Finite Group Databasebeta

← C3×D7×C29×D15 #49141574

Subgroups — C3×D7×C29×D15 #49141574

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×C5×D7×C29C211yesmaximal, characteristic, complemented
2C3×C7×C29×D15C211yesmaximal, characteristic, complemented
3C3×C29×D105C211yesmaximal, characteristic, complemented
4D7×C29×D15C311yesmaximal, characteristic, direct product factor
5C3×D5×D7×C29—31nomaximal
6C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
7C3×D3×D7×C29—51nomaximal, Hall
8C29×D105C2×C311yescharacteristic, complemented
9C7×C29×D15C2×C311yescharacteristic, complemented
10C3×C29×D35—31no—
11C3×C7×D5×C29—31no—
12C3×C5×D7×C29—21no—
13C3×C5×D7×C29D311yescharacteristic, complemented
14C3×C5×D7×C29C2×C311yescharacteristic, complemented
15C2×C3×C29×D15—71nomaximal, Hall
16D5×D7×C29—31noHall
17C3×C29×D21—51no—
18C3×D3×C7×C29—51no—
19C32×D7×C29D511yescharacteristic, complemented
20C3×C5×C7×C29—21no—
21C3×C5×C7×C29C2×D311yescharacteristic, complemented
22C3×C5×C7×C29C22×C311yescharacteristic, complemented
23C3×C29×D15—71no—
24C3×C29×D15D711yescharacteristic, direct product factor
25C2×C32×C5×C29—71no—
26C2×C3×D7×C29—151no—
27D3×D7×C29—51no—
28C29×D35—31no—
29C7×D5×C29—31no—
30C5×D7×C29C3×D311yescharacteristic, complemented
31C32×C7×C29C2×D511yescharacteristic, complemented, Hall
32C2×C29×D15—71no—
33C2×C3×D5×C29—211no—
34C32×C5×C29C2×D711yescharacteristic, complemented, Hall
35C3×D7×D15C2911yesmaximal, characteristic, direct product factor, Hall
36C2×C3×C7×C29—151no—
37C29×D21—51no—
38D3×C7×C29—51no—
39C3×D7×C29—21no—
40C3×D7×C29—151no—
41C3×D7×C29C3×D511yescharacteristic, complemented
42C3×D7×C29D1511yescharacteristic, direct product factor
43C2×C3×D3×C29—351noHall
44C5×C7×C29C2×C3×D311yescharacteristic, complemented, Hall
45C2×C3×C5×C29—71no—
46C2×C3×C5×C29—71no—
47C2×C3×C5×C29—141no—
48C29×D15—71no—
49C29×D15C3×D711yescharacteristic, direct product factor
50C3×D5×C29—31no—
51C3×D5×C29—211no—
52C2×D7×C29—151noHall
53C3×D105C2×C2911yescharacteristic, complemented
54C3×C7×D15C2×C2911yescharacteristic, complemented
55C32×C5×D7C2×C2911yescharacteristic, complemented
56C3×C7×C29—21no—
57C3×C7×C29C2×C3×D511yescharacteristic, complemented
58C3×C7×C29C2×D1511yescharacteristic, complemented
59C2×D5×C29—211noHall
60C2×C32×C29—71no—
61C3×D3×C29—51no—
62C3×D3×C29—351no—
63C3×C5×C29—21no—
64C3×C5×C29D3×D711yescharacteristic, complemented
65C3×C5×C29C2×C3×D711yescharacteristic, complemented
66D7×D15C3×C2911yescharacteristic, direct product factor
67C3×D5×D7—31no—
68C2×C7×C29—151no—
69D7×C29—151no—
70D7×C29C3×D1511yescharacteristic, direct product factor
71C22×C3×C29—1051no—
72C2×D3×C29—351no—
73C32×C5×C7C22×C2911yescharacteristic, complemented, Hall
74C2×C5×C29—71no—
75D5×C29—31no—
76D5×C29—211no—
77C32×C29D5×D711yescharacteristic, complemented, Hall
78C3×D3×D7—51noHall
79D105C2×C3×C2911yescharacteristic, complemented
80C7×D15C2×C3×C2911yescharacteristic, complemented
81C3×D35—31no—
82C3×C7×D5—31no—
83C3×C5×D7—21no—
84C3×C5×D7D3×C2911yescharacteristic, complemented
85C3×C5×D7C2×C3×C2911yescharacteristic, complemented
86C7×C29C2×C3×D1511yescharacteristic, complemented, Hall
87C2×C3×D15—71noHall
88C2×C3×C29—71no—
89C2×C3×C29—71no—
90C2×C3×C29—141no—
91C2×C3×C29—151no—
92C2×C3×C29—1051no—
93D3×C29—51no—
94D3×C29—351no—
95C5×C29C3×D3×D711yescharacteristic, complemented, Hall
96D5×D7—31noHall
97C3×D21—51no—
98C3×D3×C7—51no—
99C32×D7D5×C2911yescharacteristic, complemented
100C22×C29—1051noHall
101C3×C5×C7—21no—
102C3×C5×C7C2×D3×C2911yescharacteristic, complemented
103C3×C5×C7C22×C3×C2911yescharacteristic, complemented
104C2×C32×C5—71no—
105C3×D15—71no—
106C3×D15D7×C2911yescharacteristic, direct product factor
107C3×C29—21no—
108C3×C29C3×D5×D711yescharacteristic, complemented
109C3×C29D7×D1511yescharacteristic, direct product factor
110C2×C3×D7—151no—
111D3×D7—51no—
112D35—31no—
113C5×D7C3×D3×C2911yescharacteristic, complemented
114C7×D5—31no—
115C32×C7C2×D5×C2911yescharacteristic, complemented, Hall
116C2×D15—71no—
117C2×C3×D5—211no—
118C2×C29—71no—
119C2×C29—151no—
120C2×C29—1051no—
121C32×C5C2×D7×C2911yescharacteristic, complemented, Hall
122C2×C3×C7—151no—
123D21—51no—
124C3×D7—21no—
125C3×D7—151no—
126C3×D7C3×D5×C2911yescharacteristic, complemented
127C3×D7C29×D1511yescharacteristic, direct product factor
128D3×C7—51no—
129C2×C3×D3—351noHall
130C5×C7C2×C3×D3×C2911yescharacteristic, complemented, Hall
131C2×C3×C5—71no—
132C2×C3×C5—71no—
133C2×C3×C5—141no—
134D15—71no—
135D15C3×D7×C2911yescharacteristic, direct product factor
136C3×D5—31no—
137C3×D5—211no—
138C29C3×D7×D1511yescharacteristic, direct product factor, Sylow
139C2×D7—151noHall
140C3×C7—21no—
141C3×C7C2×C3×D5×C2911yescharacteristic, complemented
142C3×C7C2×C29×D1511yescharacteristic, complemented
143C2×D5—211noHall
144C2×C32—71no—
145C3×D3—51no—
146C3×D3—351no—
147C3×C5—21no—
148C3×C5D3×D7×C2911yescharacteristic, complemented
149C3×C5C2×C3×D7×C2911yescharacteristic, complemented
150C2×C7—151no—
151D7—151no—
152D7C3×C29×D1511yescharacteristic, direct product factor
153C22×C3—1051no—
154C2×D3—351no—
155C2×C5—71no—
156D5—31no—
157D5—211no—
158C32D5×D7×C2911yescharacteristic, complemented, Sylow
159C7C2×C3×C29×D1511yescharacteristic, complemented, Sylow
160C2×C3—71no—
161C2×C3—71no—
162C2×C3—141no—
163C2×C3—151no—
164C2×C3—1051no—
165D3—51no—
166D3—351no—
167C5C3×D3×D7×C2911yescharacteristic, complemented, Sylow
168C22—1051noSylow
169C3—21no—
170C3C3×D5×D7×C2911yescharacteristic, complemented
171C3D7×C29×D1511yescharacteristic, direct product factor
172C2—71no—
173C2—151no—
174C2—1051no—
subgroupG/H
center, hypercenterC3×C29D7×D15
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×C5×D7×C29C2semidirect
2. C3×C7×C29×D15C2semidirect
3. C3×C29×D105C2semidirect
4. D7×C29×D15C3direct (N × H)
6. C32×C5×C7×C29C22semidirect
8. C29×D105C2×C3semidirect
9. C7×C29×D15C2×C3semidirect
13. C3×C5×D7×C29D3semidirect
14. C3×C5×D7×C29C2×C3semidirect
19. C32×D7×C29D5semidirect
21. C3×C5×C7×C29C2×D3semidirect
22. C3×C5×C7×C29C22×C3semidirect
24. C3×C29×D15D7direct (N × H)
30. C5×D7×C29C3×D3semidirect
31. C32×C7×C29C2×D5semidirect
34. C32×C5×C29C2×D7semidirect
35. C3×D7×D15C29direct (N × H)
41. C3×D7×C29C3×D5semidirect
42. C3×D7×C29D15direct (N × H)
44. C5×C7×C29C2×C3×D3semidirect
49. C29×D15C3×D7direct (N × H)
53. C3×D105C2×C29semidirect
54. C3×C7×D15C2×C29semidirect
55. C32×C5×D7C2×C29semidirect
57. C3×C7×C29C2×C3×D5semidirect
58. C3×C7×C29C2×D15semidirect
64. C3×C5×C29D3×D7semidirect
65. C3×C5×C29C2×C3×D7semidirect
66. D7×D15C3×C29direct (N × H)
70. D7×C29C3×D15direct (N × H)
73. C32×C5×C7C22×C29semidirect
77. C32×C29D5×D7semidirect
79. D105C2×C3×C29semidirect
80. C7×D15C2×C3×C29semidirect
84. C3×C5×D7D3×C29semidirect
85. C3×C5×D7C2×C3×C29semidirect
86. C7×C29C2×C3×D15semidirect
95. C5×C29C3×D3×D7semidirect
99. C32×D7D5×C29semidirect
102. C3×C5×C7C2×D3×C29semidirect
103. C3×C5×C7C22×C3×C29semidirect
106. C3×D15D7×C29direct (N × H)
108. C3×C29C3×D5×D7semidirect
109. C3×C29D7×D15direct (N × H)
113. C5×D7C3×D3×C29semidirect
115. C32×C7C2×D5×C29semidirect
121. C32×C5C2×D7×C29semidirect
126. C3×D7C3×D5×C29semidirect
127. C3×D7C29×D15direct (N × H)
130. C5×C7C2×C3×D3×C29semidirect
135. D15C3×D7×C29direct (N × H)
138. C29C3×D7×D15direct (N × H)
141. C3×C7C2×C3×D5×C29semidirect
142. C3×C7C2×C29×D15semidirect
148. C3×C5D3×D7×C29semidirect
149. C3×C5C2×C3×D7×C29semidirect
152. D7C3×C29×D15direct (N × H)
158. C32D5×D7×C29semidirect
159. C7C2×C3×C29×D15semidirect
167. C5C3×D3×D7×C29semidirect
170. C3C3×D5×D7×C29semidirect
171. C3D7×C29×D15direct (N × H)

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×C7×C29×D152
C3×C29×D1052
D7×C29×D153
C3×D5×D7×C293
C3×D3×D7×C295
C2×C3×C29×D157
C3×D7×D1529