Finite Group Databasebeta

← C3×D7×C19×D15 #37561532

Subgroups — C3×D7×C19×D15 #37561532

Order 23940.

176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 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×C7×C19×D15C211yesmaximal, characteristic, complemented
3C3×C19×D105C211yesmaximal, characteristic, complemented
4D7×C19×D15C311yesmaximal, characteristic, direct product factor
5C3×D5×D7×C19—31nomaximal
6C32×C5×C7×C19C2211yescharacteristic, complemented, Hall
7C3×D3×D7×C19—51nomaximal, Hall
8C19×D105C2×C311yescharacteristic, complemented
9C7×C19×D15C2×C311yescharacteristic, complemented
10C3×C19×D35—31no—
11C3×C7×D5×C19—31no—
12C3×C5×D7×C19—21no—
13C3×C5×D7×C19D311yescharacteristic, complemented
14C3×C5×D7×C19C2×C311yescharacteristic, complemented
15C2×C3×C19×D15—71nomaximal, Hall
16D5×D7×C19—31noHall
17C3×C19×D21—51no—
18C3×D3×C7×C19—51no—
19C32×D7×C19D511yescharacteristic, complemented
20C3×C5×C7×C19—21no—
21C3×C5×C7×C19C2×D311yescharacteristic, complemented
22C3×C5×C7×C19C22×C311yescharacteristic, complemented
23C2×C32×C5×C19—71no—
24C3×C19×D15—71no—
25C3×C19×D15D711yescharacteristic, direct product factor
26C2×C3×D7×C19—151no—
27D3×D7×C19—51no—
28C19×D35—31no—
29C7×D5×C19—31no—
30C5×D7×C19C3×D311yescharacteristic, complemented
31C3×D7×D15C1911yesmaximal, characteristic, direct product factor, Hall
32C32×C7×C19C2×D511yescharacteristic, complemented, Hall
33C2×C19×D15—71no—
34C2×C3×D5×C19—211no—
35C32×C5×C19C2×D711yescharacteristic, complemented, Hall
36C2×C3×C7×C19—151no—
37C19×D21—51no—
38D3×C7×C19—51no—
39C3×D7×C19—21no—
40C3×D7×C19—151no—
41C3×D7×C19C3×D511yescharacteristic, complemented
42C3×D7×C19D1511yescharacteristic, direct product factor
43C2×C3×D3×C19—351noHall
44C5×C7×C19C2×C3×D311yescharacteristic, complemented, Hall
45C3×D105C2×C1911yescharacteristic, complemented
46C3×C7×D15C2×C1911yescharacteristic, complemented
47C32×C5×D7C2×C1911yescharacteristic, complemented
48C2×C3×C5×C19—71no—
49C2×C3×C5×C19—71no—
50C2×C3×C5×C19—141no—
51C19×D15—71no—
52C19×D15C3×D711yescharacteristic, direct product factor
53C3×D5×C19—31no—
54C3×D5×C19—211no—
55C2×D7×C19—151noHall
56D7×D15C3×C1911yescharacteristic, direct product factor
57C3×D5×D7—31no—
58C3×C7×C19—21no—
59C3×C7×C19C2×C3×D511yescharacteristic, complemented
60C3×C7×C19C2×D1511yescharacteristic, complemented
61C2×D5×C19—211noHall
62C2×C32×C19—71no—
63C3×D3×C19—51no—
64C3×D3×C19—351no—
65C32×C5×C7C22×C1911yescharacteristic, complemented, Hall
66C3×C5×C19—21no—
67C3×C5×C19D3×D711yescharacteristic, complemented
68C3×C5×C19C2×C3×D711yescharacteristic, complemented
69C2×C7×C19—151no—
70D7×C19—151no—
71D7×C19C3×D1511yescharacteristic, direct product factor
72C3×D3×D7—51noHall
73C22×C3×C19—1051no—
74C2×D3×C19—351no—
75D105C2×C3×C1911yescharacteristic, complemented
76C7×D15C2×C3×C1911yescharacteristic, complemented
77C3×D35—31no—
78C3×C7×D5—31no—
79C3×C5×D7—21no—
80C3×C5×D7D3×C1911yescharacteristic, complemented
81C3×C5×D7C2×C3×C1911yescharacteristic, complemented
82C2×C5×C19—71no—
83D5×C19—31no—
84D5×C19—211no—
85C2×C3×D15—71noHall
86C32×C19D5×D711yescharacteristic, complemented, Hall
87D5×D7—31noHall
88C7×C19C2×C3×D1511yescharacteristic, complemented, Hall
89C3×D21—51no—
90C3×D3×C7—51no—
91C32×D7D5×C1911yescharacteristic, complemented
92C2×C3×C19—71no—
93C2×C3×C19—71no—
94C2×C3×C19—141no—
95C2×C3×C19—151no—
96C2×C3×C19—1051no—
97D3×C19—51no—
98D3×C19—351no—
99C3×C5×C7—21no—
100C3×C5×C7C2×D3×C1911yescharacteristic, complemented
101C3×C5×C7C22×C3×C1911yescharacteristic, complemented
102C5×C19C3×D3×D711yescharacteristic, complemented, Hall
103C2×C32×C5—71no—
104C3×D15—71no—
105C3×D15D7×C1911yescharacteristic, direct product factor
106C2×C3×D7—151no—
107D3×D7—51no—
108C22×C19—1051noHall
109D35—31no—
110C5×D7C3×D3×C1911yescharacteristic, complemented
111C7×D5—31no—
112C32×C7C2×D5×C1911yescharacteristic, complemented, Hall
113C2×D15—71no—
114C2×C3×D5—211no—
115C3×C19—21no—
116C3×C19C3×D5×D711yescharacteristic, complemented
117C3×C19D7×D1511yescharacteristic, direct product factor
118C32×C5C2×D7×C1911yescharacteristic, complemented, Hall
119C2×C3×C7—151no—
120D21—51no—
121C3×D7—21no—
122C3×D7—151no—
123C3×D7C3×D5×C1911yescharacteristic, complemented
124C3×D7C19×D1511yescharacteristic, direct product factor
125D3×C7—51no—
126C2×C19—71no—
127C2×C19—151no—
128C2×C19—1051no—
129C2×C3×D3—351noHall
130C5×C7C2×C3×D3×C1911yescharacteristic, complemented, Hall
131C2×C3×C5—71no—
132C2×C3×C5—71no—
133C2×C3×C5—141no—
134D15—71no—
135D15C3×D7×C1911yescharacteristic, direct product factor
136C3×D5—31no—
137C3×D5—211no—
138C2×D7—151noHall
139C3×C7—21no—
140C3×C7C2×C3×D5×C1911yescharacteristic, complemented
141C3×C7C2×C19×D1511yescharacteristic, complemented
142C2×D5—211noHall
143C19C3×D7×D1511yescharacteristic, direct product factor, Sylow
144C2×C32—71no—
145C3×D3—51no—
146C3×D3—351no—
147C3×C5—21no—
148C3×C5D3×D7×C1911yescharacteristic, complemented
149C3×C5C2×C3×D7×C1911yescharacteristic, complemented
150C2×C7—151no—
151D7—151no—
152D7C3×C19×D1511yescharacteristic, direct product factor
153C22×C3—1051no—
154C2×D3—351no—
155C2×C5—71no—
156D5—31no—
157D5—211no—
158C32D5×D7×C1911yescharacteristic, complemented, Sylow
159C7C2×C3×C19×D1511yescharacteristic, complemented, Sylow
160C2×C3—71no—
161C2×C3—71no—
162C2×C3—141no—
163C2×C3—151no—
164C2×C3—1051no—
165D3—51no—
166D3—351no—
167C5C3×D3×D7×C1911yescharacteristic, complemented, Sylow
168C22—1051noSylow
169C3—21no—
170C3C3×D5×D7×C1911yescharacteristic, complemented
171C3D7×C19×D1511yescharacteristic, direct product factor
172C2—71no—
173C2—151no—
174C2—1051no—
subgroupG/H
center, hypercenterC3×C19D7×D15
commutator, cosocle, hypocenterC3×C5×C7C22×C3×C19
FrattiniC1G
Fitting, socleC32×C5×C7×C19C22
LCSG ▷ C3×C5×C7
UCSC1 ◁ C3×C19

Complements

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

NH ≅ G/Ntype
1. C32×C5×D7×C19C2semidirect
2. C3×C7×C19×D15C2semidirect
3. C3×C19×D105C2semidirect
4. D7×C19×D15C3direct (N × H)
6. C32×C5×C7×C19C22semidirect
8. C19×D105C2×C3semidirect
9. C7×C19×D15C2×C3semidirect
13. C3×C5×D7×C19D3semidirect
14. C3×C5×D7×C19C2×C3semidirect
19. C32×D7×C19D5semidirect
21. C3×C5×C7×C19C2×D3semidirect
22. C3×C5×C7×C19C22×C3semidirect
25. C3×C19×D15D7direct (N × H)
30. C5×D7×C19C3×D3semidirect
31. C3×D7×D15C19direct (N × H)
32. C32×C7×C19C2×D5semidirect
35. C32×C5×C19C2×D7semidirect
41. C3×D7×C19C3×D5semidirect
42. C3×D7×C19D15direct (N × H)
44. C5×C7×C19C2×C3×D3semidirect
45. C3×D105C2×C19semidirect
46. C3×C7×D15C2×C19semidirect
47. C32×C5×D7C2×C19semidirect
52. C19×D15C3×D7direct (N × H)
56. D7×D15C3×C19direct (N × H)
59. C3×C7×C19C2×C3×D5semidirect
60. C3×C7×C19C2×D15semidirect
65. C32×C5×C7C22×C19semidirect
67. C3×C5×C19D3×D7semidirect
68. C3×C5×C19C2×C3×D7semidirect
71. D7×C19C3×D15direct (N × H)
75. D105C2×C3×C19semidirect
76. C7×D15C2×C3×C19semidirect
80. C3×C5×D7D3×C19semidirect
81. C3×C5×D7C2×C3×C19semidirect
86. C32×C19D5×D7semidirect
88. C7×C19C2×C3×D15semidirect
91. C32×D7D5×C19semidirect
100. C3×C5×C7C2×D3×C19semidirect
101. C3×C5×C7C22×C3×C19semidirect
102. C5×C19C3×D3×D7semidirect
105. C3×D15D7×C19direct (N × H)
110. C5×D7C3×D3×C19semidirect
112. C32×C7C2×D5×C19semidirect
116. C3×C19C3×D5×D7semidirect
117. C3×C19D7×D15direct (N × H)
118. C32×C5C2×D7×C19semidirect
123. C3×D7C3×D5×C19semidirect
124. C3×D7C19×D15direct (N × H)
130. C5×C7C2×C3×D3×C19semidirect
135. D15C3×D7×C19direct (N × H)
140. C3×C7C2×C3×D5×C19semidirect
141. C3×C7C2×C19×D15semidirect
143. C19C3×D7×D15direct (N × H)
148. C3×C5D3×D7×C19semidirect
149. C3×C5C2×C3×D7×C19semidirect
152. D7C3×C19×D15direct (N × H)
158. C32D5×D7×C19semidirect
159. C7C2×C3×C19×D15semidirect
167. C5C3×D3×D7×C19semidirect
170. C3C3×D5×D7×C19semidirect
171. C3D7×C19×D15direct (N × H)

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×C7×C19×D152
C3×C19×D1052
D7×C19×D153
C3×D5×D7×C193
C3×D3×D7×C195
C2×C3×C19×D157
C3×D7×D1519