Finite Group Databasebeta

← C3×D3×C7×D5×C29 #49141578

Subgroups — C3×D3×C7×D5×C29 #49141578

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×C7×D5×C29C211yesmaximal, characteristic, complemented
2C3×C5×D3×C7×C29C211yesmaximal, characteristic, complemented
3C3×C7×C29×D15C211yesmaximal, characteristic, complemented
4C2×C3×C7×D5×C29—31nomaximal
5D3×C7×D5×C29C311yesmaximal, characteristic, direct product factor
6C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
7C2×C3×D3×C7×C29—51nomaximal, Hall
8C7×C29×D15C2×C311yescharacteristic, complemented
9C5×D3×C7×C29C2×C311yescharacteristic, complemented
10C3×C7×D5×C29—21no—
11C3×C7×D5×C29—31no—
12C3×C7×D5×C29D311yescharacteristic, direct product factor
13C3×C7×D5×C29C2×C311yescharacteristic, complemented
14C2×C3×C5×C7×C29—31no—
15C3×D3×D5×C29C711yesmaximal, characteristic, direct product factor, Hall
16C2×C7×D5×C29—31noHall
17C3×D3×C7×C29—51no—
18C3×D3×C7×C29D511yescharacteristic, direct product factor
19C2×C32×C7×C29—51no—
20C3×C5×C7×C29—21no—
21C3×C5×C7×C29C2×D311yescharacteristic, complemented
22C3×C5×C7×C29C22×C311yescharacteristic, complemented
23C3×C29×D15C2×C711yescharacteristic, complemented
24C3×C5×D3×C29C2×C711yescharacteristic, complemented
25C32×D5×C29C2×C711yescharacteristic, complemented
26C2×D3×C7×C29—51no—
27C22×C3×C7×C29—151no—
28C7×D5×C29—31no—
29C7×D5×C29C3×D311yescharacteristic, direct product factor
30C2×C5×C7×C29—31no—
31C32×C7×C29C2×D511yescharacteristic, complemented, Hall
32C2×C3×D5×C29—31no—
33D3×D5×C29C3×C711yescharacteristic, direct product factor
34C32×C5×C29C22×C711yescharacteristic, complemented, Hall
35C3×D3×C7×D5C2911yesmaximal, characteristic, direct product factor, Hall
36C2×C3×C7×C29—31no—
37C2×C3×C7×C29—51no—
38C2×C3×C7×C29—51no—
39C2×C3×C7×C29—101no—
40C2×C3×C7×C29—151no—
41D3×C7×C29—51no—
42D3×C7×C29C3×D511yescharacteristic, direct product factor
43C2×C3×D3×C29—51noHall
44C5×C7×C29C2×C3×D311yescharacteristic, complemented, Hall
45C2×C3×C5×C29—31no—
46C29×D15C2×C3×C711yescharacteristic, complemented
47C5×D3×C29C2×C3×C711yescharacteristic, complemented
48C3×D5×C29—21no—
49C3×D5×C29—31no—
50C3×D5×C29D3×C711yescharacteristic, direct product factor
51C3×D5×C29C2×C3×C711yescharacteristic, complemented
52C22×C7×C29—151noHall
53C3×C7×D15C2×C2911yescharacteristic, complemented
54C3×C5×D3×C7C2×C2911yescharacteristic, complemented
55C32×C7×D5C2×C2911yescharacteristic, complemented
56C3×C7×C29—21no—
57C3×C7×C29D3×D511yescharacteristic, direct product factor
58C3×C7×C29C2×C3×D511yescharacteristic, complemented
59C2×D5×C29—31noHall
60C2×C32×C29—51no—
61C3×D3×C29—51no—
62C3×D3×C29C7×D511yescharacteristic, direct product factor
63C3×C5×C29—21no—
64C3×C5×C29C2×D3×C711yescharacteristic, complemented
65C3×C5×C29C22×C3×C711yescharacteristic, complemented
66C2×C3×C7×D5—31no—
67D3×C7×D5C3×C2911yescharacteristic, direct product factor
68C2×C7×C29—31no—
69C2×C7×C29—51no—
70C2×C7×C29—151no—
71C22×C3×C29—151no—
72C2×D3×C29—51no—
73C32×C5×C7C22×C2911yescharacteristic, complemented, Hall
74C2×C5×C29—31no—
75D5×C29—31no—
76D5×C29C3×D3×C711yescharacteristic, direct product factor
77C32×C29C2×C7×D511yescharacteristic, complemented, Hall
78C2×C3×D3×C7—51noHall
79C2×C3×C5×C7—31no—
80C7×D15C2×C3×C2911yescharacteristic, complemented
81C5×D3×C7C2×C3×C2911yescharacteristic, complemented
82C3×C7×D5—21no—
83C3×C7×D5—31no—
84C3×C7×D5D3×C2911yescharacteristic, direct product factor
85C3×C7×D5C2×C3×C2911yescharacteristic, complemented
86C7×C29C3×D3×D511yescharacteristic, direct product factor, Hall
87C3×D3×D5C7×C2911yescharacteristic, direct product factor, Hall
88C2×C3×C29—31no—
89C2×C3×C29—51no—
90C2×C3×C29—51no—
91C2×C3×C29—101no—
92C2×C3×C29—151no—
93D3×C29—51no—
94D3×C29C3×C7×D511yescharacteristic, direct product factor
95C5×C29C2×C3×D3×C711yescharacteristic, complemented, Hall
96C2×C7×D5—31noHall
97C2×C32×C7—51no—
98C3×D3×C7—51no—
99C3×D3×C7D5×C2911yescharacteristic, direct product factor
100C22×C29—151noHall
101C3×C5×C7—21no—
102C3×C5×C7C2×D3×C2911yescharacteristic, complemented
103C3×C5×C7C22×C3×C2911yescharacteristic, complemented
104C3×D15C2×C7×C2911yescharacteristic, complemented
105C3×C5×D3C2×C7×C2911yescharacteristic, complemented
106C32×D5C2×C7×C2911yescharacteristic, complemented
107C3×C29—21no—
108C3×C29D3×C7×D511yescharacteristic, direct product factor
109C3×C29C2×C3×C7×D511yescharacteristic, complemented
110C22×C3×C7—151no—
111C2×D3×C7—51no—
112C2×C5×C7—31no—
113C7×D5—31no—
114C7×D5C3×D3×C2911yescharacteristic, direct product factor
115C32×C7C2×D5×C2911yescharacteristic, complemented, Hall
116C2×C3×D5—31no—
117D3×D5C3×C7×C2911yescharacteristic, direct product factor
118C2×C29—31no—
119C2×C29—51no—
120C2×C29—151no—
121C32×C5C22×C7×C2911yescharacteristic, complemented, Hall
122C2×C3×C7—31no—
123C2×C3×C7—51no—
124C2×C3×C7—51no—
125C2×C3×C7—101no—
126C2×C3×C7—151no—
127D3×C7—51no—
128D3×C7C3×D5×C2911yescharacteristic, direct product factor
129C2×C3×D3—51noHall
130C5×C7C2×C3×D3×C2911yescharacteristic, complemented, Hall
131C2×C3×C5—31no—
132D15C2×C3×C7×C2911yescharacteristic, complemented
133C3×D5—21no—
134C3×D5—31no—
135C3×D5D3×C7×C2911yescharacteristic, direct product factor
136C3×D5C2×C3×C7×C2911yescharacteristic, complemented
137C5×D3C2×C3×C7×C2911yescharacteristic, complemented
138C29C3×D3×C7×D511yescharacteristic, direct product factor, Sylow
139C22×C7—151noHall
140C3×C7—21no—
141C3×C7D3×D5×C2911yescharacteristic, direct product factor
142C3×C7C2×C3×D5×C2911yescharacteristic, complemented
143C2×D5—31noHall
144C2×C32—51no—
145C3×D3—51no—
146C3×D3C7×D5×C2911yescharacteristic, direct product factor
147C3×C5—21no—
148C3×C5C22×C3×C7×C2911yescharacteristic, complemented
149C3×C5C2×D3×C7×C2911yescharacteristic, complemented
150C2×C7—31no—
151C2×C7—51no—
152C2×C7—151no—
153C22×C3—151no—
154C2×D3—51no—
155C2×C5—31no—
156D5—31no—
157D5C3×D3×C7×C2911yescharacteristic, direct product factor
158C32C2×C7×D5×C2911yescharacteristic, complemented, Sylow
159C7C3×D3×D5×C2911yescharacteristic, direct product factor, Sylow
160C2×C3—31no—
161C2×C3—51no—
162C2×C3—51no—
163C2×C3—101no—
164C2×C3—151no—
165D3—51no—
166D3C3×C7×D5×C2911yescharacteristic, direct product factor
167C5C2×C3×D3×C7×C2911yescharacteristic, complemented, Sylow
168C22—151noSylow
169C3—21no—
170C3D3×C7×D5×C2911yescharacteristic, direct product factor
171C3C2×C3×C7×D5×C2911yescharacteristic, complemented
172C2—31no—
173C2—51no—
174C2—151no—
subgroupG/H
center, hypercenterC3×C7×C29D3×D5
commutator, cosocle, hypocenterC3×C5C22×C3×C7×C29
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C3×C5
UCSC1 ◁ C3×C7×C29

Complements

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

NH ≅ G/Ntype
1. C32×C7×D5×C29C2semidirect
2. C3×C5×D3×C7×C29C2semidirect
3. C3×C7×C29×D15C2semidirect
5. D3×C7×D5×C29C3direct (N × H)
6. C32×C5×C7×C29C22semidirect
8. C7×C29×D15C2×C3semidirect
9. C5×D3×C7×C29C2×C3semidirect
12. C3×C7×D5×C29D3direct (N × H)
13. C3×C7×D5×C29C2×C3semidirect
15. C3×D3×D5×C29C7direct (N × H)
18. C3×D3×C7×C29D5direct (N × H)
21. C3×C5×C7×C29C2×D3semidirect
22. C3×C5×C7×C29C22×C3semidirect
23. C3×C29×D15C2×C7semidirect
24. C3×C5×D3×C29C2×C7semidirect
25. C32×D5×C29C2×C7semidirect
29. C7×D5×C29C3×D3direct (N × H)
31. C32×C7×C29C2×D5semidirect
33. D3×D5×C29C3×C7direct (N × H)
34. C32×C5×C29C22×C7semidirect
35. C3×D3×C7×D5C29direct (N × H)
42. D3×C7×C29C3×D5direct (N × H)
44. C5×C7×C29C2×C3×D3semidirect
46. C29×D15C2×C3×C7semidirect
47. C5×D3×C29C2×C3×C7semidirect
50. C3×D5×C29D3×C7direct (N × H)
51. C3×D5×C29C2×C3×C7semidirect
53. C3×C7×D15C2×C29semidirect
54. C3×C5×D3×C7C2×C29semidirect
55. C32×C7×D5C2×C29semidirect
57. C3×C7×C29D3×D5direct (N × H)
58. C3×C7×C29C2×C3×D5semidirect
62. C3×D3×C29C7×D5direct (N × H)
64. C3×C5×C29C2×D3×C7semidirect
65. C3×C5×C29C22×C3×C7semidirect
67. D3×C7×D5C3×C29direct (N × H)
73. C32×C5×C7C22×C29semidirect
76. D5×C29C3×D3×C7direct (N × H)
77. C32×C29C2×C7×D5semidirect
80. C7×D15C2×C3×C29semidirect
81. C5×D3×C7C2×C3×C29semidirect
84. C3×C7×D5D3×C29direct (N × H)
85. C3×C7×D5C2×C3×C29semidirect
86. C7×C29C3×D3×D5direct (N × H)
87. C3×D3×D5C7×C29direct (N × H)
94. D3×C29C3×C7×D5direct (N × H)
95. C5×C29C2×C3×D3×C7semidirect
99. C3×D3×C7D5×C29direct (N × H)
102. C3×C5×C7C2×D3×C29semidirect
103. C3×C5×C7C22×C3×C29semidirect
104. C3×D15C2×C7×C29semidirect
105. C3×C5×D3C2×C7×C29semidirect
106. C32×D5C2×C7×C29semidirect
108. C3×C29D3×C7×D5direct (N × H)
109. C3×C29C2×C3×C7×D5semidirect
114. C7×D5C3×D3×C29direct (N × H)
115. C32×C7C2×D5×C29semidirect
117. D3×D5C3×C7×C29direct (N × H)
121. C32×C5C22×C7×C29semidirect
128. D3×C7C3×D5×C29direct (N × H)
130. C5×C7C2×C3×D3×C29semidirect
132. D15C2×C3×C7×C29semidirect
135. C3×D5D3×C7×C29direct (N × H)
136. C3×D5C2×C3×C7×C29semidirect
137. C5×D3C2×C3×C7×C29semidirect
138. C29C3×D3×C7×D5direct (N × H)
141. C3×C7D3×D5×C29direct (N × H)
142. C3×C7C2×C3×D5×C29semidirect
146. C3×D3C7×D5×C29direct (N × H)
148. C3×C5C22×C3×C7×C29semidirect
149. C3×C5C2×D3×C7×C29semidirect
157. D5C3×D3×C7×C29direct (N × H)
158. C32C2×C7×D5×C29semidirect
159. C7C3×D3×D5×C29direct (N × H)
166. D3C3×C7×D5×C29direct (N × H)
167. C5C2×C3×D3×C7×C29semidirect
170. C3D3×C7×D5×C29direct (N × H)
171. C3C2×C3×C7×D5×C29semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D5×C292
C3×C5×D3×C7×C292
C3×C7×C29×D152
C2×C3×C7×D5×C293
D3×C7×D5×C293
C2×C3×D3×C7×C295
C3×D3×D5×C297
C3×D3×C7×D529