Finite Group Databasebeta

← C3×D13×D195 #44478255

Subgroups — C3×D13×D195 #44478255

Order 30420.

284 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 56 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×C13×D13C211yesmaximal, characteristic, complemented
2C3×C13×D195C211yesmaximal, characteristic, complemented
3C3×C3⋊(C5⋊(C13⋊D13))C211yesmaximal, characteristic, complemented
4D13×D195C311yesmaximal, characteristic, direct product factor
5C3×D13×D65—31nomaximal
6C32×C5×C132C2211yescharacteristic, complemented, Hall
7C3×D13×D39—51nomaximal, Hall
8C3⋊(C5⋊(C13⋊D13))C2×C311yescharacteristic, complemented
9C13×D195C2×C311yescharacteristic, complemented
10C3×C5⋊(C13⋊D13)—31no—
11C3×C13×D65—31no—
12C3×C5×C13×D13—21no—
13C3×C5×C13×D13D311yescharacteristic, complemented
14C3×C5×C13×D13C2×C311yescharacteristic, complemented
15D13×D65—31noHall
16C3×C3⋊(C13⋊D13)—51no—
17C3×C13×D39—51no—
18C32×C13×D13D511yescharacteristic, complemented
19C3×C5×C132—21no—
20C3×C5×C132C2×D311yescharacteristic, complemented
21C3×C5×C132C22×C311yescharacteristic, complemented
22C2×C3×D195—131nomaximal
23C3×D13×D15—131nomaximal
24D13×D39—51no—
25C3×D132—151no—
26C5⋊(C13⋊D13)—31no—
27C13×D65—31no—
28C5×C13×D13C3×D311yescharacteristic, complemented
29C32×C132C2×D511yescharacteristic, complemented, Hall
30C2×C32×C5×C13—131no—
31C3×D195—131no—
32C3×D195—131no—
33C3×D195—266no—
34C3×D195D1311yescharacteristic, direct product factor
35C3×C13×D15—131no—
36C32×C5×D13D1311yescharacteristic, complemented
37C3⋊(C13⋊D13)—51no—
38C13×D39—51no—
39C3×C13⋊D13—151no—
40C3×C13×D13—21no—
41C3×C13×D13—151no—
42C3×C13×D13C3×D511yescharacteristic, complemented
43C3×C13×D13D1511yescharacteristic, complemented
44C5×C132C2×C3×D311yescharacteristic, complemented, Hall
45C2×D195—131no—
46C2×C3×D65—391no—
47D13×D15—131no—
48C3×D5×D13—391no—
49D132—151noHall
50C32×C5×C13—26no—
51C32×C5×C13C2×D1311yescharacteristic, complemented
52C32×C5×C13C2×D1311yescharacteristic, complemented
53C3×C132—21no—
54C3×C132C2×C3×D511yescharacteristic, complemented
55C3×C132C2×D1511yescharacteristic, complemented
56C2×C3×D39—651no—
57C3×D3×D13—651no—
58C2×C3×C5×C13—131no—
59C2×C3×C5×C13—131no—
60C2×C3×C5×C13—261no—
61D195—131no—
62D195—131no—
63D195—266no—
64D195C3×D1311yescharacteristic, direct product factor
65C13×D15—131no—
66C3×D65—31no—
67C3×D65—391no—
68C3×D65—391no—
69C3×D65—786no—
70C3×D5×C13—391no—
71C3×C5×D13—21no—
72C3×C5×D13C3×D1311yescharacteristic, complemented
73C3×C5×D13D3911yescharacteristic, complemented
74C13⋊D13—151no—
75C13×D13—151no—
76C13×D13C3×D1511yescharacteristic, complemented
77C2×D65—391no—
78D5×D13—391no—
79C2×C32×C13—131no—
80C3×D39—51no—
81C3×D39—651no—
82C3×D39—651no—
83C3×D39—1306no—
84C3×D3×C13—651no—
85C32×D13D6511yescharacteristic, complemented
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×C3×D1311yescharacteristic, complemented
94C3×C5×C13C2×D3911yescharacteristic, complemented
95C2×C3×D15—1691noHall
96C132C2×C3×D1511yescharacteristic, complemented, Sylow
97C2×D39—651no—
98C2×C3×D13—1951no—
99C2×C3×D13—1951no—
100D3×D13—651no—
101C2×C5×C13—131no—
102D65—31no—
103D65—391no—
104D65—391no—
105D65—786no—
106C5×D13C3×D3911yescharacteristic, complemented
107D5×C13—391no—
108C32×C13—26no—
109C32×C13D5×D1311yescharacteristic, complemented
110C32×C13C2×D6511yescharacteristic, complemented
111C2×C32×C5—131no—
112C3×D15—131no—
113C3×D15—1691no—
114C2×C3×C13—131no—
115C2×C3×C13—131no—
116C2×C3×C13—261no—
117C2×C3×C13—1951no—
118D39—51no—
119D39—651no—
120D39—651no—
121D39—1306no—
122C3×D13—21no—
123C3×D13—151no—
124C3×D13—3906no—
125C3×D13—1951no—
126C3×D13—1951no—
127C3×D13C3×D6511yescharacteristic, complemented
128C3×D13D19511yescharacteristic, direct product factor
129D3×C13—651no—
130C5×C13—26no—
131C5×C13C3×D3×D1311yescharacteristic, complemented
132C5×C13C2×C3×D3911yescharacteristic, complemented
133C2×D15—1691no—
134C2×C3×D5—5071no—
135C2×D13—1951no—
136C2×D13—1951no—
137C32×C5D13211yescharacteristic, complemented, Hall
138C3×C13—21no—
139C3×C13—21no—
140C3×C13—26no—
141C3×C13—26no—
142C3×C13—46no—
143C3×C13C3×D5×D1311yescharacteristic, complemented
144C3×C13D13×D1511yescharacteristic, complemented
145C3×C13C2×C3×D6511yescharacteristic, complemented
146C3×C13C2×D19511yescharacteristic, complemented
147C2×C3×D3—8451noHall
148C2×C3×C5—131no—
149C2×C3×C5—131no—
150C2×C3×C5—261no—
151D15—131no—
152D15—1691no—
153C3×D5—391no—
154C3×D5—5071no—
155C2×C13—131no—
156C2×C13—1951no—
157D13—151no—
158D13—3906no—
159D13—1951no—
160D13—1951no—
161D13C3×D19511yescharacteristic, direct product factor
162C2×D5—5071noHall
163C2×C32—131no—
164C3×D3—651no—
165C3×D3—8451no—
166C3×C5—21no—
167C3×C5C3×D13211yescharacteristic, complemented
168C3×C5D13×D3911yescharacteristic, complemented
169C13—26no—
170C13C3×D13×D1511yescharacteristic, complemented
171C13C2×C3×D19511yescharacteristic, complemented
172C22×C3—25351no—
173C2×D3—8451no—
174C2×C5—131no—
175D5—391no—
176D5—5071no—
177C32D13×D6511yescharacteristic, complemented, Sylow
178C2×C3—131no—
179C2×C3—131no—
180C2×C3—261no—
181C2×C3—1951no—
182C2×C3—25351no—
183D3—651no—
184D3—8451no—
185C5C3×D13×D3911yescharacteristic, complemented, Sylow
186C22—25351noSylow
187C3—21no—
188C3C3×D13×D6511yescharacteristic, complemented
189C3D13×D19511yescharacteristic, direct product factor
190C2—131no—
191C2—1951no—
192C2—25351no—
subgroupG/H
center, hypercenterC3D13×D195
commutator, cosocle, hypocenterC3×C5×C132C22×C3
FrattiniC1G
Fitting, socleC32×C5×C132C22
LCSG ▷ C3×C5×C132
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C5×C13×D13C2semidirect
2. C3×C13×D195C2semidirect
3. C3×C3⋊(C5⋊(C13⋊D13))C2semidirect
4. D13×D195C3direct (N × H)
6. C32×C5×C132C22semidirect
8. C3⋊(C5⋊(C13⋊D13))C2×C3semidirect
9. C13×D195C2×C3semidirect
13. C3×C5×C13×D13D3semidirect
14. C3×C5×C13×D13C2×C3semidirect
18. C32×C13×D13D5semidirect
20. C3×C5×C132C2×D3semidirect
21. C3×C5×C132C22×C3semidirect
28. C5×C13×D13C3×D3semidirect
29. C32×C132C2×D5semidirect
34. C3×D195D13direct (N × H)
36. C32×C5×D13D13semidirect
42. C3×C13×D13C3×D5semidirect
43. C3×C13×D13D15semidirect
44. C5×C132C2×C3×D3semidirect
51. C32×C5×C13C2×D13semidirect
52. C32×C5×C13C2×D13semidirect
54. C3×C132C2×C3×D5semidirect
55. C3×C132C2×D15semidirect
64. D195C3×D13direct (N × H)
72. C3×C5×D13C3×D13semidirect
73. C3×C5×D13D39semidirect
76. C13×D13C3×D15semidirect
85. C32×D13D65semidirect
91. C3×C5×C13D3×D13semidirect
92. C3×C5×C13C2×C3×D13semidirect
93. C3×C5×C13C2×C3×D13semidirect
94. C3×C5×C13C2×D39semidirect
96. C132C2×C3×D15semidirect
106. C5×D13C3×D39semidirect
109. C32×C13D5×D13semidirect
110. C32×C13C2×D65semidirect
127. C3×D13C3×D65semidirect
128. C3×D13D195direct (N × H)
131. C5×C13C3×D3×D13semidirect
132. C5×C13C2×C3×D39semidirect
137. C32×C5D132semidirect
143. C3×C13C3×D5×D13semidirect
144. C3×C13D13×D15semidirect
145. C3×C13C2×C3×D65semidirect
146. C3×C13C2×D195semidirect
161. D13C3×D195direct (N × H)
167. C3×C5C3×D132semidirect
168. C3×C5D13×D39semidirect
170. C13C3×D13×D15semidirect
171. C13C2×C3×D195semidirect
177. C32D13×D65semidirect
185. C5C3×D13×D39semidirect
188. C3C3×D13×D65semidirect
189. C3D13×D195direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×C13×D132
C3×C13×D1952
C3×C3⋊(C5⋊(C13⋊D13))2
D13×D1953
C3×D13×D653
C3×D13×D395
C2×C3×D19513
C3×D13×D1513