Finite Group Databasebeta

← C3×C5×D7×D39 #30655639

Subgroups — C3×C5×D7×D39 #30655639

Order 16380.

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
1C3×C5×D273C211yesmaximal, characteristic, complemented
2C3×C5×C7×D39C211yesmaximal, characteristic, complemented
3C32×C5×C13×D7C211yesmaximal, characteristic, complemented
4C5×D7×D39C311yesmaximal, characteristic, direct product factor
5C3×C5×D7×D13—31nomaximal
6C32×C5×C7×C13C2211yescharacteristic, complemented, Hall
7C3×D7×D39C511yesmaximal, characteristic, direct product factor, Hall
8C5×D273C2×C311yescharacteristic, complemented
9C5×C7×D39C2×C311yescharacteristic, complemented
10C3×C5×D91—31no—
11C3×C5×C13×D7—21no—
12C3×C5×C13×D7D311yescharacteristic, complemented
13C3×C5×C13×D7C2×C311yescharacteristic, complemented
14C3×C5×C7×D13—31no—
15C2×C3×C5×D39—71nomaximal, Hall
16C5×D7×D13—31noHall
17C3×D273C2×C511yescharacteristic, complemented
18C3×C7×D39C2×C511yescharacteristic, complemented
19C32×C13×D7C2×C511yescharacteristic, complemented
20C3×C5×C7×C13—21no—
21C3×C5×C7×C13C2×D311yescharacteristic, complemented
22C3×C5×C7×C13C22×C311yescharacteristic, complemented
23C3×C5×D3×D7—131nomaximal, Hall
24C2×C32×C5×C13—71no—
25C3×C5×D39—71no—
26C3×C5×D39D711yescharacteristic, direct product factor
27D7×D39C3×C511yescharacteristic, direct product factor
28C3×D7×D13—31no—
29C5×D91—31no—
30C5×C13×D7C3×D311yescharacteristic, complemented
31C5×C7×D13—31no—
32C32×C7×C13C22×C511yescharacteristic, complemented, Hall
33C2×C5×D39—71no—
34C2×C3×C5×D13—211no—
35C3×C5×D21—131no—
36C3×C5×D3×C7—131no—
37C32×C5×D7D1311yescharacteristic, complemented
38C32×C5×C13C2×D711yescharacteristic, complemented, Hall
39D273C2×C3×C511yescharacteristic, complemented
40C7×D39C2×C3×C511yescharacteristic, complemented
41C3×D91—31no—
42C3×C13×D7—21no—
43C3×C13×D7C5×D311yescharacteristic, complemented
44C3×C13×D7C2×C3×C511yescharacteristic, complemented
45C3×C7×D13—31no—
46C2×C3×D39—71noHall
47C5×C7×C13C2×C3×D311yescharacteristic, complemented, Hall
48C2×C3×C5×D7—391no—
49C5×D3×D7—131no—
50C2×C3×C5×C13—71no—
51C2×C3×C5×C13—71no—
52C2×C3×C5×C13—141no—
53C5×D39—71no—
54C5×D39C3×D711yescharacteristic, direct product factor
55C3×C5×D13—31no—
56C3×C5×D13—211no—
57D7×D13—31noHall
58C32×C5×C7C2×D1311yescharacteristic, complemented, Hall
59C3×C7×C13—21no—
60C3×C7×C13C2×C5×D311yescharacteristic, complemented
61C3×C7×C13C22×C3×C511yescharacteristic, complemented
62C2×C5×D13—211noHall
63C3×D3×D7—131noHall
64C2×C32×C13—71no—
65C3×D39—71no—
66C3×D39C5×D711yescharacteristic, direct product factor
67C2×C3×C5×C7—391no—
68C5×D21—131no—
69C5×D3×C7—131no—
70C3×C5×D7—21no—
71C3×C5×D7—391no—
72C3×C5×D7C3×D1311yescharacteristic, complemented
73C3×C5×D7D3911yescharacteristic, direct product factor
74C3×C5×C13—21no—
75C3×C5×C13D3×D711yescharacteristic, complemented
76C3×C5×C13C2×C3×D711yescharacteristic, complemented
77D91—31no—
78C7×D13—31no—
79C13×D7C3×C5×D311yescharacteristic, complemented
80C2×C3×C5×D3—911noHall
81C2×D39—71no—
82C2×C3×D13—211no—
83C2×C5×D7—391noHall
84C2×C5×C13—71no—
85C5×D13—31no—
86C5×D13—211no—
87C3×D21—131no—
88C3×D3×C7—131no—
89C32×D7C5×D1311yescharacteristic, complemented
90C32×C13C2×C5×D711yescharacteristic, complemented, Hall
91C3×C5×C7—21no—
92C3×C5×C7C2×C3×D1311yescharacteristic, complemented
93C3×C5×C7C2×D3911yescharacteristic, complemented
94C7×C13C2×C3×C5×D311yescharacteristic, complemented, Hall
95C2×C32×C5—71no—
96C3×C5×D3—131no—
97C3×C5×D3—911no—
98C2×C3×D7—391no—
99D3×D7—131no—
100C2×C3×C13—71no—
101C2×C3×C13—71no—
102C2×C3×C13—141no—
103D39—71no—
104D39C3×C5×D711yescharacteristic, direct product factor
105C3×D13—31no—
106C3×D13—211no—
107C2×C5×C7—391no—
108C5×D7—391no—
109C5×D7C3×D3911yescharacteristic, direct product factor
110C5×C13C3×D3×D711yescharacteristic, complemented, Hall
111C32×C7C2×C5×D1311yescharacteristic, complemented, Hall
112C22×C3×C5—2731no—
113C2×C5×D3—911no—
114C2×D13—211noHall
115C32×C5D7×D1311yescharacteristic, complemented, Hall
116C2×C3×C7—391no—
117D21—131no—
118C3×D7—21no—
119C3×D7—391no—
120C3×D7C3×C5×D1311yescharacteristic, complemented
121C3×D7C5×D3911yescharacteristic, direct product factor
122D3×C7—131no—
123C3×C13—21no—
124C3×C13C5×D3×D711yescharacteristic, complemented
125C3×C13C2×C3×C5×D711yescharacteristic, complemented
126C2×C3×D3—911noHall
127C5×C7C2×C3×D3911yescharacteristic, complemented, Hall
128C2×C3×C5—71no—
129C2×C3×C5—71no—
130C2×C3×C5—141no—
131C2×C3×C5—2731no—
132C2×C3×C5—391no—
133C5×D3—131no—
134C5×D3—911no—
135C2×D7—391noHall
136C2×C13—71no—
137D13—31no—
138D13—211no—
139C3×C7—21no—
140C3×C7C2×C3×C5×D1311yescharacteristic, complemented
141C3×C7C2×C5×D3911yescharacteristic, complemented
142C22×C5—2731noHall
143C2×C32—71no—
144C3×D3—131no—
145C3×D3—911no—
146C3×C5—21no—
147C3×C5C3×D7×D1311yescharacteristic, complemented
148C3×C5D7×D3911yescharacteristic, direct product factor
149C2×C7—391no—
150D7—391no—
151D7C3×C5×D3911yescharacteristic, direct product factor
152C13C3×C5×D3×D711yescharacteristic, complemented, Sylow
153C22×C3—2731no—
154C2×D3—911no—
155C2×C5—71no—
156C2×C5—2731no—
157C2×C5—391no—
158C32C5×D7×D1311yescharacteristic, complemented, Sylow
159C7C2×C3×C5×D3911yescharacteristic, complemented, Sylow
160C2×C3—71no—
161C2×C3—71no—
162C2×C3—141no—
163C2×C3—2731no—
164C2×C3—391no—
165D3—131no—
166D3—911no—
167C5C3×D7×D3911yescharacteristic, direct product factor, Sylow
168C22—2731noSylow
169C3—21no—
170C3C3×C5×D7×D1311yescharacteristic, complemented
171C3C5×D7×D3911yescharacteristic, direct product factor
172C2—71no—
173C2—2731no—
174C2—391no—
subgroupG/H
center, hypercenterC3×C5D7×D39
commutator, cosocle, hypocenterC3×C7×C13C22×C3×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C13C22
LCSG ▷ C3×C7×C13
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×D273C2semidirect
2. C3×C5×C7×D39C2semidirect
3. C32×C5×C13×D7C2semidirect
4. C5×D7×D39C3direct (N × H)
6. C32×C5×C7×C13C22semidirect
7. C3×D7×D39C5direct (N × H)
8. C5×D273C2×C3semidirect
9. C5×C7×D39C2×C3semidirect
12. C3×C5×C13×D7D3semidirect
13. C3×C5×C13×D7C2×C3semidirect
17. C3×D273C2×C5semidirect
18. C3×C7×D39C2×C5semidirect
19. C32×C13×D7C2×C5semidirect
21. C3×C5×C7×C13C2×D3semidirect
22. C3×C5×C7×C13C22×C3semidirect
26. C3×C5×D39D7direct (N × H)
27. D7×D39C3×C5direct (N × H)
30. C5×C13×D7C3×D3semidirect
32. C32×C7×C13C22×C5semidirect
37. C32×C5×D7D13semidirect
38. C32×C5×C13C2×D7semidirect
39. D273C2×C3×C5semidirect
40. C7×D39C2×C3×C5semidirect
43. C3×C13×D7C5×D3semidirect
44. C3×C13×D7C2×C3×C5semidirect
47. C5×C7×C13C2×C3×D3semidirect
54. C5×D39C3×D7direct (N × H)
58. C32×C5×C7C2×D13semidirect
60. C3×C7×C13C2×C5×D3semidirect
61. C3×C7×C13C22×C3×C5semidirect
66. C3×D39C5×D7direct (N × H)
72. C3×C5×D7C3×D13semidirect
73. C3×C5×D7D39direct (N × H)
75. C3×C5×C13D3×D7semidirect
76. C3×C5×C13C2×C3×D7semidirect
79. C13×D7C3×C5×D3semidirect
89. C32×D7C5×D13semidirect
90. C32×C13C2×C5×D7semidirect
92. C3×C5×C7C2×C3×D13semidirect
93. C3×C5×C7C2×D39semidirect
94. C7×C13C2×C3×C5×D3semidirect
104. D39C3×C5×D7direct (N × H)
109. C5×D7C3×D39direct (N × H)
110. C5×C13C3×D3×D7semidirect
111. C32×C7C2×C5×D13semidirect
115. C32×C5D7×D13semidirect
120. C3×D7C3×C5×D13semidirect
121. C3×D7C5×D39direct (N × H)
124. C3×C13C5×D3×D7semidirect
125. C3×C13C2×C3×C5×D7semidirect
127. C5×C7C2×C3×D39semidirect
140. C3×C7C2×C3×C5×D13semidirect
141. C3×C7C2×C5×D39semidirect
147. C3×C5C3×D7×D13semidirect
148. C3×C5D7×D39direct (N × H)
151. D7C3×C5×D39direct (N × H)
152. C13C3×C5×D3×D7semidirect
158. C32C5×D7×D13semidirect
159. C7C2×C3×C5×D39semidirect
167. C5C3×D7×D39direct (N × H)
170. C3C3×C5×D7×D13semidirect
171. C3C5×D7×D39direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×D2732
C3×C5×C7×D392
C32×C5×C13×D72
C5×D7×D393
C3×C5×D7×D133
C3×D7×D395
C2×C3×C5×D397
C3×C5×D3×D713