Finite Group Databasebeta

← #37561389

Subgroups — #37561389

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
1C3⋊(C5⋊#11716321)C211yesmaximal, characteristic, complemented
2C5×C3⋊#11716325C211yesmaximal, characteristic, complemented
3C3×C5⋊#11716327C211yesmaximal, characteristic, complemented
4D21⋊D95C311yesmaximal, characteristic, complemented
5#11716325⋊D5—31nomaximal
6C3×C5×#87704C2211yescharacteristic, complemented, Hall
7#11716327⋊D3—51nomaximal, Hall
8C5⋊#11716327—21no—
9C5⋊#11716327D311yescharacteristic, complemented
10C5⋊#11716321—31no—
11C5×#11716325—31no—
12C7×D285C2×C311yescharacteristic, complemented
13C5×C19×D21C2×C311yescharacteristic, complemented
14C3×D665C2×C311yescharacteristic, complemented
15D3×C5⋊(D19⋊C3)—71nomaximal, Hall
16D7×D95—31noHall
17C3⋊#11716321—51no—
18C3⋊#11716325D511yescharacteristic, complemented
19C3×#11716327—51no—
20C3×C5×C7×C19C22×C311yescharacteristic, complemented
21C5×#87704—21no—
22C5×#87704C2×D311yescharacteristic, complemented
23C3⋊(C5⋊(D19⋊C3))—141no—
24C5×D3×C19⋊C3—71no—
25C3×C5⋊(D19⋊C3)—71no—
26D21⋊D19—51no—
27#11716321⋊C2—151no—
28D665C3×D311yescharacteristic, complemented
29C7×D95—31no—
30C5×D7×C19—31no—
31D15⋊AGL(1,𝔽7)—191nomaximal, Hall
32C3×#87704C2×D511yescharacteristic, complemented, Hall
33D3×D95—71no—
34C2×C5⋊(D19⋊C3)—211no—
35C3×C5×C19⋊C3—141noHall
36C19×D21C3×D511yescharacteristic, complemented
37C7×D57—51no—
38C3×D133—51no—
39#11716327—51no—
40#11716327—101no—
41#11716325—31no—
42#11716321—151no—
43D3×D19⋊C3—351noHall
44C5×C7×C19C2×C3×D311yescharacteristic, complemented, Hall
45ΓL(1,𝔽8)×D15—191no—
46C5×C3⋊AGL(1,𝔽7)—381no—
47C3×C5⋊AGL(1,𝔽7)—191no—
48D285AGL(1,𝔽7)11yescharacteristic, complemented
49C5×D3×C19—71no—
50C3×D95—71no—
51C2×C5×C19⋊C3—211no—
52C5⋊(D19⋊C3)—71no—
53C5⋊(D19⋊C3)—141no—
54C5⋊(D19⋊C3)—421no—
55D7×D19—151noHall
56D15⋊D7—191no—
57D5×AGL(1,𝔽7)—571no—
58C3×C7×C19C2×C3×D511yescharacteristic, complemented
59#87704—21no—
60#87704D3×D511yescharacteristic, complemented
61C2×D95—211noHall
62C3⋊(D19⋊C3)—701no—
63D3×C19⋊C3—71no—
64C3×D19⋊C3—351no—
65C3×C5×ΓL(1,𝔽8)—381noHall
66C3×C5×C19C2×AGL(1,𝔽7)11yescharacteristic, complemented
67C5×C19⋊C3—141no—
68C5×C19⋊C3—141no—
69D133—51no—
70C7×D19—151no—
71D7×C19—31no—
72D3×AGL(1,𝔽7)—951noHall
73D3×D19—351no—
74C2×D19⋊C3—1051no—
75C7×D15—191no—
76C5×D21D19⋊C311yescharacteristic, complemented
77C3×D35—191no—
78C5⋊AGL(1,𝔽7)—191no—
79C5⋊AGL(1,𝔽7)—381no—
80D5×ΓL(1,𝔽8)—571no—
81C5×AGL(1,𝔽7)—571no—
82C2×C5×C19—211no—
83D95—31no—
84D95—71no—
85C3×D3×D5—1331noHall
86C3×C19⋊C3—141noHall
87D5×D7—571noHall
88C7×C19C3×D3×D511yescharacteristic, complemented, Hall
89C3⋊AGL(1,𝔽7)—381no—
90D3×ΓL(1,𝔽8)—951no—
91C3×AGL(1,𝔽7)—951no—
92D57—51no—
93C3×D19—351no—
94D3×C19—71no—
95C2×C19⋊C3—211no—
96D19⋊C3—351no—
97D19⋊C3—701no—
98D19⋊C3—2101no—
99C3×C5×C7C2×D19⋊C311yescharacteristic, complemented
100C5×ΓL(1,𝔽8)—191no—
101C5×ΓL(1,𝔽8)—761no—
102C5×C19D3×AGL(1,𝔽7)11yescharacteristic, complemented, Hall
103C3×D15—2661no—
104C3×C5×D3—2661no—
105C32×D5—1331no—
106D3×D7—951no—
107C2×AGL(1,𝔽7)—2851no—
108C2×D19—1051noHall
109D35—191no—
110C5×D7—31no—
111C7×D5—571no—
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
119D21C5⋊(D19⋊C3)11yescharacteristic, complemented
120C3×D7—951no—
121D3×C7—951no—
122C2×ΓL(1,𝔽8)—2851no—
123AGL(1,𝔽7)—951no—
124AGL(1,𝔽7)—1141no—
125AGL(1,𝔽7)—1901no—
126C2×C19—211no—
127D19—151no—
128D19—351no—
129C2×C3×D3—6651noHall
130C5×C7D3×D19⋊C311yescharacteristic, complemented, Hall
131C2×C3×C5—7981no—
132D15—191no—
133C3×D5—2661no—
134C3×D5—7981no—
135C3×D5—1331no—
136C3×D5—1331no—
137C5×D3—71no—
138C2×D7—2851noHall
139C3×C7C2×C5⋊(D19⋊C3)11yescharacteristic, complemented
140ΓL(1,𝔽8)—381no—
141ΓL(1,𝔽8)—761no—
142C2×D5—3991noHall
143C19D15⋊AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
144C2×C32—6651no—
145C3×D3—2661no—
146C3×D3—13301no—
147C3×C5—5321no—
148C3×C5—5321no—
149C3×C5#11716321⋊C211yescharacteristic, complemented
150C2×C7—2851no—
151D7—31no—
152D7—951no—
153C22×C3—19951no—
154C2×D3—6651no—
155C2×C5—211no—
156D5—571no—
157D5—1331no—
158C32—5321noSylow
159C7D3×C5⋊(D19⋊C3)11yescharacteristic, complemented, Sylow
160C2×C3—7981no—
161C2×C3—13301no—
162C2×C3—39901no—
163C2×C3—6651no—
164C2×C3—6651no—
165D3—71no—
166D3—951no—
167C5#11716327⋊D311yescharacteristic, complemented, Sylow
168C22—19951noSylow
169C3—5321no—
170C3—5321no—
171C3#11716325⋊D511yescharacteristic, complemented
172C2—211no—
173C2—2851no—
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. C3⋊(C5⋊#11716321)C2semidirect
2. C5×C3⋊#11716325C2semidirect
3. C3×C5⋊#11716327C2semidirect
4. D21⋊D95C3semidirect
6. C3×C5×#87704C22semidirect
9. C5⋊#11716327D3semidirect
12. C7×D285C2×C3semidirect
13. C5×C19×D21C2×C3semidirect
14. C3×D665C2×C3semidirect
18. C3⋊#11716325D5semidirect
20. C3×C5×C7×C19C22×C3semidirect
22. C5×#87704C2×D3semidirect
28. D665C3×D3semidirect
32. C3×#87704C2×D5semidirect
36. C19×D21C3×D5semidirect
44. C5×C7×C19C2×C3×D3semidirect
48. D285AGL(1,𝔽7)semidirect
58. C3×C7×C19C2×C3×D5semidirect
60. #87704D3×D5semidirect
66. C3×C5×C19C2×AGL(1,𝔽7)semidirect
76. C5×D21D19⋊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
119. D21C5⋊(D19⋊C3)semidirect
130. C5×C7D3×D19⋊C3semidirect
139. C3×C7C2×C5⋊(D19⋊C3)semidirect
143. C19D15⋊AGL(1,𝔽7)semidirect
149. C3×C5#11716321⋊C2semidirect
159. C7D3×C5⋊(D19⋊C3)semidirect
167. C5#11716327⋊D3semidirect
171. C3#11716325⋊D5semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C5⋊#11716321)2
C5×C3⋊#117163252
C3×C5⋊#117163272
D21⋊D953
#11716325⋊D53
#11716327⋊D35
D3×C5⋊(D19⋊C3)7
D15⋊AGL(1,𝔽7)19