Finite Group Databasebeta

← C3×C5×D21×D29 #49141557

Subgroups — C3×C5×D21×D29 #49141557

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×C7×D29C211yesmaximal, characteristic, complemented
2C3×C5×C29×D21C211yesmaximal, characteristic, complemented
3C3×C5×D609C211yesmaximal, characteristic, complemented
4C5×D21×D29C311yesmaximal, characteristic, direct product factor
5C3×C5×D7×D29—31nomaximal
6C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
7C3×D21×D29C511yesmaximal, characteristic, direct product factor, Hall
8C5×D609C2×C311yescharacteristic, complemented
9C5×C29×D21C2×C311yescharacteristic, complemented
10C3×C5×D203—31no—
11C3×C5×D7×C29—31no—
12C3×C5×C7×D29—21no—
13C3×C5×C7×D29D311yescharacteristic, complemented
14C3×C5×C7×D29C2×C311yescharacteristic, complemented
15C3×C5×D3×D29—71nomaximal, Hall
16C5×D7×D29—31noHall
17C3×D609C2×C511yescharacteristic, complemented
18C3×C29×D21C2×C511yescharacteristic, complemented
19C32×C7×D29C2×C511yescharacteristic, complemented
20C3×C5×C7×C29—21no—
21C3×C5×C7×C29C2×D311yescharacteristic, complemented
22C3×C5×C7×C29C22×C311yescharacteristic, complemented
23C3×C5×D87—71no—
24C3×C5×D3×C29—71no—
25C32×C5×D29D711yescharacteristic, complemented
26D21×D29C3×C511yescharacteristic, direct product factor
27C3×D7×D29—31no—
28C5×D203—31no—
29C5×D7×C29—31no—
30C5×C7×D29C3×D311yescharacteristic, complemented
31C32×C7×C29C22×C511yescharacteristic, complemented, Hall
32C2×C3×C5×D29—211no—
33C5×D3×D29—71no—
34C32×C5×C29C2×D711yescharacteristic, complemented, Hall
35C2×C3×C5×D21—291nomaximal, Hall
36D609C2×C3×C511yescharacteristic, complemented
37C29×D21C2×C3×C511yescharacteristic, complemented
38C3×D203—31no—
39C3×D7×C29—31no—
40C3×C7×D29—21no—
41C3×C7×D29C5×D311yescharacteristic, complemented
42C3×C7×D29C2×C3×C511yescharacteristic, complemented
43C3×D3×D29—71noHall
44C5×C7×C29C2×C3×D311yescharacteristic, complemented, Hall
45C2×C3×C5×C29—211no—
46C5×D87—71no—
47C5×D3×C29—71no—
48C3×C5×D29—21no—
49C3×C5×D29—211no—
50C3×C5×D29C3×D711yescharacteristic, complemented
51C3×C5×D29D2111yescharacteristic, direct product factor
52D7×D29—31noHall
53C2×C32×C5×C7—291no—
54C3×C5×D21—291no—
55C3×C5×D21D2911yescharacteristic, direct product factor
56C3×C7×C29—21no—
57C3×C7×C29C2×C5×D311yescharacteristic, complemented
58C3×C7×C29C22×C3×C511yescharacteristic, complemented
59C2×C5×D29—211noHall
60C3×D87—71no—
61C3×D3×C29—71no—
62C32×D29C5×D711yescharacteristic, complemented
63C3×C5×C29—21no—
64C3×C5×C29C2×C3×D711yescharacteristic, complemented
65C3×C5×C29C2×D2111yescharacteristic, complemented
66C2×C5×D21—291no—
67C2×C3×C5×D7—871no—
68D203—31no—
69C7×D29C3×C5×D311yescharacteristic, complemented
70D7×C29—31no—
71C2×C3×D29—211no—
72D3×D29—71no—
73C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
74C2×C5×C29—211no—
75C5×D29—211no—
76C5×D29C3×D2111yescharacteristic, direct product factor
77C32×C29C2×C5×D711yescharacteristic, complemented, Hall
78C2×C3×D21—291noHall
79C2×C3×C5×C7—291no—
80C2×C3×C5×C7—291no—
81C2×C3×C5×C7—581no—
82C5×D21—291no—
83C5×D21C3×D2911yescharacteristic, direct product factor
84C3×C5×D7—31no—
85C3×C5×D7—871no—
86C7×C29C2×C3×C5×D311yescharacteristic, complemented, Hall
87C2×C3×C5×D3—2031noHall
88C2×C3×C29—211no—
89D87—71no—
90C3×D29—21no—
91C3×D29—211no—
92C3×D29C3×C5×D711yescharacteristic, complemented
93C3×D29C5×D2111yescharacteristic, direct product factor
94D3×C29—71no—
95C5×C29C2×C3×D2111yescharacteristic, complemented, Hall
96C2×C5×D7—871noHall
97C2×C32×C7—291no—
98C3×D21—291no—
99C3×D21C5×D2911yescharacteristic, direct product factor
100C2×D29—211noHall
101C3×C5×C7—21no—
102C3×C5×C7D3×D2911yescharacteristic, complemented
103C3×C5×C7C2×C3×D2911yescharacteristic, complemented
104C2×C32×C5—291no—
105C3×C5×D3—71no—
106C3×C5×D3—2031no—
107C3×C29—21no—
108C3×C29C2×C3×C5×D711yescharacteristic, complemented
109C3×C29C2×C5×D2111yescharacteristic, complemented
110C2×D21—291no—
111C2×C3×D7—871no—
112C2×C5×C7—291no—
113C5×D7—31no—
114C5×D7—871no—
115C32×C7C2×C5×D2911yescharacteristic, complemented, Hall
116C22×C3×C5—6091no—
117C2×C5×D3—2031no—
118C2×C29—211no—
119D29—211no—
120D29C3×C5×D2111yescharacteristic, direct product factor
121C32×C5D7×D2911yescharacteristic, complemented, Hall
122C2×C3×C7—291no—
123C2×C3×C7—291no—
124C2×C3×C7—581no—
125D21—291no—
126D21C3×C5×D2911yescharacteristic, direct product factor
127C3×D7—31no—
128C3×D7—871no—
129C2×C3×D3—2031noHall
130C5×C7C3×D3×D2911yescharacteristic, complemented, Hall
131C2×C3×C5—211no—
132C2×C3×C5—291no—
133C2×C3×C5—291no—
134C2×C3×C5—581no—
135C2×C3×C5—6091no—
136C5×D3—71no—
137C5×D3—2031no—
138C29C2×C3×C5×D2111yescharacteristic, complemented, Sylow
139C2×D7—871noHall
140C3×C7—21no—
141C3×C7C5×D3×D2911yescharacteristic, complemented
142C3×C7C2×C3×C5×D2911yescharacteristic, complemented
143C22×C5—6091noHall
144C2×C32—291no—
145C3×D3—71no—
146C3×D3—2031no—
147C3×C5—21no—
148C3×C5C3×D7×D2911yescharacteristic, complemented
149C3×C5D21×D2911yescharacteristic, direct product factor
150C2×C7—291no—
151D7—31no—
152D7—871no—
153C22×C3—6091no—
154C2×D3—2031no—
155C2×C5—211no—
156C2×C5—291no—
157C2×C5—6091no—
158C32C5×D7×D2911yescharacteristic, complemented, Sylow
159C7C3×C5×D3×D2911yescharacteristic, complemented, Sylow
160C2×C3—211no—
161C2×C3—291no—
162C2×C3—291no—
163C2×C3—581no—
164C2×C3—6091no—
165D3—71no—
166D3—2031no—
167C5C3×D21×D2911yescharacteristic, direct product factor, Sylow
168C22—6091noSylow
169C3—21no—
170C3C3×C5×D7×D2911yescharacteristic, complemented
171C3C5×D21×D2911yescharacteristic, direct product factor
172C2—211no—
173C2—291no—
174C2—6091no—
subgroupG/H
center, hypercenterC3×C5D21×D29
commutator, cosocle, hypocenterC3×C7×C29C22×C3×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C3×C7×C29
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C32×C5×C7×D29C2semidirect
2. C3×C5×C29×D21C2semidirect
3. C3×C5×D609C2semidirect
4. C5×D21×D29C3direct (N × H)
6. C32×C5×C7×C29C22semidirect
7. C3×D21×D29C5direct (N × H)
8. C5×D609C2×C3semidirect
9. C5×C29×D21C2×C3semidirect
13. C3×C5×C7×D29D3semidirect
14. C3×C5×C7×D29C2×C3semidirect
17. C3×D609C2×C5semidirect
18. C3×C29×D21C2×C5semidirect
19. C32×C7×D29C2×C5semidirect
21. C3×C5×C7×C29C2×D3semidirect
22. C3×C5×C7×C29C22×C3semidirect
25. C32×C5×D29D7semidirect
26. D21×D29C3×C5direct (N × H)
30. C5×C7×D29C3×D3semidirect
31. C32×C7×C29C22×C5semidirect
34. C32×C5×C29C2×D7semidirect
36. D609C2×C3×C5semidirect
37. C29×D21C2×C3×C5semidirect
41. C3×C7×D29C5×D3semidirect
42. C3×C7×D29C2×C3×C5semidirect
44. C5×C7×C29C2×C3×D3semidirect
50. C3×C5×D29C3×D7semidirect
51. C3×C5×D29D21direct (N × H)
55. C3×C5×D21D29direct (N × H)
57. C3×C7×C29C2×C5×D3semidirect
58. C3×C7×C29C22×C3×C5semidirect
62. C32×D29C5×D7semidirect
64. C3×C5×C29C2×C3×D7semidirect
65. C3×C5×C29C2×D21semidirect
69. C7×D29C3×C5×D3semidirect
73. C32×C5×C7C2×D29semidirect
76. C5×D29C3×D21direct (N × H)
77. C32×C29C2×C5×D7semidirect
83. C5×D21C3×D29direct (N × H)
86. C7×C29C2×C3×C5×D3semidirect
92. C3×D29C3×C5×D7semidirect
93. C3×D29C5×D21direct (N × H)
95. C5×C29C2×C3×D21semidirect
99. C3×D21C5×D29direct (N × H)
102. C3×C5×C7D3×D29semidirect
103. C3×C5×C7C2×C3×D29semidirect
108. C3×C29C2×C3×C5×D7semidirect
109. C3×C29C2×C5×D21semidirect
115. C32×C7C2×C5×D29semidirect
120. D29C3×C5×D21direct (N × H)
121. C32×C5D7×D29semidirect
126. D21C3×C5×D29direct (N × H)
130. C5×C7C3×D3×D29semidirect
138. C29C2×C3×C5×D21semidirect
141. C3×C7C5×D3×D29semidirect
142. C3×C7C2×C3×C5×D29semidirect
148. C3×C5C3×D7×D29semidirect
149. C3×C5D21×D29direct (N × H)
158. C32C5×D7×D29semidirect
159. C7C3×C5×D3×D29semidirect
167. C5C3×D21×D29direct (N × H)
170. C3C3×C5×D7×D29semidirect
171. C3C5×D21×D29direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×C7×D292
C3×C5×C29×D212
C3×C5×D6092
C5×D21×D293
C3×C5×D7×D293
C3×D21×D295
C3×C5×D3×D297
C2×C3×C5×D2129