Finite Group Databasebeta

← C5×D3×C11×D39 #38788223

Subgroups — C5×D3×C11×D39 #38788223

Order 25740.

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×C5×D3×C11×C13C211yesmaximal, characteristic, complemented
2C3×C5×C11×D39C211yesmaximal, characteristic, complemented
3C5×C11×C3⋊D39C211yesmaximal, characteristic, complemented
4C2×C5×C11×D39—31nomaximal
5C5×D3×C11×D13—31nomaximal
6C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
7D3×C11×D39C511yesmaximal, characteristic, direct product factor, Hall
8C5×C11×D39—31no—
9C5×C11×D39—31no—
10C5×C11×D39—61no—
11C5×C11×D39D311yescharacteristic, direct product factor
12C5×D3×C11×C13D311yescharacteristic, complemented
13C3×C5×C11×D13—31no—
14C2×C3×C5×C11×C13—31no—
15C2×C5×C11×D13—91noHall
16C11×C3⋊D39C2×C511yescharacteristic, complemented
17C3×C11×D39C2×C511yescharacteristic, complemented
18C3×D3×C11×C13C2×C511yescharacteristic, complemented
19C5×D3×D39C1111yesmaximal, characteristic, direct product factor, Hall
20C3×C5×C11×C13—21no—
21C3×C5×C11×C13C2×D311yescharacteristic, complemented
22C3×C5×C11×C13C2×D311yescharacteristic, complemented
23C5×D32×C11—131nomaximal, Hall
24C2×C11×D39—31no—
25D3×C11×D13—31no—
26C2×C5×C11×C13—31no—
27C5×C11×D13—31no—
28C5×C11×D13—91no—
29C32×C11×C13C22×C511yescharacteristic, complemented, Hall
30C5×C3⋊D39C2×C1111yescharacteristic, complemented
31C3×C5×D39C2×C1111yescharacteristic, complemented
32C3×C5×D3×C13C2×C1111yescharacteristic, complemented
33C5×C11×C3⋊D3—131no—
34C3×C5×D3×C11—131no—
35C3×C5×D3×C11D1311yescharacteristic, complemented
36C2×C3×C11×C13—31no—
37C11×D39—31no—
38C11×D39—31no—
39C11×D39—61no—
40C11×D39C5×D311yescharacteristic, direct product factor
41D3×C11×C13C5×D311yescharacteristic, complemented
42C3×C11×D13—31no—
43C2×C5×D39—31no—
44C5×D3×D13—31no—
45C5×C11×C13D3211yescharacteristic, complemented, Hall
46C2×C5×D3×C11—391no—
47C2×C5×D3×C11—391no—
48C32×C5×C13C22×C1111yescharacteristic, complemented, Hall
49C2×C11×D13—91noHall
50C32×C5×C11C2×D1311yescharacteristic, complemented, Hall
51D3×D39C5×C1111yescharacteristic, direct product factor, Hall
52C3×C11×C13—21no—
53C3×C11×C13C2×C5×D311yescharacteristic, complemented
54C3×C11×C13C2×C5×D311yescharacteristic, complemented
55D32×C11—131noHall
56C2×C3×C5×C13—31no—
57C5×D39—31no—
58C5×D39—31no—
59C5×D39—61no—
60C5×D39D3×C1111yescharacteristic, direct product factor
61C5×D3×C13D3×C1111yescharacteristic, complemented
62C3×C5×D13—31no—
63C2×C3×C5×C11—31no—
64C2×C3×C5×C11—391no—
65C5×D3×C11—131no—
66C5×D3×C11—391no—
67C5×D3×C11—391no—
68C5×D3×C11—781no—
69C5×D3×C11D3911yescharacteristic, direct product factor
70C2×C11×C13—31no—
71C11×D13—31no—
72C11×D13—91no—
73C2×C5×D13—91noHall
74C3⋊D39C2×C5×C1111yescharacteristic, complemented
75C3×D39C2×C5×C1111yescharacteristic, complemented
76C3×D3×C13C2×C5×C1111yescharacteristic, complemented
77C22×C5×C11—1171noHall
78C11×C3⋊D3—131no—
79C3×D3×C11—131no—
80C3×D3×C11C5×D1311yescharacteristic, complemented
81C3×C5×C13—21no—
82C3×C5×C13C2×D3×C1111yescharacteristic, complemented
83C3×C5×C13C2×D3×C1111yescharacteristic, complemented
84C5×D32—131noHall
85C3×C5×C11—21no—
86C3×C5×C11D3×D1311yescharacteristic, complemented
87C3×C5×C11C2×D3911yescharacteristic, complemented
88C2×D39—31no—
89D3×D13—31no—
90C11×C13C5×D3211yescharacteristic, complemented, Hall
91C2×D3×C11—391no—
92C2×D3×C11—391no—
93C2×C5×C13—31no—
94C5×D13—31no—
95C5×D13—91no—
96C32×C13C22×C5×C1111yescharacteristic, complemented, Hall
97C2×C5×C11—31no—
98C2×C5×C11—391no—
99C2×C5×C11—1171no—
100C32×C11C2×C5×D1311yescharacteristic, complemented, Hall
101C5×C3⋊D3—131no—
102C3×C5×D3—131no—
103C3×C5×D3C11×D1311yescharacteristic, complemented
104C2×C3×C13—31no—
105D39—31no—
106D39—31no—
107D39—61no—
108D39C5×D3×C1111yescharacteristic, direct product factor
109C3×D13—31no—
110D3×C13C5×D3×C1111yescharacteristic, complemented
111C2×C3×C11—31no—
112C2×C3×C11—391no—
113D3×C11—131no—
114D3×C11—391no—
115D3×C11—391no—
116D3×C11—781no—
117D3×C11C5×D3911yescharacteristic, direct product factor
118C5×C13D32×C1111yescharacteristic, complemented, Hall
119C2×C5×D3—391no—
120C2×C5×D3—391no—
121C5×C11D3×D3911yescharacteristic, direct product factor, Hall
122C2×D13—91noHall
123C32×C5C2×C11×D1311yescharacteristic, complemented, Hall
124C22×C11—1171noHall
125C3×C13—21no—
126C3×C13C2×C5×D3×C1111yescharacteristic, complemented
127C3×C13C2×C5×D3×C1111yescharacteristic, complemented
128D32—131noHall
129C3×C11—21no—
130C3×C11C5×D3×D1311yescharacteristic, complemented
131C3×C11C2×C5×D3911yescharacteristic, complemented
132C2×C3×C5—31no—
133C2×C3×C5—391no—
134C5×D3—131no—
135C5×D3—391no—
136C5×D3—391no—
137C5×D3—781no—
138C5×D3C11×D3911yescharacteristic, direct product factor
139C2×C13—31no—
140D13—31no—
141D13—91no—
142C2×C11—31no—
143C2×C11—391no—
144C2×C11—1171no—
145C22×C5—1171noHall
146C3⋊D3—131no—
147C3×D3—131no—
148C3×D3C5×C11×D1311yescharacteristic, complemented
149C3×C5—21no—
150C3×C5D3×C11×D1311yescharacteristic, complemented
151C3×C5C2×C11×D3911yescharacteristic, complemented
152C13C5×D32×C1111yescharacteristic, complemented, Sylow
153C2×D3—391no—
154C2×D3—391no—
155C11C5×D3×D3911yescharacteristic, direct product factor, Sylow
156C2×C5—31no—
157C2×C5—391no—
158C2×C5—1171no—
159C32C2×C5×C11×D1311yescharacteristic, complemented, Sylow
160C2×C3—31no—
161C2×C3—391no—
162D3—131no—
163D3—391no—
164D3—391no—
165D3—781no—
166D3C5×C11×D3911yescharacteristic, direct product factor
167C5D3×C11×D3911yescharacteristic, direct product factor, Sylow
168C22—1171noSylow
169C3—21no—
170C3C5×D3×C11×D1311yescharacteristic, complemented
171C3C2×C5×C11×D3911yescharacteristic, complemented
172C2—31no—
173C2—391no—
174C2—1171no—
subgroupG/H
center, hypercenterC5×C11D3×D39
commutator, cosocle, hypocenterC32×C13C22×C5×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C32×C13
UCSC1 ◁ C5×C11

Complements

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

NH ≅ G/Ntype
1. C3×C5×D3×C11×C13C2semidirect
2. C3×C5×C11×D39C2semidirect
3. C5×C11×C3⋊D39C2semidirect
6. C32×C5×C11×C13C22semidirect
7. D3×C11×D39C5direct (N × H)
11. C5×C11×D39D3direct (N × H)
12. C5×D3×C11×C13D3semidirect
16. C11×C3⋊D39C2×C5semidirect
17. C3×C11×D39C2×C5semidirect
18. C3×D3×C11×C13C2×C5semidirect
19. C5×D3×D39C11direct (N × H)
21. C3×C5×C11×C13C2×D3semidirect
22. C3×C5×C11×C13C2×D3semidirect
29. C32×C11×C13C22×C5semidirect
30. C5×C3⋊D39C2×C11semidirect
31. C3×C5×D39C2×C11semidirect
32. C3×C5×D3×C13C2×C11semidirect
35. C3×C5×D3×C11D13semidirect
40. C11×D39C5×D3direct (N × H)
41. D3×C11×C13C5×D3semidirect
45. C5×C11×C13D32semidirect
48. C32×C5×C13C22×C11semidirect
50. C32×C5×C11C2×D13semidirect
51. D3×D39C5×C11direct (N × H)
53. C3×C11×C13C2×C5×D3semidirect
54. C3×C11×C13C2×C5×D3semidirect
60. C5×D39D3×C11direct (N × H)
61. C5×D3×C13D3×C11semidirect
69. C5×D3×C11D39direct (N × H)
74. C3⋊D39C2×C5×C11semidirect
75. C3×D39C2×C5×C11semidirect
76. C3×D3×C13C2×C5×C11semidirect
80. C3×D3×C11C5×D13semidirect
82. C3×C5×C13C2×D3×C11semidirect
83. C3×C5×C13C2×D3×C11semidirect
86. C3×C5×C11D3×D13semidirect
87. C3×C5×C11C2×D39semidirect
90. C11×C13C5×D32semidirect
96. C32×C13C22×C5×C11semidirect
100. C32×C11C2×C5×D13semidirect
103. C3×C5×D3C11×D13semidirect
108. D39C5×D3×C11direct (N × H)
110. D3×C13C5×D3×C11semidirect
117. D3×C11C5×D39direct (N × H)
118. C5×C13D32×C11semidirect
121. C5×C11D3×D39direct (N × H)
123. C32×C5C2×C11×D13semidirect
126. C3×C13C2×C5×D3×C11semidirect
127. C3×C13C2×C5×D3×C11semidirect
130. C3×C11C5×D3×D13semidirect
131. C3×C11C2×C5×D39semidirect
138. C5×D3C11×D39direct (N × H)
148. C3×D3C5×C11×D13semidirect
150. C3×C5D3×C11×D13semidirect
151. C3×C5C2×C11×D39semidirect
152. C13C5×D32×C11semidirect
155. C11C5×D3×D39direct (N × H)
159. C32C2×C5×C11×D13semidirect
166. D3C5×C11×D39direct (N × H)
167. C5D3×C11×D39direct (N × H)
170. C3C5×D3×C11×D13semidirect
171. C3C2×C5×C11×D39semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D3×C11×C132
C3×C5×C11×D392
C5×C11×C3⋊D392
C2×C5×C11×D393
C5×D3×C11×D133
D3×C11×D395
C5×D3×D3911
C5×D32×C1113