Finite Group Databasebeta

← C3×C5×D3×D7×C19 #37561522

Subgroups — C3×C5×D3×D7×C19 #37561522

Order 23940.

176 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 80 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×C5×D7×C19C211yesmaximal, characteristic, complemented
2C3×C5×D3×C7×C19C211yesmaximal, characteristic, complemented
3C3×C5×C19×D21C211yesmaximal, characteristic, complemented
4C2×C3×C5×D7×C19—31nomaximal
5C5×D3×D7×C19C311yesmaximal, characteristic, direct product factor
6C32×C5×C7×C19C2211yescharacteristic, complemented, Hall
7C3×D3×D7×C19C511yesmaximal, characteristic, direct product factor, Hall
8C5×C19×D21C2×C311yescharacteristic, complemented
9C5×D3×C7×C19C2×C311yescharacteristic, complemented
10C3×C5×D7×C19—21no—
11C3×C5×D7×C19—31no—
12C3×C5×D7×C19D311yescharacteristic, direct product factor
13C3×C5×D7×C19C2×C311yescharacteristic, complemented
14C2×C3×C5×C7×C19—31no—
15C2×C3×C5×D3×C19—71nomaximal, Hall
16C2×C5×D7×C19—31noHall
17C3×C19×D21C2×C511yescharacteristic, complemented
18C3×D3×C7×C19C2×C511yescharacteristic, complemented
19C32×D7×C19C2×C511yescharacteristic, complemented
20C3×C5×C7×C19—21no—
21C3×C5×C7×C19C2×D311yescharacteristic, complemented
22C3×C5×C7×C19C22×C311yescharacteristic, complemented
23C2×C32×C5×C19—71no—
24C3×C5×D3×C19—71no—
25C3×C5×D3×C19D711yescharacteristic, direct product factor
26C2×C3×D7×C19—31no—
27D3×D7×C19C3×C511yescharacteristic, direct product factor
28C2×C5×C7×C19—31no—
29C5×D7×C19—31no—
30C5×D7×C19C3×D311yescharacteristic, direct product factor
31C3×C5×D3×D7C1911yesmaximal, characteristic, direct product factor, Hall
32C32×C7×C19C22×C511yescharacteristic, complemented, Hall
33C22×C3×C5×C19—211no—
34C2×C5×D3×C19—71no—
35C32×C5×C19C2×D711yescharacteristic, complemented, Hall
36C2×C3×C7×C19—31no—
37C19×D21C2×C3×C511yescharacteristic, complemented
38D3×C7×C19C2×C3×C511yescharacteristic, complemented
39C3×D7×C19—21no—
40C3×D7×C19—31no—
41C3×D7×C19C5×D311yescharacteristic, direct product factor
42C3×D7×C19C2×C3×C511yescharacteristic, complemented
43C2×C3×D3×C19—71noHall
44C5×C7×C19C2×C3×D311yescharacteristic, complemented, Hall
45C3×C5×D21C2×C1911yescharacteristic, complemented
46C3×C5×D3×C7C2×C1911yescharacteristic, complemented
47C32×C5×D7C2×C1911yescharacteristic, complemented
48C2×C3×C5×C19—31no—
49C2×C3×C5×C19—71no—
50C2×C3×C5×C19—71no—
51C2×C3×C5×C19—141no—
52C2×C3×C5×C19—211no—
53C5×D3×C19—71no—
54C5×D3×C19C3×D711yescharacteristic, direct product factor
55C2×D7×C19—31noHall
56C2×C3×C5×D7—31no—
57C5×D3×D7C3×C1911yescharacteristic, direct product factor
58C3×C7×C19—21no—
59C3×C7×C19C2×C5×D311yescharacteristic, complemented
60C3×C7×C19C22×C3×C511yescharacteristic, complemented
61C22×C5×C19—211noHall
62C2×C32×C19—71no—
63C3×D3×C19—71no—
64C3×D3×C19C5×D711yescharacteristic, direct product factor
65C32×C5×C7C22×C1911yescharacteristic, complemented, Hall
66C3×C5×C19—21no—
67C3×C5×C19D3×D711yescharacteristic, direct product factor
68C3×C5×C19C2×C3×D711yescharacteristic, complemented
69C2×C7×C19—31no—
70D7×C19—31no—
71D7×C19C3×C5×D311yescharacteristic, direct product factor
72C3×D3×D7C5×C1911yescharacteristic, direct product factor, Hall
73C22×C3×C19—211no—
74C2×D3×C19—71no—
75C2×C3×C5×C7—31no—
76C5×D21C2×C3×C1911yescharacteristic, complemented
77C5×D3×C7C2×C3×C1911yescharacteristic, complemented
78C3×C5×D7—21no—
79C3×C5×D7—31no—
80C3×C5×D7D3×C1911yescharacteristic, direct product factor
81C3×C5×D7C2×C3×C1911yescharacteristic, complemented
82C2×C5×C19—31no—
83C2×C5×C19—71no—
84C2×C5×C19—211no—
85C2×C3×C5×D3—71noHall
86C32×C19C2×C5×D711yescharacteristic, complemented, Hall
87C2×C5×D7—31noHall
88C7×C19C2×C3×C5×D311yescharacteristic, complemented, Hall
89C3×D21C2×C5×C1911yescharacteristic, complemented
90C3×D3×C7C2×C5×C1911yescharacteristic, complemented
91C32×D7C2×C5×C1911yescharacteristic, complemented
92C2×C3×C19—31no—
93C2×C3×C19—71no—
94C2×C3×C19—71no—
95C2×C3×C19—141no—
96C2×C3×C19—211no—
97D3×C19—71no—
98D3×C19C3×C5×D711yescharacteristic, direct product factor
99C3×C5×C7—21no—
100C3×C5×C7C2×D3×C1911yescharacteristic, complemented
101C3×C5×C7C22×C3×C1911yescharacteristic, complemented
102C5×C19C3×D3×D711yescharacteristic, direct product factor, Hall
103C2×C32×C5—71no—
104C3×C5×D3—71no—
105C3×C5×D3D7×C1911yescharacteristic, direct product factor
106C2×C3×D7—31no—
107D3×D7C3×C5×C1911yescharacteristic, direct product factor
108C22×C19—211noHall
109C2×C5×C7—31no—
110C5×D7—31no—
111C5×D7C3×D3×C1911yescharacteristic, direct product factor
112C32×C7C22×C5×C1911yescharacteristic, complemented, Hall
113C22×C3×C5—211no—
114C2×C5×D3—71no—
115C3×C19—21no—
116C3×C19C5×D3×D711yescharacteristic, direct product factor
117C3×C19C2×C3×C5×D711yescharacteristic, complemented
118C32×C5C2×D7×C1911yescharacteristic, complemented, Hall
119C2×C3×C7—31no—
120D21C2×C3×C5×C1911yescharacteristic, complemented
121C3×D7—21no—
122C3×D7—31no—
123C3×D7C5×D3×C1911yescharacteristic, direct product factor
124C3×D7C2×C3×C5×C1911yescharacteristic, complemented
125D3×C7C2×C3×C5×C1911yescharacteristic, complemented
126C2×C19—31no—
127C2×C19—71no—
128C2×C19—211no—
129C2×C3×D3—71noHall
130C5×C7C2×C3×D3×C1911yescharacteristic, complemented, Hall
131C2×C3×C5—31no—
132C2×C3×C5—71no—
133C2×C3×C5—71no—
134C2×C3×C5—141no—
135C2×C3×C5—211no—
136C5×D3—71no—
137C5×D3C3×D7×C1911yescharacteristic, direct product factor
138C2×D7—31noHall
139C3×C7—21no—
140C3×C7C2×C5×D3×C1911yescharacteristic, complemented
141C3×C7C22×C3×C5×C1911yescharacteristic, complemented
142C22×C5—211noHall
143C19C3×C5×D3×D711yescharacteristic, direct product factor, Sylow
144C2×C32—71no—
145C3×D3—71no—
146C3×D3C5×D7×C1911yescharacteristic, direct product factor
147C3×C5—21no—
148C3×C5D3×D7×C1911yescharacteristic, direct product factor
149C3×C5C2×C3×D7×C1911yescharacteristic, complemented
150C2×C7—31no—
151D7—31no—
152D7C3×C5×D3×C1911yescharacteristic, direct product factor
153C22×C3—211no—
154C2×D3—71no—
155C2×C5—31no—
156C2×C5—71no—
157C2×C5—211no—
158C32C2×C5×D7×C1911yescharacteristic, complemented, Sylow
159C7C2×C3×C5×D3×C1911yescharacteristic, complemented, Sylow
160C2×C3—31no—
161C2×C3—71no—
162C2×C3—71no—
163C2×C3—141no—
164C2×C3—211no—
165D3—71no—
166D3C3×C5×D7×C1911yescharacteristic, direct product factor
167C5C3×D3×D7×C1911yescharacteristic, direct product factor, Sylow
168C22—211noSylow
169C3—21no—
170C3C5×D3×D7×C1911yescharacteristic, direct product factor
171C3C2×C3×C5×D7×C1911yescharacteristic, complemented
172C2—31no—
173C2—71no—
174C2—211no—
subgroupG/H
center, hypercenterC3×C5×C19D3×D7
commutator, cosocle, hypocenterC3×C7C22×C3×C5×C19
FrattiniC1G
Fitting, socleC32×C5×C7×C19C22
LCSG ▷ C3×C7
UCSC1 ◁ C3×C5×C19

Complements

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

NH ≅ G/Ntype
1. C32×C5×D7×C19C2semidirect
2. C3×C5×D3×C7×C19C2semidirect
3. C3×C5×C19×D21C2semidirect
5. C5×D3×D7×C19C3direct (N × H)
6. C32×C5×C7×C19C22semidirect
7. C3×D3×D7×C19C5direct (N × H)
8. C5×C19×D21C2×C3semidirect
9. C5×D3×C7×C19C2×C3semidirect
12. C3×C5×D7×C19D3direct (N × H)
13. C3×C5×D7×C19C2×C3semidirect
17. C3×C19×D21C2×C5semidirect
18. C3×D3×C7×C19C2×C5semidirect
19. C32×D7×C19C2×C5semidirect
21. C3×C5×C7×C19C2×D3semidirect
22. C3×C5×C7×C19C22×C3semidirect
25. C3×C5×D3×C19D7direct (N × H)
27. D3×D7×C19C3×C5direct (N × H)
30. C5×D7×C19C3×D3direct (N × H)
31. C3×C5×D3×D7C19direct (N × H)
32. C32×C7×C19C22×C5semidirect
35. C32×C5×C19C2×D7semidirect
37. C19×D21C2×C3×C5semidirect
38. D3×C7×C19C2×C3×C5semidirect
41. C3×D7×C19C5×D3direct (N × H)
42. C3×D7×C19C2×C3×C5semidirect
44. C5×C7×C19C2×C3×D3semidirect
45. C3×C5×D21C2×C19semidirect
46. C3×C5×D3×C7C2×C19semidirect
47. C32×C5×D7C2×C19semidirect
54. C5×D3×C19C3×D7direct (N × H)
57. C5×D3×D7C3×C19direct (N × H)
59. C3×C7×C19C2×C5×D3semidirect
60. C3×C7×C19C22×C3×C5semidirect
64. C3×D3×C19C5×D7direct (N × H)
65. C32×C5×C7C22×C19semidirect
67. C3×C5×C19D3×D7direct (N × H)
68. C3×C5×C19C2×C3×D7semidirect
71. D7×C19C3×C5×D3direct (N × H)
72. C3×D3×D7C5×C19direct (N × H)
76. C5×D21C2×C3×C19semidirect
77. C5×D3×C7C2×C3×C19semidirect
80. C3×C5×D7D3×C19direct (N × H)
81. C3×C5×D7C2×C3×C19semidirect
86. C32×C19C2×C5×D7semidirect
88. C7×C19C2×C3×C5×D3semidirect
89. C3×D21C2×C5×C19semidirect
90. C3×D3×C7C2×C5×C19semidirect
91. C32×D7C2×C5×C19semidirect
98. D3×C19C3×C5×D7direct (N × H)
100. C3×C5×C7C2×D3×C19semidirect
101. C3×C5×C7C22×C3×C19semidirect
102. C5×C19C3×D3×D7direct (N × H)
105. C3×C5×D3D7×C19direct (N × H)
107. D3×D7C3×C5×C19direct (N × H)
111. C5×D7C3×D3×C19direct (N × H)
112. C32×C7C22×C5×C19semidirect
116. C3×C19C5×D3×D7direct (N × H)
117. C3×C19C2×C3×C5×D7semidirect
118. C32×C5C2×D7×C19semidirect
120. D21C2×C3×C5×C19semidirect
123. C3×D7C5×D3×C19direct (N × H)
124. C3×D7C2×C3×C5×C19semidirect
125. D3×C7C2×C3×C5×C19semidirect
130. C5×C7C2×C3×D3×C19semidirect
137. C5×D3C3×D7×C19direct (N × H)
140. C3×C7C2×C5×D3×C19semidirect
141. C3×C7C22×C3×C5×C19semidirect
143. C19C3×C5×D3×D7direct (N × H)
146. C3×D3C5×D7×C19direct (N × H)
148. C3×C5D3×D7×C19direct (N × H)
149. C3×C5C2×C3×D7×C19semidirect
152. D7C3×C5×D3×C19direct (N × H)
158. C32C2×C5×D7×C19semidirect
159. C7C2×C3×C5×D3×C19semidirect
166. D3C3×C5×D7×C19direct (N × H)
167. C5C3×D3×D7×C19direct (N × H)
170. C3C5×D3×D7×C19direct (N × H)
171. C3C2×C3×C5×D7×C19semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D7×C192
C3×C5×D3×C7×C192
C3×C5×C19×D212
C2×C3×C5×D7×C193
C5×D3×D7×C193
C3×D3×D7×C195
C2×C3×C5×D3×C197
C3×C5×D3×D719