Finite Group Databasebeta

← C3×D3×C13×D65 #44478262

Subgroups — C3×D3×C13×D65 #44478262

Order 30420.

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

normal subgroups only

This group has 284 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×C13×D65C211yesmaximal, characteristic, complemented
2C3×C5×D3×C132C211yesmaximal, characteristic, complemented
3C3×C13×D195C211yesmaximal, characteristic, complemented
4C2×C3×C13×D65—31nomaximal
5D3×C13×D65C311yesmaximal, characteristic, direct product factor
6C32×C5×C132C2211yescharacteristic, complemented, Hall
7C3×D3×C13×D13—51nomaximal, Hall
8C13×D195C2×C311yescharacteristic, complemented
9C5×D3×C132C2×C311yescharacteristic, complemented
10C3×C13×D65—21no—
11C3×C13×D65—31no—
12C3×C13×D65D311yescharacteristic, direct product factor
13C3×C13×D65C2×C311yescharacteristic, complemented
14C2×C3×C5×C132—31no—
15C2×C13×D65—31noHall
16C3×C13×D39—51no—
17C3×D3×C132D511yescharacteristic, complemented
18C32×C13×D13—51no—
19C3×C5×C132—21no—
20C3×C5×C132C2×D311yescharacteristic, complemented
21C3×C5×C132C22×C311yescharacteristic, complemented
22C3×D3×D65C1311yesmaximal, characteristic, direct product factor
23C3×D3×D5×C13—131nomaximal
24C2×C3×C13×D13—151no—
25D3×C13×D13—51no—
26C2×C5×C132—31no—
27C13×D65—31no—
28C13×D65C3×D311yescharacteristic, direct product factor
29C32×C132C2×D511yescharacteristic, complemented, Hall
30C3×D195C2×C1311yescharacteristic, complemented
31C3×C13×D15—131no—
32C3×C5×D3×C13—26no—
33C3×C5×D3×C13D1311yescharacteristic, complemented
34C3×C5×D3×C13C2×C1311yescharacteristic, complemented
35C32×D65C2×C1311yescharacteristic, complemented
36C32×D5×C13—131no—
37C2×C3×C132—31no—
38C13×D39—51no—
39D3×C132C3×D511yescharacteristic, complemented
40C3×C13×D13—51no—
41C3×C13×D13—51no—
42C3×C13×D13—101no—
43C3×C13×D13—151no—
44C5×C132C2×C3×D311yescharacteristic, complemented, Hall
45C2×C3×D65—31no—
46C2×C3×D5×C13—391no—
47D3×D65C3×C1311yescharacteristic, direct product factor
48D3×D5×C13—131no—
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×D3×C13—651no—
57C3×D3×D13—51no—
58C2×C3×C5×C13—31no—
59C2×C3×C5×C13—31no—
60C2×C3×C5×C13—66no—
61D195C2×C3×C1311yescharacteristic, complemented
62C13×D15—131no—
63C5×D3×C13—26no—
64C5×D3×C13C3×D1311yescharacteristic, complemented
65C5×D3×C13C2×C3×C1311yescharacteristic, complemented
66C3×D65—21no—
67C3×D65—31no—
68C3×D65D3×C1311yescharacteristic, direct product factor
69C3×D65C2×C3×C1311yescharacteristic, complemented
70C3×D5×C13—131no—
71C3×D5×C13—131no—
72C3×D5×C13—261no—
73C3×D5×C13—391no—
74C2×C132—31no—
75C13×D13—51no—
76C13×D13—151no—
77C2×D65—31no—
78C2×D5×C13—391no—
79C2×C32×C13—651no—
80C3×D39—51no—
81C3×D3×C13—26no—
82C3×D3×C13—651no—
83C3×D3×C13D5×C1311yescharacteristic, complemented
84C3×D3×C13D6511yescharacteristic, direct product factor
85C32×D13—51no—
86C3×C5×C13—21no—
87C3×C5×C13—21no—
88C3×C5×C13—26no—
89C3×C5×C13—26no—
90C3×C5×C13—46no—
91C3×C5×C13D3×D1311yescharacteristic, complemented
92C3×C5×C13C2×C3×D1311yescharacteristic, complemented
93C3×C5×C13C2×D3×C1311yescharacteristic, complemented
94C3×C5×C13C22×C3×C1311yescharacteristic, complemented
95C3×D3×D5—131noHall
96C132C3×D3×D511yescharacteristic, complemented, Sylow
97C22×C3×C13—1951no—
98C2×D3×C13—651no—
99C2×C3×D13—151no—
100D3×D13—51no—
101C2×C5×C13—31no—
102C2×C5×C13—31no—
103C2×C5×C13—66no—
104D65—31no—
105D65C3×D3×C1311yescharacteristic, direct product factor
106D5×C13—131no—
107D5×C13—391no—
108C32×C13—26no—
109C32×C13C2×D5×C1311yescharacteristic, complemented
110C32×C13C2×D6511yescharacteristic, complemented
111C3×D15—131no—
112C3×C5×D3C13×D1311yescharacteristic, complemented
113C32×D5—131no—
114C2×C3×C13—31no—
115C2×C3×C13—31no—
116C2×C3×C13—66no—
117C2×C3×C13—651no—
118C2×C3×C13—651no—
119C2×C3×C13—1301no—
120C2×C3×C13—1951no—
121D39—51no—
122C3×D13—51no—
123C3×D13—51no—
124C3×D13—101no—
125C3×D13—151no—
126D3×C13—26no—
127D3×C13—651no—
128D3×C13C3×D5×C1311yescharacteristic, complemented
129D3×C13C3×D6511yescharacteristic, direct product factor
130C5×C13—26no—
131C5×C13C3×D3×D1311yescharacteristic, complemented
132C5×C13C2×C3×D3×C1311yescharacteristic, complemented
133C2×C3×D5—391no—
134D3×D5—131no—
135C22×C13—1951no—
136C2×D13—151no—
137C32×C5C2×C13×D1311yescharacteristic, complemented, Hall
138C3×C13—21no—
139C3×C13—21no—
140C3×C13—26no—
141C3×C13—26no—
142C3×C13—46no—
143C3×C13D3×D5×C1311yescharacteristic, complemented
144C3×C13D3×D6511yescharacteristic, direct product factor
145C3×C13C2×C3×D5×C1311yescharacteristic, complemented
146C3×C13C2×C3×D6511yescharacteristic, complemented
147C2×C3×D3—651noHall
148C2×C3×C5—31no—
149D15—131no—
150C3×D5—131no—
151C3×D5—131no—
152C3×D5—261no—
153C3×D5—391no—
154C5×D3C3×C13×D1311yescharacteristic, complemented
155C2×C13—31no—
156C2×C13—31no—
157C2×C13—66no—
158C2×C13—651no—
159C2×C13—1951no—
160D13—51no—
161D13—151no—
162C2×D5—391noHall
163C2×C32—651no—
164C3×D3—651no—
165C3×D3C13×D6511yescharacteristic, direct product factor
166C3×C5—21no—
167C3×C5D3×C13×D1311yescharacteristic, complemented
168C3×C5C2×C3×C13×D1311yescharacteristic, complemented
169C13—26no—
170C13C3×D3×D5×C1311yescharacteristic, complemented
171C13C3×D3×D6511yescharacteristic, direct product factor
172C22×C3—1951no—
173C2×D3—651no—
174C2×C5—31no—
175D5—131no—
176D5—391no—
177C32C2×C13×D6511yescharacteristic, complemented, Sylow
178C2×C3—31no—
179C2×C3—651no—
180C2×C3—651no—
181C2×C3—1301no—
182C2×C3—1951no—
183D3—651no—
184D3C3×C13×D6511yescharacteristic, direct product factor
185C5C3×D3×C13×D1311yescharacteristic, complemented, Sylow
186C22—1951noSylow
187C3—21no—
188C3D3×C13×D6511yescharacteristic, direct product factor
189C3C2×C3×C13×D6511yescharacteristic, complemented
190C2—31no—
191C2—651no—
192C2—1951no—
subgroupG/H
center, hypercenterC3×C13D3×D65
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×C13×D65C2semidirect
2. C3×C5×D3×C132C2semidirect
3. C3×C13×D195C2semidirect
5. D3×C13×D65C3direct (N × H)
6. C32×C5×C132C22semidirect
8. C13×D195C2×C3semidirect
9. C5×D3×C132C2×C3semidirect
12. C3×C13×D65D3direct (N × H)
13. C3×C13×D65C2×C3semidirect
17. C3×D3×C132D5semidirect
20. C3×C5×C132C2×D3semidirect
21. C3×C5×C132C22×C3semidirect
22. C3×D3×D65C13direct (N × H)
28. C13×D65C3×D3direct (N × H)
29. C32×C132C2×D5semidirect
30. C3×D195C2×C13semidirect
33. C3×C5×D3×C13D13semidirect
34. C3×C5×D3×C13C2×C13semidirect
35. C32×D65C2×C13semidirect
39. D3×C132C3×D5semidirect
44. C5×C132C2×C3×D3semidirect
47. D3×D65C3×C13direct (N × H)
51. C32×C5×C13C2×D13semidirect
52. C32×C5×C13C22×C13semidirect
54. C3×C132D3×D5semidirect
55. C3×C132C2×C3×D5semidirect
61. D195C2×C3×C13semidirect
64. C5×D3×C13C3×D13semidirect
65. C5×D3×C13C2×C3×C13semidirect
68. C3×D65D3×C13direct (N × H)
69. C3×D65C2×C3×C13semidirect
83. C3×D3×C13D5×C13semidirect
84. C3×D3×C13D65direct (N × H)
91. C3×C5×C13D3×D13semidirect
92. C3×C5×C13C2×C3×D13semidirect
93. C3×C5×C13C2×D3×C13semidirect
94. C3×C5×C13C22×C3×C13semidirect
96. C132C3×D3×D5semidirect
105. D65C3×D3×C13direct (N × H)
109. C32×C13C2×D5×C13semidirect
110. C32×C13C2×D65semidirect
112. C3×C5×D3C13×D13semidirect
128. D3×C13C3×D5×C13semidirect
129. D3×C13C3×D65direct (N × H)
131. C5×C13C3×D3×D13semidirect
132. C5×C13C2×C3×D3×C13semidirect
137. C32×C5C2×C13×D13semidirect
143. C3×C13D3×D5×C13semidirect
144. C3×C13D3×D65direct (N × H)
145. C3×C13C2×C3×D5×C13semidirect
146. C3×C13C2×C3×D65semidirect
154. C5×D3C3×C13×D13semidirect
165. C3×D3C13×D65direct (N × H)
167. C3×C5D3×C13×D13semidirect
168. C3×C5C2×C3×C13×D13semidirect
170. C13C3×D3×D5×C13semidirect
171. C13C3×D3×D65direct (N × H)
177. C32C2×C13×D65semidirect
184. D3C3×C13×D65direct (N × H)
185. C5C3×D3×C13×D13semidirect
188. C3D3×C13×D65direct (N × H)
189. C3C2×C3×C13×D65semidirect

Maximal subgroups

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

subgroupindex
C32×C13×D652
C3×C5×D3×C1322
C3×C13×D1952
C2×C3×C13×D653
D3×C13×D653
C3×D3×C13×D135
C3×D3×D6513
C3×D3×D5×C1313