Finite Group Databasebeta

← C29×D15⋊D21 #49141623

Subgroups — C29×D15⋊D21 #49141623

Order 36540.

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C3×C7×C29×D15C211yesmaximal, characteristic, complemented
2C3×C29×D105C211yesmaximal, characteristic, complemented
3C5×C29×C3⋊D21C211yesmaximal, characteristic, complemented
4C29×D15⋊D7—31nomaximal
5D5×C29×D21—31nomaximal
6C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
7D3×C29×D21—51nomaximal, Hall
8C29×D105D311yescharacteristic, complemented
9C7×C29×D15D311yescharacteristic, complemented
10C5×C29×D21—31no—
11C5×C29×D21—31no—
12C5×C29×D21—61no—
13C3×C29×D35—31no—
14C3×C7×D5×C29—31no—
15C29×(C3⋊D3)⋊D5—71nomaximal, Hall
16D5×D7×C29—91noHall
17C29×C3⋊D21D511yescharacteristic, complemented
18C3×C29×D21—51no—
19C3×D3×C7×C29—51no—
20C3×C5×C7×C29—21no—
21C3×C5×C7×C29C2×D311yescharacteristic, complemented
22C3×C5×C7×C29C2×D311yescharacteristic, complemented
23C5×C3⋊D3×C29—71no—
24C3×C29×D15—71no—
25C3×C29×D15D711yescharacteristic, complemented
26C2×C29×D21—151no—
27D3×D7×C29—151no—
28C29×D35—31no—
29C7×D5×C29—31no—
30C5×D7×C29—91no—
31C32×C7×C29C2×D511yescharacteristic, complemented, Hall
32D3×D5×C29—211no—
33D3×D5×C29—211no—
34C32×C5×C29C2×D711yescharacteristic, complemented, Hall
35D15⋊D21C2911yesmaximal, characteristic, direct product factor, Hall
36C2×C3×C7×C29—151no—
37C29×D21—31no—
38C29×D21—31no—
39C29×D21—51no—
40C29×D21—61no—
41D3×C7×C29—51no—
42C3×D7×C29—151no—
43D32×C29—351noHall
44C5×C7×C29D3211yescharacteristic, complemented, Hall
45C29×D15—71no—
46C29×D15D2111yescharacteristic, complemented
47C5×D3×C29—211no—
48C5×D3×C29—211no—
49C5×D3×C29—421no—
50C3×D5×C29—31no—
51C3×D5×C29—211no—
52C2×D7×C29—451noHall
53C5×C3⋊D21C2×C2911yescharacteristic, complemented
54C3×D105C2×C2911yescharacteristic, complemented
55C3×C7×D15C2×C2911yescharacteristic, complemented
56C3×C7×C29—21no—
57C3×C7×C29D3×D511yescharacteristic, complemented
58C3×C7×C29D3×D511yescharacteristic, complemented
59C2×D5×C29—631noHall
60C3⋊D3×C29—71no—
61C3×D3×C29—51no—
62C3×D3×C29—351no—
63C3×C5×C29—21no—
64C3×C5×C29D3×D711yescharacteristic, complemented
65C3×C5×C29C2×D2111yescharacteristic, complemented
66D15⋊D7—31no—
67D5×D21—31no—
68C2×C7×C29—151no—
69D7×C29—91no—
70D7×C29—151no—
71C2×D3×C29—1051no—
72C2×D3×C29—1051no—
73C32×C5×C7C22×C2911yescharacteristic, complemented, Hall
74C2×C5×C29—631no—
75D5×C29—31no—
76D5×C29—211no—
77C32×C29D5×D711yescharacteristic, complemented, Hall
78D3×D21—51noHall
79D105D3×C2911yescharacteristic, complemented
80C7×D15D3×C2911yescharacteristic, complemented
81C5×D21—31no—
82C5×D21—31no—
83C5×D21—61no—
84C3×D35—31no—
85C3×C7×D5—31no—
86C7×C29(C3⋊D3)⋊D511yescharacteristic, complemented, Hall
87(C3⋊D3)⋊D5—71noHall
88C2×C3×C29—151no—
89C2×C3×C29—1051no—
90D3×C29—51no—
91D3×C29—211no—
92D3×C29—211no—
93D3×C29—351no—
94D3×C29—421no—
95C5×C29D3×D2111yescharacteristic, complemented, Hall
96D5×D7—91noHall
97C3⋊D21D5×C2911yescharacteristic, complemented
98C3×D21—51no—
99C3×D3×C7—51no—
100C22×C29—3151noHall
101C3×C5×C7—21no—
102C3×C5×C7C2×D3×C2911yescharacteristic, complemented
103C3×C5×C7C2×D3×C2911yescharacteristic, complemented
104C5×C3⋊D3—71no—
105C3×D15—71no—
106C3×D15D7×C2911yescharacteristic, complemented
107C3×C29—21no—
108C3×C29D5×D2111yescharacteristic, complemented
109C3×C29D15⋊D711yescharacteristic, complemented
110C2×D21—151no—
111D3×D7—151no—
112D35—31no—
113C5×D7—91no—
114C7×D5—31no—
115C32×C7C2×D5×C2911yescharacteristic, complemented, Hall
116D3×D5—211no—
117D3×D5—211no—
118C2×C29—151no—
119C2×C29—631no—
120C2×C29—1051no—
121C32×C5C2×D7×C2911yescharacteristic, complemented, Hall
122C2×C3×C7—151no—
123D21—31no—
124D21—31no—
125D21—51no—
126D21—61no—
127C3×D7—151no—
128D3×C7—51no—
129D32—351noHall
130C5×C7D32×C2911yescharacteristic, complemented, Hall
131D15—71no—
132D15C29×D2111yescharacteristic, complemented
133C3×D5—31no—
134C3×D5—211no—
135C5×D3—211no—
136C5×D3—211no—
137C5×D3—421no—
138C29D15⋊D2111yescharacteristic, direct product factor, Sylow
139C2×D7—451noHall
140C3×C7—21no—
141C3×C7D3×D5×C2911yescharacteristic, complemented
142C3×C7D3×D5×C2911yescharacteristic, complemented
143C2×D5—631noHall
144C3⋊D3—71no—
145C3×D3—51no—
146C3×D3—351no—
147C3×C5—21no—
148C3×C5D3×D7×C2911yescharacteristic, complemented
149C3×C5C2×C29×D2111yescharacteristic, complemented
150C2×C7—151no—
151D7—91no—
152D7—151no—
153C2×D3—1051no—
154C2×D3—1051no—
155C2×C5—631no—
156D5—31no—
157D5—211no—
158C32D5×D7×C2911yescharacteristic, complemented, Sylow
159C7C29×(C3⋊D3)⋊D511yescharacteristic, complemented, Sylow
160C2×C3—151no—
161C2×C3—1051no—
162D3—51no—
163D3—211no—
164D3—211no—
165D3—351no—
166D3—421no—
167C5D3×C29×D2111yescharacteristic, complemented, Sylow
168C22—3151noSylow
169C3—21no—
170C3D5×C29×D2111yescharacteristic, complemented
171C3C29×D15⋊D711yescharacteristic, complemented
172C2—151no—
173C2—631no—
174C2—1051no—
subgroupG/H
center, hypercenterC29D15⋊D21
commutator, cosocle, hypocenterC32×C5×C7C22×C29
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C32×C5×C7
UCSC1 ◁ C29

Complements

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

NH ≅ G/Ntype
1. C3×C7×C29×D15C2semidirect
2. C3×C29×D105C2semidirect
3. C5×C29×C3⋊D21C2semidirect
6. C32×C5×C7×C29C22semidirect
8. C29×D105D3semidirect
9. C7×C29×D15D3semidirect
17. C29×C3⋊D21D5semidirect
21. C3×C5×C7×C29C2×D3semidirect
22. C3×C5×C7×C29C2×D3semidirect
25. C3×C29×D15D7semidirect
31. C32×C7×C29C2×D5semidirect
34. C32×C5×C29C2×D7semidirect
35. D15⋊D21C29direct (N × H)
44. C5×C7×C29D32semidirect
46. C29×D15D21semidirect
53. C5×C3⋊D21C2×C29semidirect
54. C3×D105C2×C29semidirect
55. C3×C7×D15C2×C29semidirect
57. C3×C7×C29D3×D5semidirect
58. C3×C7×C29D3×D5semidirect
64. C3×C5×C29D3×D7semidirect
65. C3×C5×C29C2×D21semidirect
73. C32×C5×C7C22×C29semidirect
77. C32×C29D5×D7semidirect
79. D105D3×C29semidirect
80. C7×D15D3×C29semidirect
86. C7×C29(C3⋊D3)⋊D5semidirect
95. C5×C29D3×D21semidirect
97. C3⋊D21D5×C29semidirect
102. C3×C5×C7C2×D3×C29semidirect
103. C3×C5×C7C2×D3×C29semidirect
106. C3×D15D7×C29semidirect
108. C3×C29D5×D21semidirect
109. C3×C29D15⋊D7semidirect
115. C32×C7C2×D5×C29semidirect
121. C32×C5C2×D7×C29semidirect
130. C5×C7D32×C29semidirect
132. D15C29×D21semidirect
138. C29D15⋊D21direct (N × H)
141. C3×C7D3×D5×C29semidirect
142. C3×C7D3×D5×C29semidirect
148. C3×C5D3×D7×C29semidirect
149. C3×C5C2×C29×D21semidirect
158. C32D5×D7×C29semidirect
159. C7C29×(C3⋊D3)⋊D5semidirect
167. C5D3×C29×D21semidirect
170. C3D5×C29×D21semidirect
171. C3C29×D15⋊D7semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C29×D152
C3×C29×D1052
C5×C29×C3⋊D212
C29×D15⋊D73
D5×C29×D213
D3×C29×D215
C29×(C3⋊D3)⋊D57
D15⋊D2129