Finite Group Databasebeta

← D3×D2145 #38788237

Subgroups — D3×D2145 #38788237

Order 25740.

176 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 52 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×D2145C211yesmaximal, characteristic, complemented
3C3⋊D2145C211yesmaximal, characteristic, complemented
4C2×D2145—31nomaximal
5D3×D715—31nomaximal
6C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
7D3×D429—51nomaximal, Hall
8D2145—31no—
9D2145—31no—
10D2145—61no—
11D2145D311yescharacteristic, direct product factor
12C5×D3×C11×C13D311yescharacteristic, complemented
13C3×D715—31no—
14C2×C3×C5×C11×C13—31no—
15C2×D715—91noHall
16C3⋊D429—51no—
17C3×D429—51no—
18C3×D3×C11×C13D511yescharacteristic, complemented
19D3×D195—111nomaximal, Hall
20C3×C5×C11×C13—21no—
21C3×C5×C11×C13C2×D311yescharacteristic, complemented
22C3×C5×C11×C13C2×D311yescharacteristic, complemented
23D3×D165—131nomaximal, Hall
24C2×D429—151no—
25D3×D143—151no—
26C2×C5×C11×C13—31no—
27D715—31no—
28D715—91no—
29C32×C11×C13C2×D511yescharacteristic, complemented, Hall
30C3⋊D195—111no—
31C3×D195—111no—
32C3×C5×D3×C13D1111yescharacteristic, complemented
33C3⋊D165—131no—
34C3×D165—131no—
35C3×C5×D3×C11D1311yescharacteristic, complemented
36C2×C3×C11×C13—31no—
37D429—51no—
38D429—151no—
39D429—151no—
40D429—301no—
41D3×C11×C13D1511yescharacteristic, complemented
42C3×D143—151no—
43C2×D195—331no—
44D3×D65—331no—
45C5×C11×C13D3211yescharacteristic, complemented, Hall
46C2×D165—391no—
47D3×D55—391no—
48C32×C5×C13C2×D1111yescharacteristic, complemented, Hall
49C2×D143—451noHall
50C32×C5×C11C2×D1311yescharacteristic, complemented, Hall
51D3×D39—551noHall
52C3×C11×C13—21no—
53C3×C11×C13D3×D511yescharacteristic, complemented
54C3×C11×C13C2×D1511yescharacteristic, complemented
55D3×D33—651noHall
56C2×C3×C5×C13—31no—
57D195—111no—
58D195—331no—
59D195—331no—
60D195—661no—
61C5×D3×C13D3311yescharacteristic, complemented
62C3×D65—331no—
63C2×C3×C5×C11—31no—
64D165—131no—
65D165—391no—
66D165—391no—
67D165—781no—
68C5×D3×C11D3911yescharacteristic, complemented
69C3×D55—391no—
70C2×C11×C13—31no—
71D143—151no—
72D143—451no—
73C2×D65—991noHall
74C3⋊D39—551no—
75C3×D39—551no—
76C3×D3×C13D5511yescharacteristic, complemented
77C2×D55—1171noHall
78C3⋊D33—651no—
79C3×D33—651no—
80C3×D3×C11D6511yescharacteristic, complemented
81C3×C5×C13—21no—
82C3×C5×C13D3×D1111yescharacteristic, complemented
83C3×C5×C13C2×D3311yescharacteristic, complemented
84D3×D15—1431noHall
85C3×C5×C11—21no—
86C3×C5×C11D3×D1311yescharacteristic, complemented
87C3×C5×C11C2×D3911yescharacteristic, complemented
88C2×D39—1651no—
89D3×D13—1651no—
90C11×C13D3×D1511yescharacteristic, complemented, Hall
91C2×D33—1951no—
92D3×D11—1951no—
93C2×C5×C13—31no—
94D65—331no—
95D65—991no—
96C32×C13C2×D5511yescharacteristic, complemented, Hall
97C2×C5×C11—31no—
98D55—391no—
99D55—1171no—
100C32×C11C2×D6511yescharacteristic, complemented, Hall
101C3⋊D15—1431no—
102C3×D15—1431no—
103C3×C5×D3D14311yescharacteristic, complemented
104C2×C3×C13—31no—
105D39—551no—
106D39—3301no—
107D39—1651no—
108D39—1651no—
109C3×D13—1651no—
110D3×C13D16511yescharacteristic, complemented
111C2×C3×C11—31no—
112D33—651no—
113D33—3901no—
114D33—1951no—
115D33—1951no—
116C3×D11—1951no—
117D3×C11D19511yescharacteristic, complemented
118C5×C13D3×D3311yescharacteristic, complemented, Hall
119C2×D15—4291no—
120D3×D5—4291no—
121C5×C11D3×D3911yescharacteristic, complemented, Hall
122C2×D13—4951noHall
123C32×C5C2×D14311yescharacteristic, complemented, Hall
124C2×D11—5851noHall
125C3×C13—21no—
126C3×C13D3×D5511yescharacteristic, complemented
127C3×C13C2×D16511yescharacteristic, complemented
128D32—7151noHall
129C3×C11—21no—
130C3×C11D3×D6511yescharacteristic, complemented
131C3×C11C2×D19511yescharacteristic, complemented
132C2×C3×C5—31no—
133D15—8581no—
134D15—1431no—
135D15—4291no—
136D15—4291no—
137C3×D5—4291no—
138C5×D3D42911yescharacteristic, complemented
139C2×C13—31no—
140D13—1651no—
141D13—4951no—
142C2×C11—31no—
143D11—5851no—
144D11—1951no—
145C2×D5—12871noHall
146C3⋊D3—7151no—
147C3×D3—7151no—
148C3×D3D71511yescharacteristic, complemented
149C3×C5—21no—
150C3×C5D3×D14311yescharacteristic, complemented
151C3×C5C2×D42911yescharacteristic, complemented
152C13D3×D16511yescharacteristic, complemented, Sylow
153C2×D3—21451no—
154C2×D3—21451no—
155C11D3×D19511yescharacteristic, complemented, Sylow
156C2×C5—31no—
157D5—12871no—
158D5—4291no—
159C32C2×D71511yescharacteristic, complemented, Sylow
160C2×C3—31no—
161C2×C3—21451no—
162D3—21451no—
163D3—21451no—
164D3—42901no—
165D3—7151no—
166D3D214511yescharacteristic, direct product factor
167C5D3×D42911yescharacteristic, complemented, Sylow
168C22—64351noSylow
169C3—21no—
170C3D3×D71511yescharacteristic, complemented
171C3C2×D214511yescharacteristic, complemented
172C2—31no—
173C2—64351no—
174C2—21451no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C11×C13C22
LCSG ▷ C32×C5×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×D3×C11×C13C2semidirect
2. C3×D2145C2semidirect
3. C3⋊D2145C2semidirect
6. C32×C5×C11×C13C22semidirect
11. D2145D3direct (N × H)
12. C5×D3×C11×C13D3semidirect
18. C3×D3×C11×C13D5semidirect
21. C3×C5×C11×C13C2×D3semidirect
22. C3×C5×C11×C13C2×D3semidirect
29. C32×C11×C13C2×D5semidirect
32. C3×C5×D3×C13D11semidirect
35. C3×C5×D3×C11D13semidirect
41. D3×C11×C13D15semidirect
45. C5×C11×C13D32semidirect
48. C32×C5×C13C2×D11semidirect
50. C32×C5×C11C2×D13semidirect
53. C3×C11×C13D3×D5semidirect
54. C3×C11×C13C2×D15semidirect
61. C5×D3×C13D33semidirect
68. C5×D3×C11D39semidirect
76. C3×D3×C13D55semidirect
80. C3×D3×C11D65semidirect
82. C3×C5×C13D3×D11semidirect
83. C3×C5×C13C2×D33semidirect
86. C3×C5×C11D3×D13semidirect
87. C3×C5×C11C2×D39semidirect
90. C11×C13D3×D15semidirect
96. C32×C13C2×D55semidirect
100. C32×C11C2×D65semidirect
103. C3×C5×D3D143semidirect
110. D3×C13D165semidirect
117. D3×C11D195semidirect
118. C5×C13D3×D33semidirect
121. C5×C11D3×D39semidirect
123. C32×C5C2×D143semidirect
126. C3×C13D3×D55semidirect
127. C3×C13C2×D165semidirect
130. C3×C11D3×D65semidirect
131. C3×C11C2×D195semidirect
138. C5×D3D429semidirect
148. C3×D3D715semidirect
150. C3×C5D3×D143semidirect
151. C3×C5C2×D429semidirect
152. C13D3×D165semidirect
155. C11D3×D195semidirect
159. C32C2×D715semidirect
166. D3D2145direct (N × H)
167. C5D3×D429semidirect
170. C3D3×D715semidirect
171. C3C2×D2145semidirect

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×D21452
C3⋊D21452
C2×D21453
D3×D7153
D3×D4295
D3×D19511
D3×D16513