Finite Group Databasebeta

← C29×D15×D21 #49141616

Subgroups — C29×D15×D21 #49141616

Order 36540.

176 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 52 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×C5×C29×D21C211yesmaximal, characteristic, complemented
2C3×C7×C29×D15C211yesmaximal, characteristic, complemented
3C29×C3⋊D105C211yesmaximal, characteristic, complemented
4D5×C29×D21—31nomaximal
5D7×C29×D15—31nomaximal
6C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
7D3×C29×D21—51nomaximal, Hall
8C29×D105—31no—
9C29×D105—31no—
10C29×D105—61no—
11C7×C29×D15D311yescharacteristic, complemented
12C5×C29×D21D311yescharacteristic, complemented
13C3×C7×D5×C29—31no—
14C3×C5×D7×C29—31no—
15D3×C29×D15—71nomaximal, Hall
16D5×D7×C29—91noHall
17C29×C3⋊D21—51no—
18C3×C29×D21D511yescharacteristic, complemented
19C3×D3×C7×C29—51no—
20C3×C5×C7×C29—21no—
21C3×C5×C7×C29C2×D311yescharacteristic, complemented
22C3×C5×C7×C29C2×D311yescharacteristic, complemented
23C29×C3⋊D15—71no—
24C3×C29×D15D711yescharacteristic, complemented
25C3×C5×D3×C29—71no—
26C2×C29×D21—151no—
27D3×D7×C29—151no—
28C29×D35—91no—
29C7×D5×C29—31no—
30C5×D7×C29—31no—
31C32×C7×C29C2×D511yescharacteristic, complemented, Hall
32C2×C29×D15—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—151no—
38C29×D21—151no—
39C29×D21—301no—
40C29×D21D1511yescharacteristic, direct product factor
41D3×C7×C29—51no—
42C3×D7×C29—31no—
43D32×C29—351noHall
44C5×C7×C29D3211yescharacteristic, complemented, Hall
45C2×C3×C5×C29—211no—
46C29×D15—211no—
47C29×D15—211no—
48C29×D15—421no—
49C29×D15D2111yescharacteristic, direct product factor
50C5×D3×C29—71no—
51C3×D5×C29—31no—
52C2×D7×C29—451noHall
53C3⋊D105C2×C2911yescharacteristic, complemented
54C3×C7×D15C2×C2911yescharacteristic, complemented
55C3×C5×D21C2×C2911yescharacteristic, complemented
56C3×C7×C29—21no—
57C3×C7×C29D3×D511yescharacteristic, complemented
58C3×C7×C29C2×D1511yescharacteristic, complemented
59C2×D5×C29—631noHall
60C3⋊D3×C29—351no—
61C3×D3×C29—51no—
62C3×D3×C29—71no—
63C3×C5×C29—21no—
64C3×C5×C29D3×D711yescharacteristic, complemented
65C3×C5×C29C2×D2111yescharacteristic, complemented
66D5×D21—31no—
67D7×D15—31no—
68C2×C7×C29—151no—
69D7×C29—31no—
70D7×C29—451no—
71C2×D3×C29—1051no—
72C2×D3×C29—1051no—
73C32×C5×C7C22×C2911yescharacteristic, complemented, Hall
74C2×C5×C29—211no—
75D5×C29—31no—
76D5×C29—631no—
77C32×C29D5×D711yescharacteristic, complemented, Hall
78D3×D21—51noHall
79D105—31no—
80D105—31no—
81D105—61no—
82C7×D15D3×C2911yescharacteristic, complemented
83C5×D21D3×C2911yescharacteristic, complemented
84C3×C7×D5—31no—
85C3×C5×D7—31no—
86C7×C29D3×D1511yescharacteristic, complemented, Hall
87D3×D15—71noHall
88C2×C3×C29—151no—
89C2×C3×C29—211no—
90D3×C29—51no—
91D3×C29—71no—
92D3×C29—1051no—
93D3×C29—1051no—
94D3×C29—2101no—
95C5×C29D3×D2111yescharacteristic, complemented, Hall
96D5×D7—91noHall
97C3⋊D21—51no—
98C3×D21D5×C2911yescharacteristic, complemented
99C3×D3×C7—51no—
100C22×C29—3151noHall
101C3×C5×C7—21no—
102C3×C5×C7C2×D3×C2911yescharacteristic, complemented
103C3×C5×C7C2×D3×C2911yescharacteristic, complemented
104C3⋊D15—71no—
105C3×D15D7×C2911yescharacteristic, complemented
106C3×C5×D3—71no—
107C3×C29—21no—
108C3×C29D7×D1511yescharacteristic, complemented
109C3×C29D5×D2111yescharacteristic, complemented
110C2×D21—151no—
111D3×D7—151no—
112D35—91no—
113C5×D7—31no—
114C7×D5—31no—
115C32×C7C2×D5×C2911yescharacteristic, complemented, Hall
116C2×D15—211no—
117D3×D5—211no—
118C2×C29—151no—
119C2×C29—211no—
120C2×C29—3151no—
121C32×C5C2×D7×C2911yescharacteristic, complemented, Hall
122C2×C3×C7—151no—
123D21—151no—
124D21—151no—
125D21—301no—
126D21C29×D1511yescharacteristic, direct product factor
127C3×D7—31no—
128D3×C7—51no—
129D32—351noHall
130C5×C7D32×C2911yescharacteristic, complemented, Hall
131C2×C3×C5—211no—
132D15—211no—
133D15—211no—
134D15—421no—
135D15C29×D2111yescharacteristic, direct product factor
136C3×D5—31no—
137C5×D3—71no—
138C29D15×D2111yescharacteristic, direct product factor, Sylow
139C2×D7—451noHall
140C3×C7—21no—
141C3×C7D3×D5×C2911yescharacteristic, complemented
142C3×C7C2×C29×D1511yescharacteristic, complemented
143C2×D5—631noHall
144C3⋊D3—351no—
145C3×D3—51no—
146C3×D3—71no—
147C3×C5—21no—
148C3×C5D3×D7×C2911yescharacteristic, complemented
149C3×C5C2×C29×D2111yescharacteristic, complemented
150C2×C7—151no—
151D7—31no—
152D7—451no—
153C2×D3—1051no—
154C2×D3—1051no—
155C2×C5—211no—
156D5—31no—
157D5—631no—
158C32D5×D7×C2911yescharacteristic, complemented, Sylow
159C7D3×C29×D1511yescharacteristic, complemented, Sylow
160C2×C3—151no—
161C2×C3—211no—
162D3—51no—
163D3—71no—
164D3—1051no—
165D3—1051no—
166D3—2101no—
167C5D3×C29×D2111yescharacteristic, complemented, Sylow
168C22—3151noSylow
169C3—21no—
170C3D7×C29×D1511yescharacteristic, complemented
171C3D5×C29×D2111yescharacteristic, complemented
172C2—151no—
173C2—211no—
174C2—3151no—
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×C5×C29×D21C2semidirect
2. C3×C7×C29×D15C2semidirect
3. C29×C3⋊D105C2semidirect
6. C32×C5×C7×C29C22semidirect
11. C7×C29×D15D3semidirect
12. C5×C29×D21D3semidirect
18. C3×C29×D21D5semidirect
21. C3×C5×C7×C29C2×D3semidirect
22. C3×C5×C7×C29C2×D3semidirect
24. C3×C29×D15D7semidirect
31. C32×C7×C29C2×D5semidirect
34. C32×C5×C29C2×D7semidirect
35. D15×D21C29direct (N × H)
40. C29×D21D15direct (N × H)
44. C5×C7×C29D32semidirect
49. C29×D15D21direct (N × H)
53. C3⋊D105C2×C29semidirect
54. C3×C7×D15C2×C29semidirect
55. C3×C5×D21C2×C29semidirect
57. C3×C7×C29D3×D5semidirect
58. C3×C7×C29C2×D15semidirect
64. C3×C5×C29D3×D7semidirect
65. C3×C5×C29C2×D21semidirect
73. C32×C5×C7C22×C29semidirect
77. C32×C29D5×D7semidirect
82. C7×D15D3×C29semidirect
83. C5×D21D3×C29semidirect
86. C7×C29D3×D15semidirect
95. C5×C29D3×D21semidirect
98. C3×D21D5×C29semidirect
102. C3×C5×C7C2×D3×C29semidirect
103. C3×C5×C7C2×D3×C29semidirect
105. C3×D15D7×C29semidirect
108. C3×C29D7×D15semidirect
109. C3×C29D5×D21semidirect
115. C32×C7C2×D5×C29semidirect
121. C32×C5C2×D7×C29semidirect
126. D21C29×D15direct (N × H)
130. C5×C7D32×C29semidirect
135. D15C29×D21direct (N × H)
138. C29D15×D21direct (N × H)
141. C3×C7D3×D5×C29semidirect
142. C3×C7C2×C29×D15semidirect
148. C3×C5D3×D7×C29semidirect
149. C3×C5C2×C29×D21semidirect
158. C32D5×D7×C29semidirect
159. C7D3×C29×D15semidirect
167. C5D3×C29×D21semidirect
170. C3D7×C29×D15semidirect
171. C3D5×C29×D21semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C29×D212
C3×C7×C29×D152
C29×C3⋊D1052
D5×C29×D213
D7×C29×D153
D3×C29×D215
D3×C29×D157
D15×D2129