Finite Group Databasebeta

← D3×C29×D105 #49141608

Subgroups — D3×C29×D105 #49141608

Order 36540.

176 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 56 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×D3×C7×C29C211yesmaximal, characteristic, complemented
2C3×C29×D105C211yesmaximal, characteristic, complemented
3C29×C3⋊D105C211yesmaximal, characteristic, complemented
4C2×C29×D105—31nomaximal
5D3×C29×D35—31nomaximal
6C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
7D3×C29×D21—51nomaximal, Hall
8C29×D105—31no—
9C29×D105—31no—
10C29×D105—61no—
11C29×D105D311yescharacteristic, direct product factor
12C5×D3×C7×C29D311yescharacteristic, complemented
13C3×C29×D35—31no—
14C2×C3×C5×C7×C29—31no—
15D3×C29×D15—71nomaximal, Hall
16C2×C29×D35—91noHall
17C29×C3⋊D21—51no—
18C3×C29×D21—51no—
19C3×D3×C7×C29D511yescharacteristic, complemented
20C3×C5×C7×C29—21no—
21C3×C5×C7×C29C2×D311yescharacteristic, complemented
22C3×C5×C7×C29C2×D311yescharacteristic, complemented
23C29×C3⋊D15—71no—
24C3×C29×D15—71no—
25C3×C5×D3×C29D711yescharacteristic, complemented
26C2×C29×D21—151no—
27D3×D7×C29—151no—
28C29×D35—31no—
29C29×D35—91no—
30C2×C5×C7×C29—31no—
31C32×C7×C29C2×D511yescharacteristic, complemented, Hall
32C2×C29×D15—211no—
33D3×D5×C29—211no—
34C32×C5×C29C2×D711yescharacteristic, complemented, Hall
35D3×D105C2911yesmaximal, characteristic, direct product factor, Hall
36C2×C3×C7×C29—31no—
37C29×D21—51no—
38C29×D21—151no—
39C29×D21—151no—
40C29×D21—301no—
41D3×C7×C29D1511yescharacteristic, complemented
42C3×D7×C29—151no—
43D32×C29—351noHall
44C5×C7×C29D3211yescharacteristic, complemented, Hall
45C2×C3×C5×C29—31no—
46C29×D15—71no—
47C29×D15—211no—
48C29×D15—211no—
49C29×D15—421no—
50C5×D3×C29D2111yescharacteristic, complemented
51C3×D5×C29—211no—
52C2×D7×C29—451noHall
53C3⋊D105C2×C2911yescharacteristic, complemented
54C3×D105C2×C2911yescharacteristic, complemented
55C3×C5×D3×C7C2×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—351no—
62C3×D3×C29D3511yescharacteristic, complemented
63C3×C5×C29—21no—
64C3×C5×C29D3×D711yescharacteristic, complemented
65C3×C5×C29C2×D2111yescharacteristic, complemented
66C2×D105—31no—
67D3×D35—31no—
68C2×C7×C29—31no—
69D7×C29—151no—
70D7×C29—451no—
71C2×D3×C29—1051no—
72C2×D3×C29—1051no—
73C32×C5×C7C22×C2911yescharacteristic, complemented, Hall
74C2×C5×C29—31no—
75D5×C29—211no—
76D5×C29—631no—
77C32×C29C2×D3511yescharacteristic, complemented, Hall
78D3×D21—51noHall
79C2×C3×C5×C7—31no—
80D105—31no—
81D105—31no—
82D105—61no—
83D105D3×C2911yescharacteristic, direct product factor
84C5×D3×C7D3×C2911yescharacteristic, complemented
85C3×D35—31no—
86C7×C29D3×D1511yescharacteristic, complemented, Hall
87D3×D15—71noHall
88C2×C3×C29—31no—
89C2×C3×C29—1051no—
90D3×C29—351no—
91D3×C29—1051no—
92D3×C29—1051no—
93D3×C29—2101no—
94D3×C29D10511yescharacteristic, direct product factor
95C5×C29D3×D2111yescharacteristic, complemented, Hall
96C2×D35—91noHall
97C3⋊D21—51no—
98C3×D21—51no—
99C3×D3×C7D5×C2911yescharacteristic, complemented
100C22×C29—3151noHall
101C3×C5×C7—21no—
102C3×C5×C7C2×D3×C2911yescharacteristic, complemented
103C3×C5×C7C2×D3×C2911yescharacteristic, complemented
104C3⋊D15—71no—
105C3×D15—71no—
106C3×C5×D3D7×C2911yescharacteristic, complemented
107C3×C29—21no—
108C3×C29D3×D3511yescharacteristic, complemented
109C3×C29C2×D10511yescharacteristic, complemented
110C2×D21—151no—
111D3×D7—151no—
112C2×C5×C7—31no—
113D35—31no—
114D35—91no—
115C32×C7C2×D5×C2911yescharacteristic, complemented, Hall
116C2×D15—211no—
117D3×D5—211no—
118C2×C29—31no—
119C2×C29—3151no—
120C2×C29—1051no—
121C32×C5C2×D7×C2911yescharacteristic, complemented, Hall
122C2×C3×C7—31no—
123D21—51no—
124D21—151no—
125D21—151no—
126D21—301no—
127C3×D7—151no—
128D3×C7C29×D1511yescharacteristic, complemented
129D32—351noHall
130C5×C7D32×C2911yescharacteristic, complemented, Hall
131C2×C3×C5—31no—
132D15—71no—
133D15—211no—
134D15—211no—
135D15—421no—
136C3×D5—211no—
137C5×D3C29×D2111yescharacteristic, complemented
138C29D3×D10511yescharacteristic, 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—351no—
146C3×D3C29×D3511yescharacteristic, complemented
147C3×C5—21no—
148C3×C5D3×D7×C2911yescharacteristic, complemented
149C3×C5C2×C29×D2111yescharacteristic, complemented
150C2×C7—31no—
151D7—151no—
152D7—451no—
153C2×D3—1051no—
154C2×D3—1051no—
155C2×C5—31no—
156D5—211no—
157D5—631no—
158C32C2×C29×D3511yescharacteristic, complemented, Sylow
159C7D3×C29×D1511yescharacteristic, complemented, Sylow
160C2×C3—31no—
161C2×C3—1051no—
162D3—351no—
163D3—1051no—
164D3—1051no—
165D3—2101no—
166D3C29×D10511yescharacteristic, direct product factor
167C5D3×C29×D2111yescharacteristic, complemented, Sylow
168C22—3151noSylow
169C3—21no—
170C3D3×C29×D3511yescharacteristic, complemented
171C3C2×C29×D10511yescharacteristic, complemented
172C2—31no—
173C2—3151no—
174C2—1051no—
subgroupG/H
center, hypercenterC29D3×D105
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×D3×C7×C29C2semidirect
2. C3×C29×D105C2semidirect
3. C29×C3⋊D105C2semidirect
6. C32×C5×C7×C29C22semidirect
11. C29×D105D3direct (N × H)
12. C5×D3×C7×C29D3semidirect
19. C3×D3×C7×C29D5semidirect
21. C3×C5×C7×C29C2×D3semidirect
22. C3×C5×C7×C29C2×D3semidirect
25. C3×C5×D3×C29D7semidirect
31. C32×C7×C29C2×D5semidirect
34. C32×C5×C29C2×D7semidirect
35. D3×D105C29direct (N × H)
41. D3×C7×C29D15semidirect
44. C5×C7×C29D32semidirect
50. C5×D3×C29D21semidirect
53. C3⋊D105C2×C29semidirect
54. C3×D105C2×C29semidirect
55. C3×C5×D3×C7C2×C29semidirect
57. C3×C7×C29D3×D5semidirect
58. C3×C7×C29C2×D15semidirect
62. C3×D3×C29D35semidirect
64. C3×C5×C29D3×D7semidirect
65. C3×C5×C29C2×D21semidirect
73. C32×C5×C7C22×C29semidirect
77. C32×C29C2×D35semidirect
83. D105D3×C29direct (N × H)
84. C5×D3×C7D3×C29semidirect
86. C7×C29D3×D15semidirect
94. D3×C29D105direct (N × H)
95. C5×C29D3×D21semidirect
99. C3×D3×C7D5×C29semidirect
102. C3×C5×C7C2×D3×C29semidirect
103. C3×C5×C7C2×D3×C29semidirect
106. C3×C5×D3D7×C29semidirect
108. C3×C29D3×D35semidirect
109. C3×C29C2×D105semidirect
115. C32×C7C2×D5×C29semidirect
121. C32×C5C2×D7×C29semidirect
128. D3×C7C29×D15semidirect
130. C5×C7D32×C29semidirect
137. C5×D3C29×D21semidirect
138. C29D3×D105direct (N × H)
141. C3×C7D3×D5×C29semidirect
142. C3×C7C2×C29×D15semidirect
146. C3×D3C29×D35semidirect
148. C3×C5D3×D7×C29semidirect
149. C3×C5C2×C29×D21semidirect
158. C32C2×C29×D35semidirect
159. C7D3×C29×D15semidirect
166. D3C29×D105direct (N × H)
167. C5D3×C29×D21semidirect
170. C3D3×C29×D35semidirect
171. C3C2×C29×D105semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D3×C7×C292
C3×C29×D1052
C29×C3⋊D1052
C2×C29×D1053
D3×C29×D353
D3×C29×D215
D3×C29×D157
D3×D10529