Finite Group Databasebeta

← C29×D21⋊D15 #49141612

Subgroups — C29×D21⋊D15 #49141612

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×C5×C29×D21C211yesmaximal, characteristic, complemented
2C3×C29×D105C211yesmaximal, characteristic, complemented
3C7×C29×C3⋊D15C211yesmaximal, characteristic, complemented
4C29×D15⋊D7—31nomaximal
5D7×C29×D15—31nomaximal
6C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
7C29×(C3⋊D3)⋊D7—51nomaximal, Hall
8C29×D105D311yescharacteristic, complemented
9C7×C29×D15—31no—
10C7×C29×D15—31no—
11C7×C29×D15—61no—
12C5×C29×D21D311yescharacteristic, complemented
13C3×C29×D35—31no—
14C3×C5×D7×C29—31no—
15D3×C29×D15—71nomaximal, Hall
16D5×D7×C29—91noHall
17C7×C3⋊D3×C29—51no—
18C3×C29×D21—51no—
19C3×C29×D21D511yescharacteristic, complemented
20C3×C5×C7×C29—21no—
21C3×C5×C7×C29C2×D311yescharacteristic, complemented
22C3×C5×C7×C29C2×D311yescharacteristic, complemented
23C29×C3⋊D15D711yescharacteristic, complemented
24C3×C29×D15—71no—
25C3×C5×D3×C29—71no—
26D3×D7×C29—151no—
27D3×D7×C29—151no—
28C29×D35—31no—
29C7×D5×C29—91no—
30C5×D7×C29—31no—
31C32×C7×C29C2×D511yescharacteristic, complemented, Hall
32C2×C29×D15—211no—
33D3×D5×C29—211no—
34C32×C5×C29C2×D711yescharacteristic, complemented, Hall
35D21⋊D15C2911yesmaximal, characteristic, direct product factor, Hall
36C29×D21—51no—
37C29×D21D1511yescharacteristic, complemented
38D3×C7×C29—151no—
39D3×C7×C29—151no—
40D3×C7×C29—301no—
41C3×D7×C29—31no—
42C3×D7×C29—151no—
43D32×C29—351noHall
44C5×C7×C29D3211yescharacteristic, complemented, Hall
45C2×C3×C5×C29—211no—
46C29×D15—31no—
47C29×D15—31no—
48C29×D15—61no—
49C29×D15—71no—
50C5×D3×C29—71no—
51C3×D5×C29—211no—
52C2×D7×C29—451noHall
53C7×C3⋊D15C2×C2911yescharacteristic, complemented
54C3×D105C2×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—51no—
61C3×D3×C29—71no—
62C3×D3×C29—351no—
63C3×C5×C29—21no—
64C3×C5×C29D3×D711yescharacteristic, complemented
65C3×C5×C29D3×D711yescharacteristic, complemented
66D15⋊D7—31no—
67D7×D15—31no—
68C2×C7×C29—451no—
69D7×C29—31no—
70D7×C29—151no—
71C2×D3×C29—1051no—
72C2×D3×C29—1051no—
73C32×C5×C7C22×C2911yescharacteristic, complemented, Hall
74C2×C5×C29—211no—
75D5×C29—91no—
76D5×C29—211no—
77C32×C29D5×D711yescharacteristic, complemented, Hall
78(C3⋊D3)⋊D7—51noHall
79D105D3×C2911yescharacteristic, complemented
80C7×D15—31no—
81C7×D15—31no—
82C7×D15—61no—
83C5×D21D3×C2911yescharacteristic, complemented
84C3×D35—31no—
85C3×C5×D7—31no—
86C7×C29D3×D1511yescharacteristic, complemented, Hall
87D3×D15—71noHall
88C2×C3×C29—211no—
89C2×C3×C29—1051no—
90D3×C29—71no—
91D3×C29—151no—
92D3×C29—151no—
93D3×C29—301no—
94D3×C29—351no—
95C5×C29(C3⋊D3)⋊D711yescharacteristic, complemented, Hall
96D5×D7—91noHall
97C7×C3⋊D3—51no—
98C3×D21—51no—
99C3×D21D5×C2911yescharacteristic, complemented
100C22×C29—3151noHall
101C3×C5×C7—21no—
102C3×C5×C7C2×D3×C2911yescharacteristic, complemented
103C3×C5×C7C2×D3×C2911yescharacteristic, complemented
104C3⋊D15D7×C2911yescharacteristic, complemented
105C3×D15—71no—
106C3×C5×D3—71no—
107C3×C29—21no—
108C3×C29D7×D1511yescharacteristic, complemented
109C3×C29D15⋊D711yescharacteristic, complemented
110D3×D7—151no—
111D3×D7—151no—
112D35—31no—
113C5×D7—31no—
114C7×D5—91no—
115C32×C7C2×D5×C2911yescharacteristic, complemented, Hall
116C2×D15—211no—
117D3×D5—211no—
118C2×C29—211no—
119C2×C29—451no—
120C2×C29—1051no—
121C32×C5C2×D7×C2911yescharacteristic, complemented, Hall
122D21—51no—
123D21C29×D1511yescharacteristic, complemented
124C3×D7—31no—
125C3×D7—151no—
126D3×C7—151no—
127D3×C7—151no—
128D3×C7—301no—
129D32—351noHall
130C5×C7D32×C2911yescharacteristic, complemented, Hall
131C2×C3×C5—211no—
132D15—31no—
133D15—31no—
134D15—61no—
135D15—71no—
136C3×D5—211no—
137C5×D3—71no—
138C29D21⋊D1511yescharacteristic, 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—51no—
145C3×D3—71no—
146C3×D3—351no—
147C3×C5—21no—
148C3×C5D3×D7×C2911yescharacteristic, complemented
149C3×C5D3×D7×C2911yescharacteristic, complemented
150C2×C7—451no—
151D7—31no—
152D7—151no—
153C2×D3—1051no—
154C2×D3—1051no—
155C2×C5—211no—
156D5—91no—
157D5—211no—
158C32D5×D7×C2911yescharacteristic, complemented, Sylow
159C7D3×C29×D1511yescharacteristic, complemented, Sylow
160C2×C3—211no—
161C2×C3—1051no—
162D3—71no—
163D3—151no—
164D3—151no—
165D3—301no—
166D3—351no—
167C5C29×(C3⋊D3)⋊D711yescharacteristic, complemented, Sylow
168C22—3151noSylow
169C3—21no—
170C3D7×C29×D1511yescharacteristic, complemented
171C3C29×D15⋊D711yescharacteristic, complemented
172C2—211no—
173C2—451no—
174C2—1051no—
subgroupG/H
center, hypercenterC29D21⋊D15
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×C29×D105C2semidirect
3. C7×C29×C3⋊D15C2semidirect
6. C32×C5×C7×C29C22semidirect
8. C29×D105D3semidirect
12. C5×C29×D21D3semidirect
19. C3×C29×D21D5semidirect
21. C3×C5×C7×C29C2×D3semidirect
22. C3×C5×C7×C29C2×D3semidirect
23. C29×C3⋊D15D7semidirect
31. C32×C7×C29C2×D5semidirect
34. C32×C5×C29C2×D7semidirect
35. D21⋊D15C29direct (N × H)
37. C29×D21D15semidirect
44. C5×C7×C29D32semidirect
53. C7×C3⋊D15C2×C29semidirect
54. C3×D105C2×C29semidirect
55. C3×C5×D21C2×C29semidirect
57. C3×C7×C29D3×D5semidirect
58. C3×C7×C29C2×D15semidirect
64. C3×C5×C29D3×D7semidirect
65. C3×C5×C29D3×D7semidirect
73. C32×C5×C7C22×C29semidirect
77. C32×C29D5×D7semidirect
79. D105D3×C29semidirect
83. C5×D21D3×C29semidirect
86. C7×C29D3×D15semidirect
95. C5×C29(C3⋊D3)⋊D7semidirect
99. C3×D21D5×C29semidirect
102. C3×C5×C7C2×D3×C29semidirect
103. C3×C5×C7C2×D3×C29semidirect
104. C3⋊D15D7×C29semidirect
108. C3×C29D7×D15semidirect
109. C3×C29D15⋊D7semidirect
115. C32×C7C2×D5×C29semidirect
121. C32×C5C2×D7×C29semidirect
123. D21C29×D15semidirect
130. C5×C7D32×C29semidirect
138. C29D21⋊D15direct (N × H)
141. C3×C7D3×D5×C29semidirect
142. C3×C7C2×C29×D15semidirect
148. C3×C5D3×D7×C29semidirect
149. C3×C5D3×D7×C29semidirect
158. C32D5×D7×C29semidirect
159. C7D3×C29×D15semidirect
167. C5C29×(C3⋊D3)⋊D7semidirect
170. C3D7×C29×D15semidirect
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×C5×C29×D212
C3×C29×D1052
C7×C29×C3⋊D152
C29×D15⋊D73
D7×C29×D153
C29×(C3⋊D3)⋊D75
D3×C29×D157
D21⋊D1529