Finite Group Databasebeta

← C3×C5×D7×D57 #37561523

Subgroups — C3×C5×D7×D57 #37561523

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×C5×C7×D57C211yesmaximal, characteristic, complemented
3C3×C5×D399C211yesmaximal, characteristic, complemented
4C5×D7×D57C311yesmaximal, characteristic, direct product factor
5C3×C5×D7×D19—31nomaximal
6C32×C5×C7×C19C2211yescharacteristic, complemented, Hall
7C3×D7×D57C511yesmaximal, characteristic, direct product factor, Hall
8C5×D399C2×C311yescharacteristic, complemented
9C5×C7×D57C2×C311yescharacteristic, complemented
10C3×C5×D133—31no—
11C3×C5×D7×C19—21no—
12C3×C5×D7×C19D311yescharacteristic, complemented
13C3×C5×D7×C19C2×C311yescharacteristic, complemented
14C3×C5×C7×D19—31no—
15C2×C3×C5×D57—71nomaximal, Hall
16C5×D7×D19—31noHall
17C3×D399C2×C511yescharacteristic, complemented
18C3×C7×D57C2×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×D57—71no—
25C3×C5×D57D711yescharacteristic, direct product factor
26D7×D57C3×C511yescharacteristic, direct product factor
27C3×D7×D19—31no—
28C5×D133—31no—
29C5×D7×C19C3×D311yescharacteristic, complemented
30C5×C7×D19—31no—
31C3×C5×D3×D7—191nomaximal, Hall
32C32×C7×C19C22×C511yescharacteristic, complemented, Hall
33C2×C5×D57—71no—
34C2×C3×C5×D19—211no—
35C32×C5×C19C2×D711yescharacteristic, complemented, Hall
36D399C2×C3×C511yescharacteristic, complemented
37C7×D57C2×C3×C511yescharacteristic, complemented
38C3×D133—31no—
39C3×D7×C19—21no—
40C3×D7×C19C5×D311yescharacteristic, complemented
41C3×D7×C19C2×C3×C511yescharacteristic, complemented
42C3×C7×D19—31no—
43C2×C3×D57—71noHall
44C5×C7×C19C2×C3×D311yescharacteristic, complemented, Hall
45C3×C5×D21—191no—
46C3×C5×D3×C7—191no—
47C32×C5×D7D1911yescharacteristic, complemented
48C2×C3×C5×C19—71no—
49C2×C3×C5×C19—71no—
50C2×C3×C5×C19—141no—
51C5×D57—71no—
52C5×D57C3×D711yescharacteristic, direct product factor
53C3×C5×D19—31no—
54C3×C5×D19—211no—
55D7×D19—31noHall
56C2×C3×C5×D7—571no—
57C5×D3×D7—191no—
58C3×C7×C19—21no—
59C3×C7×C19C2×C5×D311yescharacteristic, complemented
60C3×C7×C19C22×C3×C511yescharacteristic, complemented
61C2×C5×D19—211noHall
62C2×C32×C19—71no—
63C3×D57—71no—
64C3×D57C5×D711yescharacteristic, direct product factor
65C32×C5×C7C2×D1911yescharacteristic, complemented, Hall
66C3×C5×C19—21no—
67C3×C5×C19D3×D711yescharacteristic, complemented
68C3×C5×C19C2×C3×D711yescharacteristic, complemented
69D133—31no—
70C7×D19—31no—
71D7×C19C3×C5×D311yescharacteristic, complemented
72C3×D3×D7—191noHall
73C2×D57—71no—
74C2×C3×D19—211no—
75C2×C3×C5×C7—571no—
76C5×D21—191no—
77C5×D3×C7—191no—
78C3×C5×D7—21no—
79C3×C5×D7—571no—
80C3×C5×D7C3×D1911yescharacteristic, complemented
81C3×C5×D7D5711yescharacteristic, direct product factor
82C2×C5×C19—71no—
83C5×D19—31no—
84C5×D19—211no—
85C2×C3×C5×D3—1331noHall
86C32×C19C2×C5×D711yescharacteristic, complemented, Hall
87C2×C5×D7—571noHall
88C7×C19C2×C3×C5×D311yescharacteristic, complemented, Hall
89C3×D21—191no—
90C3×D3×C7—191no—
91C32×D7C5×D1911yescharacteristic, complemented
92C2×C3×C19—71no—
93C2×C3×C19—71no—
94C2×C3×C19—141no—
95D57—71no—
96D57C3×C5×D711yescharacteristic, direct product factor
97C3×D19—31no—
98C3×D19—211no—
99C3×C5×C7—21no—
100C3×C5×C7C2×C3×D1911yescharacteristic, complemented
101C3×C5×C7C2×D5711yescharacteristic, complemented
102C5×C19C3×D3×D711yescharacteristic, complemented, Hall
103C2×C32×C5—71no—
104C3×C5×D3—191no—
105C3×C5×D3—1331no—
106C2×C3×D7—571no—
107D3×D7—191no—
108C2×D19—211noHall
109C2×C5×C7—571no—
110C5×D7—571no—
111C5×D7C3×D5711yescharacteristic, direct product factor
112C32×C7C2×C5×D1911yescharacteristic, complemented, Hall
113C22×C3×C5—3991no—
114C2×C5×D3—1331no—
115C3×C19—21no—
116C3×C19C5×D3×D711yescharacteristic, complemented
117C3×C19C2×C3×C5×D711yescharacteristic, complemented
118C32×C5D7×D1911yescharacteristic, complemented, Hall
119C2×C3×C7—571no—
120D21—191no—
121C3×D7—21no—
122C3×D7—571no—
123C3×D7C3×C5×D1911yescharacteristic, complemented
124C3×D7C5×D5711yescharacteristic, direct product factor
125D3×C7—191no—
126C2×C19—71no—
127D19—31no—
128D19—211no—
129C2×C3×D3—1331noHall
130C5×C7C2×C3×D5711yescharacteristic, complemented, Hall
131C2×C3×C5—71no—
132C2×C3×C5—71no—
133C2×C3×C5—141no—
134C2×C3×C5—571no—
135C2×C3×C5—3991no—
136C5×D3—191no—
137C5×D3—1331no—
138C2×D7—571noHall
139C3×C7—21no—
140C3×C7C2×C3×C5×D1911yescharacteristic, complemented
141C3×C7C2×C5×D5711yescharacteristic, complemented
142C22×C5—3991noHall
143C19C3×C5×D3×D711yescharacteristic, complemented, Sylow
144C2×C32—71no—
145C3×D3—191no—
146C3×D3—1331no—
147C3×C5—21no—
148C3×C5C3×D7×D1911yescharacteristic, complemented
149C3×C5D7×D5711yescharacteristic, direct product factor
150C2×C7—571no—
151D7—571no—
152D7C3×C5×D5711yescharacteristic, direct product factor
153C22×C3—3991no—
154C2×D3—1331no—
155C2×C5—71no—
156C2×C5—571no—
157C2×C5—3991no—
158C32C5×D7×D1911yescharacteristic, complemented, Sylow
159C7C2×C3×C5×D5711yescharacteristic, complemented, Sylow
160C2×C3—71no—
161C2×C3—71no—
162C2×C3—141no—
163C2×C3—571no—
164C2×C3—3991no—
165D3—191no—
166D3—1331no—
167C5C3×D7×D5711yescharacteristic, direct product factor, Sylow
168C22—3991noSylow
169C3—21no—
170C3C3×C5×D7×D1911yescharacteristic, complemented
171C3C5×D7×D5711yescharacteristic, direct product factor
172C2—71no—
173C2—571no—
174C2—3991no—
subgroupG/H
center, hypercenterC3×C5D7×D57
commutator, cosocle, hypocenterC3×C7×C19C22×C3×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C19C22
LCSG ▷ C3×C7×C19
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C32×C5×D7×C19C2semidirect
2. C3×C5×C7×D57C2semidirect
3. C3×C5×D399C2semidirect
4. C5×D7×D57C3direct (N × H)
6. C32×C5×C7×C19C22semidirect
7. C3×D7×D57C5direct (N × H)
8. C5×D399C2×C3semidirect
9. C5×C7×D57C2×C3semidirect
12. C3×C5×D7×C19D3semidirect
13. C3×C5×D7×C19C2×C3semidirect
17. C3×D399C2×C5semidirect
18. C3×C7×D57C2×C5semidirect
19. C32×D7×C19C2×C5semidirect
21. C3×C5×C7×C19C2×D3semidirect
22. C3×C5×C7×C19C22×C3semidirect
25. C3×C5×D57D7direct (N × H)
26. D7×D57C3×C5direct (N × H)
29. C5×D7×C19C3×D3semidirect
32. C32×C7×C19C22×C5semidirect
35. C32×C5×C19C2×D7semidirect
36. D399C2×C3×C5semidirect
37. C7×D57C2×C3×C5semidirect
40. C3×D7×C19C5×D3semidirect
41. C3×D7×C19C2×C3×C5semidirect
44. C5×C7×C19C2×C3×D3semidirect
47. C32×C5×D7D19semidirect
52. C5×D57C3×D7direct (N × H)
59. C3×C7×C19C2×C5×D3semidirect
60. C3×C7×C19C22×C3×C5semidirect
64. C3×D57C5×D7direct (N × H)
65. C32×C5×C7C2×D19semidirect
67. C3×C5×C19D3×D7semidirect
68. C3×C5×C19C2×C3×D7semidirect
71. D7×C19C3×C5×D3semidirect
80. C3×C5×D7C3×D19semidirect
81. C3×C5×D7D57direct (N × H)
86. C32×C19C2×C5×D7semidirect
88. C7×C19C2×C3×C5×D3semidirect
91. C32×D7C5×D19semidirect
96. D57C3×C5×D7direct (N × H)
100. C3×C5×C7C2×C3×D19semidirect
101. C3×C5×C7C2×D57semidirect
102. C5×C19C3×D3×D7semidirect
111. C5×D7C3×D57direct (N × H)
112. C32×C7C2×C5×D19semidirect
116. C3×C19C5×D3×D7semidirect
117. C3×C19C2×C3×C5×D7semidirect
118. C32×C5D7×D19semidirect
123. C3×D7C3×C5×D19semidirect
124. C3×D7C5×D57direct (N × H)
130. C5×C7C2×C3×D57semidirect
140. C3×C7C2×C3×C5×D19semidirect
141. C3×C7C2×C5×D57semidirect
143. C19C3×C5×D3×D7semidirect
148. C3×C5C3×D7×D19semidirect
149. C3×C5D7×D57direct (N × H)
152. D7C3×C5×D57direct (N × H)
158. C32C5×D7×D19semidirect
159. C7C2×C3×C5×D57semidirect
167. C5C3×D7×D57direct (N × H)
170. C3C3×C5×D7×D19semidirect
171. C3C5×D7×D57direct (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×C5×C7×D572
C3×C5×D3992
C5×D7×D573
C3×C5×D7×D193
C3×D7×D575
C2×C3×C5×D577
C3×C5×D3×D719