Finite Group Databasebeta

← C3×D5×C29×D21 #49141582

Subgroups — C3×D5×C29×D21 #49141582

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×C7×D5×C29C211yesmaximal, characteristic, complemented
2C3×C5×C29×D21C211yesmaximal, characteristic, complemented
3C3×C29×D105C211yesmaximal, characteristic, complemented
4D5×C29×D21C311yesmaximal, characteristic, direct product factor
5C3×D5×D7×C29—31nomaximal
6C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
7C2×C3×C29×D21—51nomaximal, Hall
8C29×D105C2×C311yescharacteristic, complemented
9C5×C29×D21C2×C311yescharacteristic, complemented
10C3×C29×D35—31no—
11C3×C7×D5×C29—21no—
12C3×C7×D5×C29D311yescharacteristic, complemented
13C3×C7×D5×C29C2×C311yescharacteristic, complemented
14C3×C5×D7×C29—31no—
15C3×D3×D5×C29—71nomaximal, Hall
16D5×D7×C29—31noHall
17C3×C29×D21—51no—
18C3×C29×D21D511yescharacteristic, 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×D15—71no—
24C3×C5×D3×C29—71no—
25C32×D5×C29D711yescharacteristic, complemented
26C2×C29×D21—51no—
27C2×C3×D7×C29—151no—
28C29×D35—31no—
29C7×D5×C29C3×D311yescharacteristic, complemented
30C5×D7×C29—31no—
31C32×C7×C29C2×D511yescharacteristic, complemented, Hall
32C2×C3×D5×C29—211no—
33D3×D5×C29—71no—
34C32×C5×C29C2×D711yescharacteristic, complemented, Hall
35C3×D5×D21C2911yesmaximal, characteristic, direct product factor, Hall
36C2×C3×C7×C29—51no—
37C2×C3×C7×C29—51no—
38C2×C3×C7×C29—101no—
39C29×D21—51no—
40C29×D21C3×D511yescharacteristic, direct product factor
41C3×D7×C29—31no—
42C3×D7×C29—151no—
43C2×C3×D3×C29—351noHall
44C5×C7×C29C2×C3×D311yescharacteristic, complemented, Hall
45C2×C3×C5×C29—211no—
46C29×D15—71no—
47C5×D3×C29—71no—
48C3×D5×C29—21no—
49C3×D5×C29—211no—
50C3×D5×C29C3×D711yescharacteristic, complemented
51C3×D5×C29D2111yescharacteristic, direct product factor
52C2×D7×C29—151noHall
53C3×D105C2×C2911yescharacteristic, complemented
54C3×C5×D21C2×C2911yescharacteristic, complemented
55C32×C7×D5C2×C2911yescharacteristic, complemented
56C3×C7×C29—21no—
57C3×C7×C29D3×D511yescharacteristic, complemented
58C3×C7×C29C2×C3×D511yescharacteristic, complemented
59C2×D5×C29—211noHall
60C2×C32×C29—51no—
61C3×D3×C29—71no—
62C3×D3×C29—351no—
63C3×C5×C29—21no—
64C3×C5×C29C2×C3×D711yescharacteristic, complemented
65C3×C5×C29C2×D2111yescharacteristic, complemented
66D5×D21C3×C2911yescharacteristic, direct product factor
67C3×D5×D7—31no—
68C2×C7×C29—51no—
69D7×C29—31no—
70D7×C29—151no—
71C22×C3×C29—1051no—
72C2×D3×C29—351no—
73C32×C5×C7C22×C2911yescharacteristic, complemented, Hall
74C2×C5×C29—211no—
75D5×C29—211no—
76D5×C29C3×D2111yescharacteristic, direct product factor
77C32×C29D5×D711yescharacteristic, complemented, Hall
78C2×C3×D21—51noHall
79D105C2×C3×C2911yescharacteristic, complemented
80C5×D21C2×C3×C2911yescharacteristic, complemented
81C3×D35—31no—
82C3×C7×D5—21no—
83C3×C7×D5D3×C2911yescharacteristic, complemented
84C3×C7×D5C2×C3×C2911yescharacteristic, complemented
85C3×C5×D7—31no—
86C7×C29C3×D3×D511yescharacteristic, complemented, Hall
87C3×D3×D5—71noHall
88C2×C3×C29—51no—
89C2×C3×C29—51no—
90C2×C3×C29—101no—
91C2×C3×C29—211no—
92C2×C3×C29—1051no—
93D3×C29—71no—
94D3×C29—351no—
95C5×C29C2×C3×D2111yescharacteristic, complemented, Hall
96D5×D7—31noHall
97C2×C32×C7—51no—
98C3×D21—51no—
99C3×D21D5×C2911yescharacteristic, direct product factor
100C22×C29—1051noHall
101C3×C5×C7—21no—
102C3×C5×C7C2×D3×C2911yescharacteristic, complemented
103C3×C5×C7C22×C3×C2911yescharacteristic, complemented
104C3×D15—71no—
105C3×C5×D3—71no—
106C32×D5D7×C2911yescharacteristic, complemented
107C3×C29—21no—
108C3×C29C3×D5×D711yescharacteristic, complemented
109C3×C29D5×D2111yescharacteristic, direct product factor
110C2×D21—51no—
111C2×C3×D7—151no—
112D35—31no—
113C5×D7—31no—
114C7×D5C3×D3×C2911yescharacteristic, complemented
115C32×C7C2×D5×C2911yescharacteristic, complemented, Hall
116C2×C3×D5—211no—
117D3×D5—71no—
118C2×C29—51no—
119C2×C29—211no—
120C2×C29—1051no—
121C32×C5C2×D7×C2911yescharacteristic, complemented, Hall
122C2×C3×C7—51no—
123C2×C3×C7—51no—
124C2×C3×C7—101no—
125D21—51no—
126D21C3×D5×C2911yescharacteristic, direct product factor
127C3×D7—31no—
128C3×D7—151no—
129C2×C3×D3—351noHall
130C5×C7C2×C3×D3×C2911yescharacteristic, complemented, Hall
131C2×C3×C5—211no—
132D15—71no—
133C3×D5—21no—
134C3×D5—211no—
135C3×D5C3×D7×C2911yescharacteristic, complemented
136C3×D5C29×D2111yescharacteristic, direct product factor
137C5×D3—71no—
138C29C3×D5×D2111yescharacteristic, 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—51no—
145C3×D3—71no—
146C3×D3—351no—
147C3×C5—21no—
148C3×C5C2×C3×D7×C2911yescharacteristic, complemented
149C3×C5C2×C29×D2111yescharacteristic, complemented
150C2×C7—51no—
151D7—31no—
152D7—151no—
153C22×C3—1051no—
154C2×D3—351no—
155C2×C5—211no—
156D5—211no—
157D5C3×C29×D2111yescharacteristic, direct product factor
158C32D5×D7×C2911yescharacteristic, complemented, Sylow
159C7C3×D3×D5×C2911yescharacteristic, complemented, Sylow
160C2×C3—51no—
161C2×C3—51no—
162C2×C3—101no—
163C2×C3—211no—
164C2×C3—1051no—
165D3—71no—
166D3—351no—
167C5C2×C3×C29×D2111yescharacteristic, complemented, Sylow
168C22—1051noSylow
169C3—21no—
170C3C3×D5×D7×C2911yescharacteristic, complemented
171C3D5×C29×D2111yescharacteristic, direct product factor
172C2—51no—
173C2—211no—
174C2—1051no—
subgroupG/H
center, hypercenterC3×C29D5×D21
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×C7×D5×C29C2semidirect
2. C3×C5×C29×D21C2semidirect
3. C3×C29×D105C2semidirect
4. D5×C29×D21C3direct (N × H)
6. C32×C5×C7×C29C22semidirect
8. C29×D105C2×C3semidirect
9. C5×C29×D21C2×C3semidirect
12. C3×C7×D5×C29D3semidirect
13. C3×C7×D5×C29C2×C3semidirect
18. C3×C29×D21D5direct (N × H)
21. C3×C5×C7×C29C2×D3semidirect
22. C3×C5×C7×C29C22×C3semidirect
25. C32×D5×C29D7semidirect
29. C7×D5×C29C3×D3semidirect
31. C32×C7×C29C2×D5semidirect
34. C32×C5×C29C2×D7semidirect
35. C3×D5×D21C29direct (N × H)
40. C29×D21C3×D5direct (N × H)
44. C5×C7×C29C2×C3×D3semidirect
50. C3×D5×C29C3×D7semidirect
51. C3×D5×C29D21direct (N × H)
53. C3×D105C2×C29semidirect
54. C3×C5×D21C2×C29semidirect
55. C32×C7×D5C2×C29semidirect
57. C3×C7×C29D3×D5semidirect
58. C3×C7×C29C2×C3×D5semidirect
64. C3×C5×C29C2×C3×D7semidirect
65. C3×C5×C29C2×D21semidirect
66. D5×D21C3×C29direct (N × H)
73. C32×C5×C7C22×C29semidirect
76. D5×C29C3×D21direct (N × H)
77. C32×C29D5×D7semidirect
79. D105C2×C3×C29semidirect
80. C5×D21C2×C3×C29semidirect
83. C3×C7×D5D3×C29semidirect
84. C3×C7×D5C2×C3×C29semidirect
86. C7×C29C3×D3×D5semidirect
95. C5×C29C2×C3×D21semidirect
99. C3×D21D5×C29direct (N × H)
102. C3×C5×C7C2×D3×C29semidirect
103. C3×C5×C7C22×C3×C29semidirect
106. C32×D5D7×C29semidirect
108. C3×C29C3×D5×D7semidirect
109. C3×C29D5×D21direct (N × H)
114. C7×D5C3×D3×C29semidirect
115. C32×C7C2×D5×C29semidirect
121. C32×C5C2×D7×C29semidirect
126. D21C3×D5×C29direct (N × H)
130. C5×C7C2×C3×D3×C29semidirect
135. C3×D5C3×D7×C29semidirect
136. C3×D5C29×D21direct (N × H)
138. C29C3×D5×D21direct (N × H)
141. C3×C7D3×D5×C29semidirect
142. C3×C7C2×C3×D5×C29semidirect
148. C3×C5C2×C3×D7×C29semidirect
149. C3×C5C2×C29×D21semidirect
157. D5C3×C29×D21direct (N × H)
158. C32D5×D7×C29semidirect
159. C7C3×D3×D5×C29semidirect
167. C5C2×C3×C29×D21semidirect
170. C3C3×D5×D7×C29semidirect
171. C3D5×C29×D21direct (N × H)

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×C29×D212
C3×C29×D1052
D5×C29×D213
C3×D5×D7×C293
C2×C3×C29×D215
C3×D3×D5×C297
C3×D5×D2129