Finite Group Databasebeta

← D15⋊#11716327 #37561391

Subgroups — D15⋊#11716327 #37561391

Order 23940.

176 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 35 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
1D15×#87704C211yesmaximal, characteristic, complemented
2C5×C3⋊#11716327C211yesmaximal, characteristic, complemented
3C3×C5⋊#11716327C211yesmaximal, characteristic, complemented
4D15⋊D133C311yesmaximal, characteristic, complemented
5D5×#11716327—31nomaximal
6C3×C5×#87704C2211yescharacteristic, complemented, Hall
7D3×#11716327—51nomaximal, Hall
8C5⋊#11716327—21no—
9C5⋊#11716327D311yescharacteristic, complemented
10D5×#87704—31no—
11C5×#11716327—31no—
12C7×C19×D15C2×C311yescharacteristic, complemented
13C5×D399C2×C311yescharacteristic, complemented
14C3×D665C2×C311yescharacteristic, complemented
15D15⋊(D19⋊C3)—71nomaximal, Hall
16D5×D133—31noHall
17D3×#87704—51no—
18C3⋊#11716327D511yescharacteristic, complemented
19C3×#11716327—51no—
20C3×C5×C7×C19C22×C311yescharacteristic, complemented
21C5×#87704—21no—
22C5×#87704C2×D311yescharacteristic, complemented
23D15×C19⋊C3—141no—
24C5×C3⋊(D19⋊C3)—71no—
25C3×C5⋊(D19⋊C3)—71no—
26D3×D133—51no—
27C2×#11716327—151no—
28D665C3×D311yescharacteristic, complemented
29C7×D5×C19—31no—
30C5×D133—31no—
31D15⋊AGL(1,𝔽7)—191nomaximal, Hall
32C3×#87704C2×D511yescharacteristic, complemented, Hall
33D15⋊D19—71no—
34D5×D19⋊C3—211no—
35C3×C5×C19⋊C3—141noHall
36D399C3×D511yescharacteristic, complemented
37D3×C7×C19—51no—
38C3×D133—51no—
39C2×#87704—151no—
40#11716327—31no—
41#11716327—51no—
42#11716327—101no—
43D3×D19⋊C3—351noHall
44C5×C7×C19C2×C3×D311yescharacteristic, complemented, Hall
45ΓL(1,𝔽8)×D15—191no—
46C5×C3⋊AGL(1,𝔽7)—191no—
47C3×C5⋊AGL(1,𝔽7)—191no—
48C19×D15AGL(1,𝔽7)11yescharacteristic, complemented
49C5×D57—71no—
50C3×D95—71no—
51C5⋊(D19⋊C3)—71no—
52C5⋊(D19⋊C3)—141no—
53D5×C19⋊C3—421no—
54C5×D19⋊C3—211no—
55C2×D133—151noHall
56D15⋊D7—191no—
57D5×AGL(1,𝔽7)—571no—
58C3×C7×C19C2×C3×D511yescharacteristic, complemented
59#87704—21no—
60#87704D3×D511yescharacteristic, complemented
61D5×D19—211noHall
62C3⋊(D19⋊C3)—71no—
63D3×C19⋊C3—701no—
64C3×D19⋊C3—351no—
65C3×C5×ΓL(1,𝔽8)—191noHall
66C3×C5×C19C2×AGL(1,𝔽7)11yescharacteristic, complemented
67C5×C19⋊C3—141no—
68C5×C19⋊C3—141no—
69C2×C7×C19—151no—
70D133—31no—
71D133—51no—
72D3×AGL(1,𝔽7)—951noHall
73D3×D19—351no—
74C2×D19⋊C3—1051no—
75C7×D15D19⋊C311yescharacteristic, complemented
76C5×D21—191no—
77C3×D35—191no—
78C5⋊AGL(1,𝔽7)—191no—
79C5⋊AGL(1,𝔽7)—381no—
80D5×ΓL(1,𝔽8)—1141no—
81C5×AGL(1,𝔽7)—571no—
82D95—71no—
83C5×D19—211no—
84D5×C19—31no—
85C3×D3×D5—1331noHall
86C3×C19⋊C3—141noHall
87D5×D7—571noHall
88C7×C19C3×D3×D511yescharacteristic, complemented, Hall
89C3⋊AGL(1,𝔽7)—191no—
90D3×ΓL(1,𝔽8)—1901no—
91C3×AGL(1,𝔽7)—951no—
92D57—71no—
93C3×D19—351no—
94D3×C19—51no—
95C2×C19⋊C3—2101no—
96D19⋊C3—211no—
97D19⋊C3—351no—
98D19⋊C3—701no—
99C3×C5×C7C2×D19⋊C311yescharacteristic, complemented
100C5×ΓL(1,𝔽8)—381no—
101C5×ΓL(1,𝔽8)—761no—
102C5×C19D3×AGL(1,𝔽7)11yescharacteristic, complemented, Hall
103C3×D15—2661no—
104C3×C5×D3—1331no—
105C32×D5—1331no—
106D3×D7—951no—
107C2×AGL(1,𝔽7)—2851no—
108C2×D19—1051noHall
109D35—191no—
110C5×D7—571no—
111C7×D5—31no—
112C3×ΓL(1,𝔽8)—381noHall
113C2×C3×D5—3991no—
114D3×D5—1331no—
115C3×C19D5×AGL(1,𝔽7)11yescharacteristic, complemented
116C19⋊C3—141no—
117C19⋊C3—281no—
118C32×C5—2661noHall
119D21—191no—
120C3×D7—951no—
121D3×C7—51no—
122C2×ΓL(1,𝔽8)—5701no—
123AGL(1,𝔽7)—571no—
124AGL(1,𝔽7)—951no—
125AGL(1,𝔽7)—1901no—
126C2×C19—151no—
127D19—211no—
128D19—351no—
129C2×C3×D3—6651noHall
130C5×C7D3×D19⋊C311yescharacteristic, complemented, Hall
131C2×C3×C5—3991no—
132D15#1171632711yescharacteristic, complemented
133C3×D5—2661no—
134C3×D5—7981no—
135C3×D5—1331no—
136C3×D5—1331no—
137C5×D3—1331no—
138C2×D7—2851noHall
139C3×C7D5×D19⋊C311yescharacteristic, complemented
140ΓL(1,𝔽8)—381no—
141ΓL(1,𝔽8)—761no—
142C2×D5—3991noHall
143C19D15⋊AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
144C2×C32—6651no—
145C3×D3—13301no—
146C3×D3—1331no—
147C3×C5—2661no—
148C3×C5—5321no—
149C3×C5C2×#1171632711yescharacteristic, complemented
150C2×C7—151no—
151D7—571no—
152D7—951no—
153C22×C3—19951no—
154C2×D3—6651no—
155C2×C5—3991no—
156D5—31no—
157D5—1331no—
158C32—2661noSylow
159C7D15⋊(D19⋊C3)11yescharacteristic, complemented, Sylow
160C2×C3—13301no—
161C2×C3—3991no—
162C2×C3—39901no—
163C2×C3—6651no—
164C2×C3—6651no—
165D3—51no—
166D3—1331no—
167C5D3×#1171632711yescharacteristic, complemented, Sylow
168C22—19951noSylow
169C3—2661no—
170C3—5321no—
171C3D5×#1171632711yescharacteristic, complemented
172C2—151no—
173C2—3991no—
174C2—6651no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C7×C19C22×C3
LCSG ▷ C3×C5×C7×C19
UCSC1

Complements

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

NH ≅ G/Ntype
1. D15×#87704C2semidirect
2. C5×C3⋊#11716327C2semidirect
3. C3×C5⋊#11716327C2semidirect
4. D15⋊D133C3semidirect
6. C3×C5×#87704C22semidirect
9. C5⋊#11716327D3semidirect
12. C7×C19×D15C2×C3semidirect
13. C5×D399C2×C3semidirect
14. C3×D665C2×C3semidirect
18. C3⋊#11716327D5semidirect
20. C3×C5×C7×C19C22×C3semidirect
22. C5×#87704C2×D3semidirect
28. D665C3×D3semidirect
32. C3×#87704C2×D5semidirect
36. D399C3×D5semidirect
44. C5×C7×C19C2×C3×D3semidirect
48. C19×D15AGL(1,𝔽7)semidirect
58. C3×C7×C19C2×C3×D5semidirect
60. #87704D3×D5semidirect
66. C3×C5×C19C2×AGL(1,𝔽7)semidirect
75. C7×D15D19⋊C3semidirect
88. C7×C19C3×D3×D5semidirect
99. C3×C5×C7C2×D19⋊C3semidirect
102. C5×C19D3×AGL(1,𝔽7)semidirect
115. C3×C19D5×AGL(1,𝔽7)semidirect
130. C5×C7D3×D19⋊C3semidirect
132. D15#11716327semidirect
139. C3×C7D5×D19⋊C3semidirect
143. C19D15⋊AGL(1,𝔽7)semidirect
149. C3×C5C2×#11716327semidirect
159. C7D15⋊(D19⋊C3)semidirect
167. C5D3×#11716327semidirect
171. C3D5×#11716327semidirect

Maximal subgroups

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

subgroupindex
D15×#877042
C5×C3⋊#117163272
C3×C5⋊#117163272
D15⋊D1333
D5×#117163273
D3×#117163275
D15⋊(D19⋊C3)7
D15⋊AGL(1,𝔽7)19