharacteristic, direct product factor
30C2×C5×C7×C29—31no—
31C32×C7×C29C2×D511yescharacteristic, complemented, Hall
32C2×C3×D5×C29—211no—
33D3×D5×C29—71no—
34C32×C5×C29C2×D711yescharacteristic, complemented, Hall
35C3×D3×D35C2911yesmaximal, characteristic, direct product factor, Hall
36C2×C3×C7×C29—31no—
37C29×D21—51no—
38D3×C7×C29C3×D511yescharacteristic, complemented
39C3×D7×C29—51no—
40C3×D7×C29—51no—
41C3×D7×C29—101no—
42C3×D7×C29—151no—
43C2×C3×D3×C29—351noHall
44C5×C7×C29C2×C3×D311yescharacteristic, complemented, Hall
45C2×C3×C5×C29—31no—
46C29×D15—71no—
47C5×D3×C29C3×D711yescharacteristic, complemented
48C3×D5×C29—71no—
49C3×D5×C29—71no—
50C3×D5×C29—141no—
51C3×D5×C29—211no—
52C2×D7×C29—151noHall
53C3×D105C2×C2911yescharacteristic, complemented
54C3×C5×D3×C7C2×C2911yescharacteristic, complemented
55C32×D35C2×C2911yescharacteristic, complemented
56C3×C7×C29—21no—
57C3×C7×C29D3×D511yescharacteristic, complemented
58C3×C7×C29C2×C3×D511yescharacteristic, complemented
59C2×D5×C29—211noHall
60C2×C32×C29—351no—
61C3×D3×C29—351no—
62C3×D3×C29D3511yescharacteristic, direct product factor
63C3×C5×C29—21no—
64C3×C5×C29D3×D711yescharacteristic, complemented
65C3×C5×C29C2×C3×D711yescharacteristic, complemented
66C2×C3×D35—31no—
67D3×D35C3×C2911yescharacteristic, direct product factor
68C2×C7×C29—31no—
69D7×C29—51no—
70D7×C29—151no—
71C22×C3×C29—1051no—
72C2×D3×C29—351no—
73C32×C5×C7C22×C2911yescharacteristic, complemented, Hall
74C2×C5×C29—31no—
75D5×C29—71no—
76D5×C29—211no—
77C32×C29C2×D3511yescharacteristic, complemented, Hall
78C3×D3×D7—51noHall
79C2×C3×C5×C7—31no—
80D105C2×C3×C2911yescharacteristic, complemented
81C5×D3×C7C2×C3×C2911yescharacteristic, complemented
82C3×D35—21no—
83C3×D35—31no—
84C3×D35D3×C2911yescharacteristic, direct product factor
85C3×D35C2×C3×C2911yescharacteristic, complemented
86C7×C29C3×D3×D511yescharacteristic, complemented, Hall
87C3×D3×D5—71noHall
88C2×C3×C29—31no—
89C2×C3×C29—351no—
90C2×C3×C29—351no—
91C2×C3×C29—701no—
92C2×C3×C29—1051no—
93D3×C29—351no—
94D3×C29C3×D3511yescharacteristic, direct product factor
95C5×C29C3×D3×D711yescharacteristic, complemented, Hall
96C2×D35—31noHall
97C3×D21—51no—
98C3×D3×C7D5×C2911yescharacteristic, complemented
99C32×D7—51no—
100C22×C29—1051noHall
101C3×C5×C7—21no—
102C3×C5×C7C2×D3×C2911yescharacteristic, complemented
103C3×C5×C7C22×C3×C2911yescharacteristic, complemented
104C3×D15—71no—
105C3×C5×D3D7×C2911yescharacteristic, complemented
106C32×D5—71no—
107C3×C29—21no—
108C3×C29D3×D3511yescharacteristic, direct product factor
109C3×C29C2×C3×D3511yescharacteristic, complemented
110C2×C3×D7—151no—
111D3×D7—51no—
112C2×C5×C7—31no—
113D35—31no—
114D35C3×D3×C2911yescharacteristic, direct product factor
115C32×C7C2×D5×C2911yescharacteristic, complemented, Hall
116C2×C3×D5—211no—
117D3×D5—71no—
118C2×C29—31no—
119C2×C29—351no—
120C2×C29—1051no—
121C32×C5C2×D7×C2911yescharacteristic, complemented, Hall
122C2×C3×C7—31no—
123D21—51no—
124C3×D7—51no—
125C3×D7—51no—
126C3×D7—101no—
127C3×D7—151no—
128D3×C7C3×D5×C2911yescharacteristic, complemented
129C2×C3×D3—351noHall
130C5×C7C2×C3×D3×C2911yescharacteristic, complemented, Hall
131C2×C3×C5—31no—
132D15—71no—
133C3×D5—71no—
134C3×D5—71no—
135C3×D5—141no—
136C3×D5—211no—
137C5×D3C3×D7×C2911yescharacteristic, complemented
138C29C3×D3×D3511yescharacteristic, direct product factor, Sylow
139C2×D7—151noHall
140C3×C7—21no—
141C3×C7D3×D5×C2911yescharacteristic, complemented
142C3×C7C2×C3×D5×C2911yescharacteristic, complemented
143C2×D5—211noHall
144C2×C32—351no—
145C3×D3—351no—
146C3×D3C29×D3511yescharacteristic, direct product factor
147C3×C5—21no—
148C3×C5D3×D7×C2911yescharacteristic, complemented
149C3×C5C2×C3×D7×C2911yescharacteristic, complemented
150C2×C7—31no—
151D7—51no—
152D7—151no—
153C22×C3—1051no—
154C2×D3—351no—
155C2×C5—31no—
156D5—71no—
157D5—211no—
158C32C2×C29×D3511yescharacteristic, complemented, Sylow
159C7C3×D3×D5×C2911yescharacteristic, complemented, Sylow
160C2×C3—31no—
161C2×C3—351no—
162C2×C3—351no—
163C2×C3—701no—
164C2×C3—1051no—
165D3—351no—
166D3C3×C29×D3511yescharacteristic, direct product factor
167C5C3×D3×D7×C2911yescharacteristic, complemented, Sylow
168C22—1051noSylow
169C3—21no—
170C3D3×C29×D3511yescharacteristic, direct product factor
171C3C2×C3×C29×D3511yescharacteristic, complemented
172C2—31no—
173C2—351no—
174C2—1051no—
subgroupG/H
center, hypercenterC3×C29D3×D35
commutator, cosocle, hypocenterC3×C5×C7C22×C3×C29
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C3×C5×C7
UCSC1 ◁ C3×C29

Complements

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

NH ≅ G/Ntype
1. C32×C29×D35C2semidirect
2. C3×C5×D3×C7×C29C2semidirect
3. C3×C29×D105C2semidirect
5. D3×C29×D35C3direct (N × H)
6. C32×C5×C7×C29C22semidirect
8. C29×D105C2×C3semidirect
9. C5×D3×C7×C29C2×C3semidirect
12. C3×C29×D35D3direct (N × H)
13. C3×C29×D35C2×C3semidirect
18. C3×D3×C7×C29D5semidirect
21. C3×C5×C7×C29C2×D3semidirect
22. C3×C5×C7×C29C22×C3semidirect
24. C3×C5×D3×C29D7semidirect
29. C29×D35C3×D3direct (N × H)
31. C32×C7×C29C2×D5semidirect
34. C32×C5×C29C2×D7semidirect
35. C3×D3×D35C29direct (N × H)
38. D3×C7×C29C3×D5semidirect
44. C5×C7×C29C2×C3×D3semidirect
47. C5×D3×C29C3×D7semidirect
53. C3×D105C2×C29semidirect
54. C3×C5×D3×C7C2×C29semidirect
55. C32×D35C2×C29semidirect
57. C3×C7×C29D3×D5semidirect
58. C3×C7×C29C2×C3×D5semidirect
62. C3×D3×C29D35direct (N × H)
64. C3×C5×C29D3×D7semidirect
65. C3×C5×C29C2×C3×D7semidirect
67. D3×D35C3×C29direct (N × H)
73. C32×C5×C7C22×C29semidirect
77. C32×C29C2×D35semidirect
80. D105C2×C3×C29semidirect
81. C5×D3×C7C2×C3×C29semidirect
84. C3×D35D3×C29direct (N × H)
85. C3×D35C2×C3×C29semidirect
86. C7×C29C3×D3×D5semidirect
94. D3×C29C3×D35direct (N × H)
95. C5×C29C3×D3×D7semidirect
98. C3×D3×C7D5×C29semidirect
102. C3×C5×C7C2×D3×C29semidirect
103. C3×C5×C7C22×C3×C29semidirect
105. C3×C5×D3D7×C29semidirect
108. C3×C29D3×D35direct (N × H)
109. C3×C29C2×C3×D35semidirect
114. D35C3×D3×C29direct (N × H)
115. C32×C7C2×D5×C29semidirect
121. C32×C5C2×D7×C29semidirect
128. D3×C7C3×D5×C29semidirect
130. C5×C7C2×C3×D3×C29semidirect
137. C5×D3C3×D7×C29semidirect
138. C29C3×D3×D35direct (N × H)
141. C3×C7D3×D5×C29semidirect
142. C3×C7C2×C3×D5×C29semidirect
146. C3×D3C29×D35direct (N × H)
148. C3×C5D3×D7×C29semidirect
149. C3×C5C2×C3×D7×C29semidirect
158. C32C2×C29×D35semidirect
159. C7C3×D3×D5×C29semidirect
166. D3C3×C29×D35direct (N × H)
167. C5C3×D3×D7×C29semidirect
170. C3D3×C29×D35direct (N × H)
171. C3C2×C3×C29×D35semidirect

Maximal subgroups

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

subgroupindex
C32×C29×D352
C3×C5×D3×C7×C292
C3×C29×D1052
C2×C3×C29×D353
D3×C29×D353
C3×D3×D7×C295
C3×D3×D5×C297
C3×D3×D3529