Finite Group Databasebeta

← D15⋊D399 #37561582

Subgroups — D15⋊D399 #37561582

Order 23940.

176 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 45 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×C7×C19×D15C211yesmaximal, characteristic, complemented
2C3×D1995C211yesmaximal, characteristic, complemented
3C5×C3⋊D399C211yesmaximal, characteristic, complemented
4D15⋊D133—31nomaximal
5D5×D399—31nomaximal
6C32×C5×C7×C19C2211yescharacteristic, complemented, Hall
7D3×D399—51nomaximal, Hall
8D1995D311yescharacteristic, complemented
9C7×C19×D15D311yescharacteristic, complemented
10C5×D399—31no—
11C5×D399—31no—
12C5×D399—61no—
13C3×D665—31no—
14C3×C7×D5×C19—31no—
15D15⋊D57—71nomaximal, Hall
16D5×D133—91noHall
17C3⋊D399D511yescharacteristic, complemented
18C3×D399—51no—
19C3×D3×C7×C19—51no—
20C3×C5×C7×C19—21no—
21C3×C5×C7×C19C2×D311yescharacteristic, complemented
22C3×C5×C7×C19C2×D311yescharacteristic, complemented
23C5×C3⋊D57—71no—
24C3×D285—71no—
25C3×C19×D15D711yescharacteristic, complemented
26C2×D399—151no—
27D3×D133—151no—
28D665—31no—
29C7×D5×C19—31no—
30C5×D133—91no—
31D15⋊D21—191nomaximal, Hall
32C32×C7×C19C2×D511yescharacteristic, complemented, Hall
33D15⋊D19—211no—
34D5×D57—211no—
35C32×C5×C19C2×D711yescharacteristic, complemented, Hall
36C2×C3×C7×C19—151no—
37D399—31no—
38D399—31no—
39D399—51no—
40D399—61no—
41D3×C7×C19—51no—
42C3×D133—151no—
43D3×D57—351noHall
44C5×C7×C19D3211yescharacteristic, complemented, Hall
45C5×C3⋊D21—191no—
46C3×D105—191no—
47C3×C7×D15D1911yescharacteristic, complemented
48D285—71no—
49C19×D15D2111yescharacteristic, complemented
50C5×D57—211no—
51C5×D57—211no—
52C5×D57—421no—
53C3×D95—211no—
54C3×D5×C19—31no—
55C2×D133—451noHall
56D15⋊D7—571no—
57D5×D21—571no—
58C3×C7×C19—21no—
59C3×C7×C19D3×D511yescharacteristic, complemented
60C3×C7×C19D3×D511yescharacteristic, complemented
61D5×D19—631noHall
62C3⋊D57—71no—
63C3×D57—351no—
64C3×D3×C19—51no—
65C32×C5×C7C2×D1911yescharacteristic, complemented, Hall
66C3×C5×C19—21no—
67C3×C5×C19D3×D711yescharacteristic, complemented
68C3×C5×C19C2×D2111yescharacteristic, complemented
69C2×C7×C19—151no—
70D133—91no—
71D133—151no—
72D3×D21—951noHall
73C2×D57—1051no—
74D3×D19—1051no—
75D105—191no—
76C7×D15D5711yescharacteristic, complemented
77C5×D21—571no—
78C5×D21—571no—
79C5×D21—1141no—
80C3×D35—571no—
81C3×C7×D5—31no—
82D95—211no—
83C5×D19—631no—
84D5×C19—31no—
85(C3⋊D3)⋊D5—1331noHall
86C32×C19D5×D711yescharacteristic, complemented, Hall
87D5×D7—1711noHall
88C7×C19(C3⋊D3)⋊D511yescharacteristic, complemented, Hall
89C3⋊D21—191no—
90C3×D21—951no—
91C3×D3×C7—51no—
92C2×C3×C19—151no—
93D57—211no—
94D57—211no—
95D57—351no—
96D57—421no—
97C3×D19—1051no—
98D3×C19—51no—
99C3×C5×C7—21no—
100C3×C5×C7D3×D1911yescharacteristic, complemented
101C3×C5×C7C2×D5711yescharacteristic, complemented
102C5×C19D3×D2111yescharacteristic, complemented, Hall
103C5×C3⋊D3—1331no—
104C3×D15—1331no—
105C3×D15D13311yescharacteristic, complemented
106C2×D21—2851no—
107D3×D7—2851no—
108C2×D19—3151noHall
109D35—571no—
110C5×D7—1711no—
111C7×D5—31no—
112C32×C7D5×D1911yescharacteristic, complemented, Hall
113D3×D5—3991no—
114D3×D5—3991no—
115C3×C19—21no—
116C3×C19D5×D2111yescharacteristic, complemented
117C3×C19D15⋊D711yescharacteristic, complemented
118C32×C5C2×D13311yescharacteristic, complemented, Hall
119C2×C3×C7—151no—
120D21—571no—
121D21—571no—
122D21—951no—
123D21—1141no—
124C3×D7—2851no—
125D3×C7—51no—
126C2×C19—151no—
127D19—631no—
128D19—1051no—
129D32—6651noHall
130C5×C7D3×D5711yescharacteristic, complemented, Hall
131D15—1331no—
132D15D39911yescharacteristic, complemented
133C3×D5—31no—
134C3×D5—3991no—
135C5×D3—7981no—
136C5×D3—3991no—
137C5×D3—3991no—
138C2×D7—8551noHall
139C3×C7—21no—
140C3×C7D5×D5711yescharacteristic, complemented
141C3×C7D15⋊D1911yescharacteristic, complemented
142C2×D5—11971noHall
143C19D15⋊D2111yescharacteristic, complemented, Sylow
144C3⋊D3—1331no—
145C3×D3—51no—
146C3×D3—6651no—
147C3×C5—21no—
148C3×C5D3×D13311yescharacteristic, complemented
149C3×C5C2×D39911yescharacteristic, complemented
150C2×C7—151no—
151D7—2851no—
152D7—1711no—
153C2×D3—19951no—
154C2×D3—19951no—
155C2×C5—11971no—
156D5—31no—
157D5—3991no—
158C32D5×D13311yescharacteristic, complemented, Sylow
159C7D15⋊D5711yescharacteristic, complemented, Sylow
160C2×C3—151no—
161C2×C3—19951no—
162D3—51no—
163D3—7981no—
164D3—3991no—
165D3—3991no—
166D3—6651no—
167C5D3×D39911yescharacteristic, complemented, Sylow
168C22—59851noSylow
169C3—21no—
170C3D5×D39911yescharacteristic, complemented
171C3D15⋊D13311yescharacteristic, complemented
172C2—151no—
173C2—11971no—
174C2—19951no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C19C22
LCSG ▷ C32×C5×C7×C19
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C7×C19×D15C2semidirect
2. C3×D1995C2semidirect
3. C5×C3⋊D399C2semidirect
6. C32×C5×C7×C19C22semidirect
8. D1995D3semidirect
9. C7×C19×D15D3semidirect
17. C3⋊D399D5semidirect
21. C3×C5×C7×C19C2×D3semidirect
22. C3×C5×C7×C19C2×D3semidirect
25. C3×C19×D15D7semidirect
32. C32×C7×C19C2×D5semidirect
35. C32×C5×C19C2×D7semidirect
44. C5×C7×C19D32semidirect
47. C3×C7×D15D19semidirect
49. C19×D15D21semidirect
59. C3×C7×C19D3×D5semidirect
60. C3×C7×C19D3×D5semidirect
65. C32×C5×C7C2×D19semidirect
67. C3×C5×C19D3×D7semidirect
68. C3×C5×C19C2×D21semidirect
76. C7×D15D57semidirect
86. C32×C19D5×D7semidirect
88. C7×C19(C3⋊D3)⋊D5semidirect
100. C3×C5×C7D3×D19semidirect
101. C3×C5×C7C2×D57semidirect
102. C5×C19D3×D21semidirect
105. C3×D15D133semidirect
112. C32×C7D5×D19semidirect
116. C3×C19D5×D21semidirect
117. C3×C19D15⋊D7semidirect
118. C32×C5C2×D133semidirect
130. C5×C7D3×D57semidirect
132. D15D399semidirect
140. C3×C7D5×D57semidirect
141. C3×C7D15⋊D19semidirect
143. C19D15⋊D21semidirect
148. C3×C5D3×D133semidirect
149. C3×C5C2×D399semidirect
158. C32D5×D133semidirect
159. C7D15⋊D57semidirect
167. C5D3×D399semidirect
170. C3D5×D399semidirect
171. C3D15⋊D133semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C19×D152
C3×D19952
C5×C3⋊D3992
D15⋊D1333
D5×D3993
D3×D3995
D15⋊D577
D15⋊D2119