Finite Group Databasebeta

← C5×D3×C13×D39 #44478271

Subgroups — C5×D3×C13×D39 #44478271

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
1C3×C5×D3×C132C211yesmaximal, characteristic, complemented
2C3×C5×C13×D39C211yesmaximal, characteristic, complemented
3C5×C13×C3⋊D39C211yesmaximal, characteristic, complemented
4C2×C5×C13×D39—31nomaximal
5C5×D3×C13×D13—31nomaximal
6C32×C5×C132C2211yescharacteristic, complemented, Hall
7D3×C13×D39C511yesmaximal, characteristic, direct product factor, Hall
8C5×C13×D39—31no—
9C5×C13×D39—31no—
10C5×C13×D39—61no—
11C5×C13×D39D311yescharacteristic, direct product factor
12C5×D3×C132D311yescharacteristic, complemented
13C3×C5×C13×D13—31no—
14C2×C3×C5×C132—31no—
15C2×C5×C13×D13—91noHall
16C13×C3⋊D39C2×C511yescharacteristic, complemented
17C3×C13×D39C2×C511yescharacteristic, complemented
18C3×D3×C132C2×C511yescharacteristic, complemented
19C3×C5×C132—21no—
20C3×C5×C132C2×D311yescharacteristic, complemented
21C3×C5×C132C2×D311yescharacteristic, complemented
22C5×D3×D39C1311yesmaximal, characteristic, direct product factor
23C5×D32×C13—131nomaximal
24C2×C13×D39—31no—
25D3×C13×D13—31no—
26C2×C5×C132—31no—
27C5×C13×D13—31no—
28C5×C13×D13—91no—
29C32×C132C22×C511yescharacteristic, complemented, Hall
30C5×C3⋊D39C2×C1311yescharacteristic, complemented
31C5×C13×C3⋊D3—131no—
32C3×C5×D39C2×C1311yescharacteristic, complemented
33C3×C5×D3×C13—26no—
34C3×C5×D3×C13—131no—
35C3×C5×D3×C13D1311yescharacteristic, complemented
36C3×C5×D3×C13C2×C1311yescharacteristic, complemented
37C2×C3×C132—31no—
38C13×D39—31no—
39C13×D39—31no—
40C13×D39—61no—
41C13×D39C5×D311yescharacteristic, direct product factor
42D3×C132C5×D311yescharacteristic, complemented
43C3×C13×D13—31no—
44C5×C132D3211yescharacteristic, complemented, Hall
45C2×C5×D39—31no—
46C2×C5×D3×C13—391no—
47C2×C5×D3×C13—391no—
48C5×D3×D13—31no—
49C2×C13×D13—91noHall
50C32×C5×C13—26no—
51C32×C5×C13C2×D1311yescharacteristic, complemented
52C32×C5×C13C22×C1311yescharacteristic, complemented
53C3×C132—21no—
54C3×C132C2×C5×D311yescharacteristic, complemented
55C3×C132C2×C5×D311yescharacteristic, complemented
56D3×D39C5×C1311yescharacteristic, direct product factor
57D32×C13—131no—
58C2×C3×C5×C13—31no—
59C2×C3×C5×C13—31no—
60C2×C3×C5×C13—66no—
61C2×C3×C5×C13—391no—
62C5×D39—31no—
63C5×D39—31no—
64C5×D39—61no—
65C5×D39D3×C1311yescharacteristic, direct product factor
66C5×D3×C13—26no—
67C5×D3×C13—131no—
68C5×D3×C13—391no—
69C5×D3×C13—391no—
70C5×D3×C13—781no—
71C5×D3×C13D3×C1311yescharacteristic, complemented
72C5×D3×C13D3911yescharacteristic, direct product factor
73C3×C5×D13—31no—
74C2×C132—31no—
75C13×D13—31no—
76C13×D13—91no—
77C22×C5×C13—1171no—
78C2×C5×D13—91no—
79C3⋊D39C2×C5×C1311yescharacteristic, complemented
80C13×C3⋊D3—131no—
81C3×D39C2×C5×C1311yescharacteristic, complemented
82C3×D3×C13—26no—
83C3×D3×C13—131no—
84C3×D3×C13C5×D1311yescharacteristic, complemented
85C3×D3×C13C2×C5×C1311yescharacteristic, 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×D3×C1311yescharacteristic, complemented
93C3×C5×C13C2×D3×C1311yescharacteristic, complemented
94C3×C5×C13C2×D3911yescharacteristic, complemented
95C5×D32—131noHall
96C132C5×D3211yescharacteristic, complemented, Sylow
97C2×D39—31no—
98C2×D3×C13—391no—
99C2×D3×C13—391no—
100D3×D13—31no—
101C2×C5×C13—31no—
102C2×C5×C13—31no—
103C2×C5×C13—66no—
104C2×C5×C13—391no—
105C2×C5×C13—1171no—
106C5×D13—31no—
107C5×D13—91no—
108C32×C13—26no—
109C32×C13C2×C5×D1311yescharacteristic, complemented
110C32×C13C22×C5×C1311yescharacteristic, complemented
111C5×C3⋊D3—131no—
112C3×C5×D3—131no—
113C3×C5×D3C13×D1311yescharacteristic, complemented
114C2×C3×C13—31no—
115C2×C3×C13—31no—
116C2×C3×C13—66no—
117C2×C3×C13—391no—
118D39—31no—
119D39—31no—
120D39—61no—
121D39C5×D3×C1311yescharacteristic, direct product factor
122C3×D13—31no—
123D3×C13—26no—
124D3×C13—131no—
125D3×C13—391no—
126D3×C13—391no—
127D3×C13—781no—
128D3×C13C5×D3×C1311yescharacteristic, complemented
129D3×C13C5×D3911yescharacteristic, direct product factor
130C5×C13—26no—
131C5×C13D32×C1311yescharacteristic, complemented
132C5×C13D3×D3911yescharacteristic, direct product factor
133C2×C5×D3—391no—
134C2×C5×D3—391no—
135C22×C13—1171no—
136C2×D13—91no—
137C32×C5C2×C13×D1311yescharacteristic, complemented, Hall
138C3×C13—21no—
139C3×C13—21no—
140C3×C13—26no—
141C3×C13—26no—
142C3×C13—46no—
143C3×C13C5×D3×D1311yescharacteristic, complemented
144C3×C13C2×C5×D3×C1311yescharacteristic, complemented
145C3×C13C2×C5×D3×C1311yescharacteristic, complemented
146C3×C13C2×C5×D3911yescharacteristic, complemented
147D32—131noHall
148C2×C3×C5—31no—
149C2×C3×C5—391no—
150C5×D3—131no—
151C5×D3—391no—
152C5×D3—391no—
153C5×D3—781no—
154C5×D3C13×D3911yescharacteristic, direct product factor
155C2×C13—31no—
156C2×C13—31no—
157C2×C13—66no—
158C2×C13—391no—
159C2×C13—1171no—
160D13—31no—
161D13—91no—
162C22×C5—1171noHall
163C3⋊D3—131no—
164C3×D3—131no—
165C3×D3C5×C13×D1311yescharacteristic, complemented
166C3×C5—21no—
167C3×C5D3×C13×D1311yescharacteristic, complemented
168C3×C5C2×C13×D3911yescharacteristic, complemented
169C13—26no—
170C13C5×D32×C1311yescharacteristic, complemented
171C13C5×D3×D3911yescharacteristic, direct product factor
172C2×D3—391no—
173C2×D3—391no—
174C2×C5—31no—
175C2×C5—391no—
176C2×C5—1171no—
177C32C2×C5×C13×D1311yescharacteristic, complemented, Sylow
178C2×C3—31no—
179C2×C3—391no—
180D3—131no—
181D3—391no—
182D3—391no—
183D3—781no—
184D3C5×C13×D3911yescharacteristic, direct product factor
185C5D3×C13×D3911yescharacteristic, direct product factor, Sylow
186C22—1171noSylow
187C3—21no—
188C3C5×D3×C13×D1311yescharacteristic, complemented
189C3C2×C5×C13×D3911yescharacteristic, complemented
190C2—31no—
191C2—391no—
192C2—1171no—
subgroupG/H
center, hypercenterC5×C13D3×D39
commutator, cosocle, hypocenterC32×C13C22×C5×C13
FrattiniC1G
Fitting, socleC32×C5×C132C22
LCSG ▷ C32×C13
UCSC1 ◁ C5×C13

Complements

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

NH ≅ G/Ntype
1. C3×C5×D3×C132C2semidirect
2. C3×C5×C13×D39C2semidirect
3. C5×C13×C3⋊D39C2semidirect
6. C32×C5×C132C22semidirect
7. D3×C13×D39C5direct (N × H)
11. C5×C13×D39D3direct (N × H)
12. C5×D3×C132D3semidirect
16. C13×C3⋊D39C2×C5semidirect
17. C3×C13×D39C2×C5semidirect
18. C3×D3×C132C2×C5semidirect
20. C3×C5×C132C2×D3semidirect
21. C3×C5×C132C2×D3semidirect
22. C5×D3×D39C13direct (N × H)
29. C32×C132C22×C5semidirect
30. C5×C3⋊D39C2×C13semidirect
32. C3×C5×D39C2×C13semidirect
35. C3×C5×D3×C13D13semidirect
36. C3×C5×D3×C13C2×C13semidirect
41. C13×D39C5×D3direct (N × H)
42. D3×C132C5×D3semidirect
44. C5×C132D32semidirect
51. C32×C5×C13C2×D13semidirect
52. C32×C5×C13C22×C13semidirect
54. C3×C132C2×C5×D3semidirect
55. C3×C132C2×C5×D3semidirect
56. D3×D39C5×C13direct (N × H)
65. C5×D39D3×C13direct (N × H)
71. C5×D3×C13D3×C13semidirect
72. C5×D3×C13D39direct (N × H)
79. C3⋊D39C2×C5×C13semidirect
81. C3×D39C2×C5×C13semidirect
84. C3×D3×C13C5×D13semidirect
85. C3×D3×C13C2×C5×C13semidirect
91. C3×C5×C13D3×D13semidirect
92. C3×C5×C13C2×D3×C13semidirect
93. C3×C5×C13C2×D3×C13semidirect
94. C3×C5×C13C2×D39semidirect
96. C132C5×D32semidirect
109. C32×C13C2×C5×D13semidirect
110. C32×C13C22×C5×C13semidirect
113. C3×C5×D3C13×D13semidirect
121. D39C5×D3×C13direct (N × H)
128. D3×C13C5×D3×C13semidirect
129. D3×C13C5×D39direct (N × H)
131. C5×C13D32×C13semidirect
132. C5×C13D3×D39direct (N × H)
137. C32×C5C2×C13×D13semidirect
143. C3×C13C5×D3×D13semidirect
144. C3×C13C2×C5×D3×C13semidirect
145. C3×C13C2×C5×D3×C13semidirect
146. C3×C13C2×C5×D39semidirect
154. C5×D3C13×D39direct (N × H)
165. C3×D3C5×C13×D13semidirect
167. C3×C5D3×C13×D13semidirect
168. C3×C5C2×C13×D39semidirect
170. C13C5×D32×C13semidirect
171. C13C5×D3×D39direct (N × H)
177. C32C2×C5×C13×D13semidirect
184. D3C5×C13×D39direct (N × H)
185. C5D3×C13×D39direct (N × H)
188. C3C5×D3×C13×D13semidirect
189. C3C2×C5×C13×D39semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D3×C1322
C3×C5×C13×D392
C5×C13×C3⋊D392
C2×C5×C13×D393
C5×D3×C13×D133
D3×C13×D395
C5×D3×D3913
C5×D32×C1313