Finite Group Databasebeta

← C3×D5×C13×D39 #44478261

Subgroups — C3×D5×C13×D39 #44478261

Order 30420.

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

normal subgroups only

This group has 320 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×D5×C132C211yesmaximal, characteristic, complemented
2C3×C5×C13×D39C211yesmaximal, characteristic, complemented
3C3×C13×D195C211yesmaximal, characteristic, complemented
4D5×C13×D39C311yesmaximal, characteristic, direct product factor
5C3×D5×C13×D13—31nomaximal
6C32×C5×C132C2211yescharacteristic, complemented, Hall
7C2×C3×C13×D39—51nomaximal, Hall
8C13×D195C2×C311yescharacteristic, complemented
9C5×C13×D39C2×C311yescharacteristic, complemented
10C3×C13×D65—31no—
11C3×D5×C132—21no—
12C3×D5×C132D311yescharacteristic, complemented
13C3×D5×C132C2×C311yescharacteristic, complemented
14C3×C5×C13×D13—31no—
15D5×C13×D13—31noHall
16C3×C13×D39—51no—
17C3×C13×D39D511yescharacteristic, direct product factor
18C2×C32×C132—51no—
19C3×C5×C132—21no—
20C3×C5×C132C2×D311yescharacteristic, complemented
21C3×C5×C132C22×C311yescharacteristic, complemented
22C3×D5×D39C1311yesmaximal, characteristic, direct product factor
23C3×D3×D5×C13—131nomaximal
24C2×C13×D39—51no—
25C2×C3×C13×D13—151no—
26C13×D65—31no—
27D5×C132C3×D311yescharacteristic, complemented
28C5×C13×D13—31no—
29C32×C132C2×D511yescharacteristic, complemented, Hall
30C3×D195C2×C1311yescharacteristic, complemented
31C3×C13×D15—131no—
32C3×C5×D39C2×C1311yescharacteristic, complemented
33C3×C5×D3×C13—131no—
34C32×D5×C13—26no—
35C32×D5×C13D1311yescharacteristic, complemented
36C32×D5×C13C2×C1311yescharacteristic, complemented
37C2×C3×C132—51no—
38C2×C3×C132—51no—
39C2×C3×C132—101no—
40C13×D39—51no—
41C13×D39C3×D511yescharacteristic, direct product factor
42C3×C13×D13—31no—
43C3×C13×D13—151no—
44C5×C132C2×C3×D311yescharacteristic, complemented, Hall
45C2×C3×D5×C13—391no—
46D5×D39C3×C1311yescharacteristic, direct product factor
47D3×D5×C13—131no—
48C3×D5×D13—31no—
49C2×C13×D13—151noHall
50C32×C5×C13—26no—
51C32×C5×C13C2×D1311yescharacteristic, complemented
52C32×C5×C13C22×C1311yescharacteristic, complemented
53C3×C132—21no—
54C3×C132D3×D511yescharacteristic, complemented
55C3×C132C2×C3×D511yescharacteristic, complemented
56C2×C3×D39—51no—
57C2×C3×D3×C13—651no—
58C2×C3×C5×C13—391no—
59D195C2×C3×C1311yescharacteristic, complemented
60C13×D15—131no—
61C5×D39C2×C3×C1311yescharacteristic, complemented
62C5×D3×C13—131no—
63C3×D65—31no—
64C3×D5×C13—212no—
65C3×D5×C13—26no—
66C3×D5×C13—26no—
67C3×D5×C13—21no—
68C3×D5×C13—21no—
69C3×D5×C13—391no—
70C3×D5×C13D3×C1311yescharacteristic, complemented
71C3×D5×C13C3×D1311yescharacteristic, complemented
72C3×D5×C13D3911yescharacteristic, direct product factor
73C3×D5×C13C2×C3×C1311yescharacteristic, complemented
74C3×C5×D13—31no—
75C2×C132—51no—
76C13×D13—31no—
77C13×D13—151no—
78C2×D5×C13—391no—
79D5×D13—31no—
80C2×C32×C13—51no—
81C2×C32×C13—51no—
82C2×C32×C13—106no—
83C3×D39—51no—
84C3×D39D5×C1311yescharacteristic, direct product factor
85C3×D3×C13—131no—
86C3×D3×C13—651no—
87C3×C5×C13—212no—
88C3×C5×C13—21no—
89C3×C5×C13—21no—
90C3×C5×C13—26no—
91C3×C5×C13—26no—
92C3×C5×C13C2×C3×D1311yescharacteristic, complemented
93C3×C5×C13C2×D3×C1311yescharacteristic, complemented
94C3×C5×C13C2×D3911yescharacteristic, complemented
95C3×C5×C13C22×C3×C1311yescharacteristic, complemented
96C3×D3×D5—131noHall
97C132C3×D3×D511yescharacteristic, complemented, Sylow
98C22×C3×C13—1951no—
99C2×D39—51no—
100C2×D3×C13—651no—
101C2×C3×D13—151no—
102C2×C5×C13—391no—
103D65—31no—
104C5×D13—31no—
105D5×C13—26no—
106D5×C13—391no—
107D5×C13C3×D3×C1311yescharacteristic, complemented
108D5×C13C3×D3911yescharacteristic, direct product factor
109C32×C13—26no—
110C32×C13D5×D1311yescharacteristic, complemented
111C32×C13C2×D5×C1311yescharacteristic, complemented
112C3×D15—131no—
113C3×C5×D3—131no—
114C32×D5C13×D1311yescharacteristic, complemented
115C2×C3×C13—51no—
116C2×C3×C13—51no—
117C2×C3×C13—51no—
118C2×C3×C13—51no—
119C2×C3×C13—106no—
120C2×C3×C13—106no—
121C2×C3×C13—101no—
122C2×C3×C13—101no—
123C2×C3×C13—1012no—
124C2×C3×C13—391no—
125C2×C3×C13—1951no—
126D39—51no—
127D39C3×D5×C1311yescharacteristic, direct product factor
128C3×D13—31no—
129C3×D13—151no—
130D3×C13—131no—
131D3×C13—651no—
132C5×C13—26no—
133C5×C13C2×C3×D3×C1311yescharacteristic, complemented
134C5×C13C2×C3×D3911yescharacteristic, complemented
135C2×C3×D5—391no—
136D3×D5—131no—
137C22×C13—1951no—
138C2×D13—151no—
139C32×C5C2×C13×D1311yescharacteristic, complemented, Hall
140C3×C13—212no—
141C3×C13—21no—
142C3×C13—21no—
143C3×C13—26no—
144C3×C13—26no—
145C3×C13C3×D5×D1311yescharacteristic, complemented
146C3×C13D3×D5×C1311yescharacteristic, complemented
147C3×C13D5×D3911yescharacteristic, direct product factor
148C3×C13C2×C3×D5×C1311yescharacteristic, complemented
149C2×C3×D3—651noHall
150C2×C3×C5—391no—
151D15—131no—
152C3×D5—21no—
153C3×D5—391no—
154C3×D5C3×C13×D1311yescharacteristic, complemented
155C3×D5C13×D3911yescharacteristic, direct product factor
156C5×D3—131no—
157C2×C13—51no—
158C2×C13—51no—
159C2×C13—106no—
160C2×C13—391no—
161C2×C13—1951no—
162D13—31no—
163D13—151no—
164C2×D5—391noHall
165C2×C32—51no—
166C3×D3—131no—
167C3×D3—651no—
168C3×C5—21no—
169C3×C5C2×C3×C13×D1311yescharacteristic, complemented
170C3×C5C2×C13×D3911yescharacteristic, complemented
171C13—26no—
172C13C3×D3×D5×C1311yescharacteristic, complemented
173C13C3×D5×D3911yescharacteristic, direct product factor
174C22×C3—1951no—
175C2×D3—651no—
176C2×C5—391no—
177D5—391no—
178D5C3×C13×D3911yescharacteristic, direct product factor
179C32D5×C13×D1311yescharacteristic, complemented, Sylow
180C2×C3—51no—
181C2×C3—51no—
182C2×C3—101no—
183C2×C3—391no—
184C2×C3—1951no—
185D3—131no—
186D3—651no—
187C5C2×C3×C13×D3911yescharacteristic, complemented, Sylow
188C22—1951noSylow
189C3—21no—
190C3C3×D5×C13×D1311yescharacteristic, complemented
191C3D5×C13×D3911yescharacteristic, direct product factor
192C2—51no—
193C2—391no—
194C2—1951no—
subgroupG/H
center, hypercenterC3×C13D5×D39
commutator, cosocle, hypocenterC3×C5×C13C22×C3×C13
FrattiniC1G
Fitting, socleC32×C5×C132C22
LCSG ▷ C3×C5×C13
UCSC1 ◁ C3×C13

Complements

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

NH ≅ G/Ntype
1. C32×D5×C132C2semidirect
2. C3×C5×C13×D39C2semidirect
3. C3×C13×D195C2semidirect
4. D5×C13×D39C3direct (N × H)
6. C32×C5×C132C22semidirect
8. C13×D195C2×C3semidirect
9. C5×C13×D39C2×C3semidirect
12. C3×D5×C132D3semidirect
13. C3×D5×C132C2×C3semidirect
17. C3×C13×D39D5direct (N × H)
20. C3×C5×C132C2×D3semidirect
21. C3×C5×C132C22×C3semidirect
22. C3×D5×D39C13direct (N × H)
27. D5×C132C3×D3semidirect
29. C32×C132C2×D5semidirect
30. C3×D195C2×C13semidirect
32. C3×C5×D39C2×C13semidirect
35. C32×D5×C13D13semidirect
36. C32×D5×C13C2×C13semidirect
41. C13×D39C3×D5direct (N × H)
44. C5×C132C2×C3×D3semidirect
46. D5×D39C3×C13direct (N × H)
51. C32×C5×C13C2×D13semidirect
52. C32×C5×C13C22×C13semidirect
54. C3×C132D3×D5semidirect
55. C3×C132C2×C3×D5semidirect
59. D195C2×C3×C13semidirect
61. C5×D39C2×C3×C13semidirect
70. C3×D5×C13D3×C13semidirect
71. C3×D5×C13C3×D13semidirect
72. C3×D5×C13D39direct (N × H)
73. C3×D5×C13C2×C3×C13semidirect
84. C3×D39D5×C13direct (N × H)
92. C3×C5×C13C2×C3×D13semidirect
93. C3×C5×C13C2×D3×C13semidirect
94. C3×C5×C13C2×D39semidirect
95. C3×C5×C13C22×C3×C13semidirect
97. C132C3×D3×D5semidirect
107. D5×C13C3×D3×C13semidirect
108. D5×C13C3×D39direct (N × H)
110. C32×C13D5×D13semidirect
111. C32×C13C2×D5×C13semidirect
114. C32×D5C13×D13semidirect
127. D39C3×D5×C13direct (N × H)
133. C5×C13C2×C3×D3×C13semidirect
134. C5×C13C2×C3×D39semidirect
139. C32×C5C2×C13×D13semidirect
145. C3×C13C3×D5×D13semidirect
146. C3×C13D3×D5×C13semidirect
147. C3×C13D5×D39direct (N × H)
148. C3×C13C2×C3×D5×C13semidirect
154. C3×D5C3×C13×D13semidirect
155. C3×D5C13×D39direct (N × H)
169. C3×C5C2×C3×C13×D13semidirect
170. C3×C5C2×C13×D39semidirect
172. C13C3×D3×D5×C13semidirect
173. C13C3×D5×D39direct (N × H)
178. D5C3×C13×D39direct (N × H)
179. C32D5×C13×D13semidirect
187. C5C2×C3×C13×D39semidirect
190. C3C3×D5×C13×D13semidirect
191. C3D5×C13×D39direct (N × H)

Maximal subgroups

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

subgroupindex
C32×D5×C1322
C3×C5×C13×D392
C3×C13×D1952
D5×C13×D393
C3×D5×C13×D133
C2×C3×C13×D395
C3×D5×D3913
C3×D3×D5×C1313