Finite Group Databasebeta

← C3×D3×C13×D35 #30655666

Subgroups — C3×D3×C13×D35 #30655666

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×C13×D105C211yesmaximal, characteristic, complemented
2C3×C5×D3×C7×C13C211yesmaximal, characteristic, complemented
3C32×C13×D35C211yesmaximal, characteristic, complemented
4C2×C3×C13×D35—31nomaximal
5D3×C13×D35C311yesmaximal, characteristic, direct product factor
6C32×C5×C7×C13C2211yescharacteristic, complemented, Hall
7C3×D3×C13×D7—51nomaximal, Hall
8C13×D105C2×C311yescharacteristic, complemented
9C5×D3×C7×C13C2×C311yescharacteristic, complemented
10C3×C13×D35—21no—
11C3×C13×D35—31no—
12C3×C13×D35D311yescharacteristic, direct product factor
13C3×C13×D35C2×C311yescharacteristic, complemented
14C2×C3×C5×C7×C13—31no—
15C3×D3×D5×C13—71nomaximal, Hall
16C2×C13×D35—31noHall
17C3×C13×D21—51no—
18C3×D3×C7×C13D511yescharacteristic, complemented
19C32×C13×D7—51no—
20C3×C5×C7×C13—21no—
21C3×C5×C7×C13C2×D311yescharacteristic, complemented
22C3×C5×C7×C13C22×C311yescharacteristic, complemented
23C3×D3×D35C1311yesmaximal, characteristic, direct product factor, Hall
24C3×C13×D15—71no—
25C3×C5×D3×C13D711yescharacteristic, complemented
26C32×D5×C13—71no—
27C2×C3×C13×D7—151no—
28D3×C13×D7—51no—
29C2×C5×C7×C13—31no—
30C13×D35—31no—
31C13×D35C3×D311yescharacteristic, direct product factor
32C32×C7×C13C2×D511yescharacteristic, complemented, Hall
33C2×C3×D5×C13—211no—
34D3×D5×C13—71no—
35C3×D105C2×C1311yescharacteristic, complemented
36C3×C5×D3×C7C2×C1311yescharacteristic, complemented
37C32×D35C2×C1311yescharacteristic, complemented
38C32×C5×C13C2×D711yescharacteristic, complemented, Hall
39C2×C3×C7×C13—31no—
40C13×D21—51no—
41D3×C7×C13C3×D511yescharacteristic, complemented
42C3×C13×D7—51no—
43C3×C13×D7—51no—
44C3×C13×D7—101no—
45C3×C13×D7—151no—
46C2×C3×D3×C13—351noHall
47C5×C7×C13C2×C3×D311yescharacteristic, complemented, Hall
48C2×C3×D35—31no—
49D3×D35C3×C1311yescharacteristic, direct product factor
50C2×C3×C5×C13—31no—
51C13×D15—71no—
52C5×D3×C13C3×D711yescharacteristic, complemented
53C3×D5×C13—71no—
54C3×D5×C13—71no—
55C3×D5×C13—141no—
56C3×D5×C13—211no—
57C2×C13×D7—151noHall
58C32×C5×C7C22×C1311yescharacteristic, complemented, Hall
59C3×C7×C13—21no—
60C3×C7×C13D3×D511yescharacteristic, complemented
61C3×C7×C13C2×C3×D511yescharacteristic, complemented
62C2×D5×C13—211noHall
63C3×D3×D7—51noHall
64C2×C32×C13—351no—
65C3×D3×C13—351no—
66C3×D3×C13D3511yescharacteristic, direct product factor
67C2×C3×C5×C7—31no—
68D105C2×C3×C1311yescharacteristic, complemented
69C5×D3×C7C2×C3×C1311yescharacteristic, complemented
70C3×D35—21no—
71C3×D35—31no—
72C3×D35D3×C1311yescharacteristic, direct product factor
73C3×D35C2×C3×C1311yescharacteristic, complemented
74C3×C5×C13—21no—
75C3×C5×C13D3×D711yescharacteristic, complemented
76C3×C5×C13C2×C3×D711yescharacteristic, complemented
77C2×C7×C13—31no—
78C13×D7—51no—
79C13×D7—151no—
80C3×D3×D5—71noHall
81C22×C3×C13—1051no—
82C2×D3×C13—351no—
83C2×D35—31noHall
84C2×C5×C13—31no—
85D5×C13—71no—
86D5×C13—211no—
87C3×D21—51no—
88C3×D3×C7D5×C1311yescharacteristic, complemented
89C32×D7—51no—
90C32×C13C2×D3511yescharacteristic, complemented, Hall
91C3×C5×C7—21no—
92C3×C5×C7C2×D3×C1311yescharacteristic, complemented
93C3×C5×C7C22×C3×C1311yescharacteristic, complemented
94C7×C13C3×D3×D511yescharacteristic, complemented, Hall
95C3×D15—71no—
96C3×C5×D3C13×D711yescharacteristic, complemented
97C32×D5—71no—
98C2×C3×D7—151no—
99D3×D7—51no—
100C2×C3×C13—31no—
101C2×C3×C13—351no—
102C2×C3×C13—351no—
103C2×C3×C13—701no—
104C2×C3×C13—1051no—
105D3×C13—351no—
106D3×C13C3×D3511yescharacteristic, direct product factor
107C2×C5×C7—31no—
108D35—31no—
109D35C3×D3×C1311yescharacteristic, direct product factor
110C5×C13C3×D3×D711yescharacteristic, complemented, Hall
111C32×C7C2×D5×C1311yescharacteristic, complemented, Hall
112C2×C3×D5—211no—
113D3×D5—71no—
114C22×C13—1051noHall
115C32×C5C2×C13×D711yescharacteristic, complemented, Hall
116C2×C3×C7—31no—
117D21—51no—
118C3×D7—51no—
119C3×D7—51no—
120C3×D7—101no—
121C3×D7—151no—
122D3×C7C3×D5×C1311yescharacteristic, complemented
123C3×C13—21no—
124C3×C13D3×D3511yescharacteristic, direct product factor
125C3×C13C2×C3×D3511yescharacteristic, complemented
126C2×C3×D3—351noHall
127C5×C7C2×C3×D3×C1311yescharacteristic, complemented, Hall
128C2×C3×C5—31no—
129D15—71no—
130C3×D5—71no—
131C3×D5—71no—
132C3×D5—141no—
133C3×D5—211no—
134C5×D3C3×C13×D711yescharacteristic, complemented
135C2×D7—151noHall
136C2×C13—31no—
137C2×C13—351no—
138C2×C13—1051no—
139C3×C7—21no—
140C3×C7D3×D5×C1311yescharacteristic, complemented
141C3×C7C2×C3×D5×C1311yescharacteristic, complemented
142C2×D5—211noHall
143C2×C32—351no—
144C3×D3—351no—
145C3×D3C13×D3511yescharacteristic, direct product factor
146C3×C5—21no—
147C3×C5D3×C13×D711yescharacteristic, complemented
148C3×C5C2×C3×C13×D711yescharacteristic, complemented
149C2×C7—31no—
150D7—51no—
151D7—151no—
152C13C3×D3×D3511yescharacteristic, direct product factor, Sylow
153C22×C3—1051no—
154C2×D3—351no—
155C2×C5—31no—
156D5—71no—
157D5—211no—
158C32C2×C13×D3511yescharacteristic, complemented, Sylow
159C7C3×D3×D5×C1311yescharacteristic, complemented, Sylow
160C2×C3—31no—
161C2×C3—351no—
162C2×C3—351no—
163C2×C3—701no—
164C2×C3—1051no—
165D3—351no—
166D3C3×C13×D3511yescharacteristic, direct product factor
167C5C3×D3×C13×D711yescharacteristic, complemented, Sylow
168C22—1051noSylow
169C3—21no—
170C3D3×C13×D3511yescharacteristic, direct product factor
171C3C2×C3×C13×D3511yescharacteristic, complemented
172C2—31no—
173C2—351no—
174C2—1051no—
subgroupG/H
center, hypercenterC3×C13D3×D35
commutator, cosocle, hypocenterC3×C5×C7C22×C3×C13
FrattiniC1G
Fitting, socleC32×C5×C7×C13C22
LCSG ▷ C3×C5×C7
UCSC1 ◁ C3×C13

Complements

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

NH ≅ G/Ntype
1. C3×C13×D105C2semidirect
2. C3×C5×D3×C7×C13C2semidirect
3. C32×C13×D35C2semidirect
5. D3×C13×D35C3direct (N × H)
6. C32×C5×C7×C13C22semidirect
8. C13×D105C2×C3semidirect
9. C5×D3×C7×C13C2×C3semidirect
12. C3×C13×D35D3direct (N × H)
13. C3×C13×D35C2×C3semidirect
18. C3×D3×C7×C13D5semidirect
21. C3×C5×C7×C13C2×D3semidirect
22. C3×C5×C7×C13C22×C3semidirect
23. C3×D3×D35C13direct (N × H)
25. C3×C5×D3×C13D7semidirect
31. C13×D35C3×D3direct (N × H)
32. C32×C7×C13C2×D5semidirect
35. C3×D105C2×C13semidirect
36. C3×C5×D3×C7C2×C13semidirect
37. C32×D35C2×C13semidirect
38. C32×C5×C13C2×D7semidirect
41. D3×C7×C13C3×D5semidirect
47. C5×C7×C13C2×C3×D3semidirect
49. D3×D35C3×C13direct (N × H)
52. C5×D3×C13C3×D7semidirect
58. C32×C5×C7C22×C13semidirect
60. C3×C7×C13D3×D5semidirect
61. C3×C7×C13C2×C3×D5semidirect
66. C3×D3×C13D35direct (N × H)
68. D105C2×C3×C13semidirect
69. C5×D3×C7C2×C3×C13semidirect
72. C3×D35D3×C13direct (N × H)
73. C3×D35C2×C3×C13semidirect
75. C3×C5×C13D3×D7semidirect
76. C3×C5×C13C2×C3×D7semidirect
88. C3×D3×C7D5×C13semidirect
90. C32×C13C2×D35semidirect
92. C3×C5×C7C2×D3×C13semidirect
93. C3×C5×C7C22×C3×C13semidirect
94. C7×C13C3×D3×D5semidirect
96. C3×C5×D3C13×D7semidirect
106. D3×C13C3×D35direct (N × H)
109. D35C3×D3×C13direct (N × H)
110. C5×C13C3×D3×D7semidirect
111. C32×C7C2×D5×C13semidirect
115. C32×C5C2×C13×D7semidirect
122. D3×C7C3×D5×C13semidirect
124. C3×C13D3×D35direct (N × H)
125. C3×C13C2×C3×D35semidirect
127. C5×C7C2×C3×D3×C13semidirect
134. C5×D3C3×C13×D7semidirect
140. C3×C7D3×D5×C13semidirect
141. C3×C7C2×C3×D5×C13semidirect
145. C3×D3C13×D35direct (N × H)
147. C3×C5D3×C13×D7semidirect
148. C3×C5C2×C3×C13×D7semidirect
152. C13C3×D3×D35direct (N × H)
158. C32C2×C13×D35semidirect
159. C7C3×D3×D5×C13semidirect
166. D3C3×C13×D35direct (N × H)
167. C5C3×D3×C13×D7semidirect
170. C3D3×C13×D35direct (N × H)
171. C3C2×C3×C13×D35semidirect

Maximal subgroups

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

subgroupindex
C3×C13×D1052
C3×C5×D3×C7×C132
C32×C13×D352
C2×C3×C13×D353
D3×C13×D353
C3×D3×C13×D75
C3×D3×D5×C137
C3×D3×D3513