Finite Group Databasebeta

← C5×#10587721⋊D3 #30655396

Subgroups — C5×#10587721⋊D3 #30655396

Order 16380.

176 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 46 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
1C5×C3⋊#10587717C211yesmaximal, characteristic, complemented
2C5×C3⋊#10587723C211yesmaximal, characteristic, complemented
3C3×C5×#10587721C211yesmaximal, characteristic, complemented
4C5×D7×D39C311yesmaximal, characteristic, complemented
5C5×#10587717⋊C2—31nomaximal
6C3×C5×#63271C2211yescharacteristic, complemented, Hall
7#10587721⋊D3C511yesmaximal, characteristic, direct product factor, Hall
8C5×#10587723—31no—
9C5×#10587721—21no—
10C5×#10587721D311yescharacteristic, complemented
11C5×#10587717—31no—
12C5×D273C2×C311yescharacteristic, complemented
13C5×C7×D39C2×C311yescharacteristic, complemented
14C3×C5×C13×D7C2×C311yescharacteristic, complemented
15C2×C5×C3⋊(D13⋊C3)—71nomaximal, Hall
16C5×D7×D13—31noHall
17C3⋊#10587723C2×C511yescharacteristic, complemented
18C3⋊#10587717C2×C511yescharacteristic, complemented
19C3×#10587721C2×C511yescharacteristic, complemented
20C3×C5×C7×C13C22×C311yescharacteristic, complemented
21C5×#63271—21no—
22C5×#63271C2×D311yescharacteristic, complemented
23C5×D3×AGL(1,𝔽7)—131nomaximal, Hall
24C2×C3×C5×C13⋊C3—71no—
25C5×C3⋊(D13⋊C3)—71no—
26C5×C3⋊(D13⋊C3)—71no—
27D7×D39C3×C511yescharacteristic, complemented
28#10587717⋊C2—31no—
29C5×D91—31no—
30C5×C13×D7C3×D311yescharacteristic, complemented
31C5×C7×D13—31no—
32C3×#63271C22×C511yescharacteristic, complemented, Hall
33C2×C5×D39—71no—
34C2×C5×D13⋊C3—211no—
35C5×C3⋊AGL(1,𝔽7)—131no—
36C5×D3×ΓL(1,𝔽8)—131no—
37C3×C5×AGL(1,𝔽7)—131no—
38C3×C5×C13⋊C3—71noHall
39D273C2×C3×C511yescharacteristic, complemented
40C7×D39C2×C3×C511yescharacteristic, complemented
41C3×C13×D7C2×C3×C511yescharacteristic, complemented
42#10587723—31no—
43#10587721—21no—
44#10587721C5×D311yescharacteristic, complemented
45#10587717—31no—
46C2×C3⋊(D13⋊C3)—71noHall
47C5×C7×C13C2×C3×D311yescharacteristic, complemented, Hall
48C5×D3×D7—131no—
49C2×C5×AGL(1,𝔽7)—391no—
50C2×C3×C5×C13—71no—
51C5×D39—71no—
52C5×D39AGL(1,𝔽7)11yescharacteristic, complemented
53C2×C5×C13⋊C3—71no—
54C2×C5×C13⋊C3—141no—
55C5×D13⋊C3—211no—
56C5×D13⋊C3—211no—
57D7×D13—31noHall
58C3×C5×ΓL(1,𝔽8)—131noHall
59C3×C7×C13C22×C3×C511yescharacteristic, complemented
60#63271—21no—
61#63271C2×C5×D311yescharacteristic, complemented
62C2×C5×D13—211noHall
63D3×AGL(1,𝔽7)—131noHall
64C2×C3×C13⋊C3—71no—
65C3⋊(D13⋊C3)—71no—
66C3⋊(D13⋊C3)—71no—
67C5×D21—131no—
68C5×D3×C7—131no—
69C3×C5×D7D13⋊C311yescharacteristic, complemented
70C2×C5×ΓL(1,𝔽8)—391no—
71C5×AGL(1,𝔽7)—131no—
72C5×AGL(1,𝔽7)—261no—
73C5×AGL(1,𝔽7)—391no—
74C3×C5×C13C2×AGL(1,𝔽7)11yescharacteristic, complemented
75C5×C13⋊C3—71no—
76C5×C13⋊C3—141no—
77D91—31no—
78C7×D13—31no—
79C13×D7C3×C5×D311yescharacteristic, complemented
80C2×C3×C5×D3—911noHall
81C2×D39—71no—
82C2×D13⋊C3—211no—
83C2×C5×D7—391noHall
84C2×C5×C13—71no—
85C5×D13—31no—
86C5×D13—211no—
87C3⋊AGL(1,𝔽7)—131no—
88D3×ΓL(1,𝔽8)—131no—
89C3×AGL(1,𝔽7)—131no—
90C3×C13⋊C3—71noHall
91C3×C5×C7C2×D13⋊C311yescharacteristic, complemented
92C5×ΓL(1,𝔽8)—131no—
93C5×ΓL(1,𝔽8)—261no—
94C7×C13C2×C3×C5×D311yescharacteristic, complemented, Hall
95C2×C32×C5—911no—
96C3×C5×D3—911no—
97C3×C5×D3—911no—
98D3×D7—131no—
99C2×AGL(1,𝔽7)—391no—
100C2×C3×C13—71no—
101D39—71no—
102D39C5×AGL(1,𝔽7)11yescharacteristic, complemented
103C2×C13⋊C3—71no—
104C2×C13⋊C3—141no—
105D13⋊C3—211no—
106D13⋊C3—211no—
107C2×C5×C7—391no—
108C5×D7—391no—
109C5×D7C3⋊(D13⋊C3)11yescharacteristic, complemented
110C5×C13D3×AGL(1,𝔽7)11yescharacteristic, complemented, Hall
111C3×ΓL(1,𝔽8)—131noHall
112C22×C3×C5—2731no—
113C2×C5×D3—911no—
114C2×D13—211noHall
115C32×C5—911noHall
116D21—131no—
117C3×D7C5×D13⋊C311yescharacteristic, complemented
118D3×C7—131no—
119C2×ΓL(1,𝔽8)—391no—
120AGL(1,𝔽7)—131no—
121AGL(1,𝔽7)—261no—
122AGL(1,𝔽7)—391no—
123C3×C13C2×C5×AGL(1,𝔽7)11yescharacteristic, complemented
124C13⋊C3—71no—
125C13⋊C3—141no—
126C2×C3×D3—911noHall
127C5×C7C2×C3⋊(D13⋊C3)11yescharacteristic, complemented, Hall
128C2×C3×C5—71no—
129C2×C3×C5—2731no—
130C2×C3×C5—2731no—
131C2×C3×C5—911no—
132C2×C3×C5—1821no—
133C5×D3—131no—
134C5×D3—911no—
135C2×D7—391noHall
136C2×C13—71no—
137D13—31no—
138D13—211no—
139C3×C7C2×C5×D13⋊C311yescharacteristic, complemented
140ΓL(1,𝔽8)—131no—
141ΓL(1,𝔽8)—261no—
142C22×C5—2731noHall
143C2×C32—911no—
144C3×D3—911no—
145C3×D3—911no—
146C3×C5—911no—
147C3×C5—1821no—
148C3×C5#10587717⋊C211yescharacteristic, complemented
149C2×C7—391no—
150D7—391no—
151D7C5×C3⋊(D13⋊C3)11yescharacteristic, complemented
152C13C5×D3×AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
153C22×C3—2731no—
154C2×D3—911no—
155C2×C5—71no—
156C2×C5—2731no—
157C2×C5—391no—
158C32—911noSylow
159C7C2×C5×C3⋊(D13⋊C3)11yescharacteristic, complemented, Sylow
160C2×C3—71no—
161C2×C3—2731no—
162C2×C3—2731no—
163C2×C3—911no—
164C2×C3—1821no—
165D3—131no—
166D3—911no—
167C5#10587721⋊D311yescharacteristic, direct product factor, Sylow
168C22—2731noSylow
169C3—911no—
170C3—1821no—
171C3C5×#10587717⋊C211yescharacteristic, complemented
172C2—71no—
173C2—2731no—
174C2—391no—
subgroupG/H
center, hypercenterC5#10587721⋊D3
commutator, cosocle, hypocenterC3×C7×C13C22×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C13C22×C3
LCSG ▷ C3×C7×C13
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×C3⋊#10587717C2semidirect
2. C5×C3⋊#10587723C2semidirect
3. C3×C5×#10587721C2semidirect
4. C5×D7×D39C3semidirect
6. C3×C5×#63271C22semidirect
7. #10587721⋊D3C5direct (N × H)
10. C5×#10587721D3semidirect
12. C5×D273C2×C3semidirect
13. C5×C7×D39C2×C3semidirect
14. C3×C5×C13×D7C2×C3semidirect
17. C3⋊#10587723C2×C5semidirect
18. C3⋊#10587717C2×C5semidirect
19. C3×#10587721C2×C5semidirect
20. C3×C5×C7×C13C22×C3semidirect
22. C5×#63271C2×D3semidirect
27. D7×D39C3×C5semidirect
30. C5×C13×D7C3×D3semidirect
32. C3×#63271C22×C5semidirect
39. D273C2×C3×C5semidirect
40. C7×D39C2×C3×C5semidirect
41. C3×C13×D7C2×C3×C5semidirect
44. #10587721C5×D3semidirect
47. C5×C7×C13C2×C3×D3semidirect
52. C5×D39AGL(1,𝔽7)semidirect
59. C3×C7×C13C22×C3×C5semidirect
61. #63271C2×C5×D3semidirect
69. C3×C5×D7D13⋊C3semidirect
74. C3×C5×C13C2×AGL(1,𝔽7)semidirect
79. C13×D7C3×C5×D3semidirect
91. C3×C5×C7C2×D13⋊C3semidirect
94. C7×C13C2×C3×C5×D3semidirect
102. D39C5×AGL(1,𝔽7)semidirect
109. C5×D7C3⋊(D13⋊C3)semidirect
110. C5×C13D3×AGL(1,𝔽7)semidirect
117. C3×D7C5×D13⋊C3semidirect
123. C3×C13C2×C5×AGL(1,𝔽7)semidirect
127. C5×C7C2×C3⋊(D13⋊C3)semidirect
139. C3×C7C2×C5×D13⋊C3semidirect
148. C3×C5#10587717⋊C2semidirect
151. D7C5×C3⋊(D13⋊C3)semidirect
152. C13C5×D3×AGL(1,𝔽7)semidirect
159. C7C2×C5×C3⋊(D13⋊C3)semidirect
167. C5#10587721⋊D3direct (N × H)
171. C3C5×#10587717⋊C2semidirect

Maximal subgroups

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

subgroupindex
C5×C3⋊#105877172
C5×C3⋊#105877232
C3×C5×#105877212
C5×D7×D393
C5×#10587717⋊C23
#10587721⋊D35
C2×C5×C3⋊(D13⋊C3)7
C5×D3×AGL(1,𝔽7)13