Finite Group Databasebeta

← C5×D3×C7×D57 #37561553

Subgroups — C5×D3×C7×D57 #37561553

Order 23940.

176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 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×C7×C19C211yesmaximal, characteristic, complemented
2C3×C5×C7×D57C211yesmaximal, characteristic, complemented
3C5×C7×C3⋊D57C211yesmaximal, characteristic, complemented
4C2×C5×C7×D57—31nomaximal
5C5×D3×C7×D19—31nomaximal
6C32×C5×C7×C19C2211yescharacteristic, complemented, Hall
7D3×C7×D57C511yesmaximal, characteristic, direct product factor, Hall
8C5×C7×D57—31no—
9C5×C7×D57—31no—
10C5×C7×D57—61no—
11C5×C7×D57D311yescharacteristic, direct product factor
12C5×D3×C7×C19D311yescharacteristic, complemented
13C3×C5×C7×D19—31no—
14C2×C3×C5×C7×C19—31no—
15C5×D3×D57C711yesmaximal, characteristic, direct product factor, Hall
16C2×C5×C7×D19—91noHall
17C7×C3⋊D57C2×C511yescharacteristic, complemented
18C3×C7×D57C2×C511yescharacteristic, complemented
19C3×D3×C7×C19C2×C511yescharacteristic, complemented
20C3×C5×C7×C19—21no—
21C3×C5×C7×C19C2×D311yescharacteristic, complemented
22C3×C5×C7×C19C2×D311yescharacteristic, complemented
23C5×C3⋊D57C2×C711yescharacteristic, complemented
24C3×C5×D57C2×C711yescharacteristic, complemented
25C3×C5×D3×C19C2×C711yescharacteristic, complemented
26C2×C7×D57—31no—
27D3×C7×D19—31no—
28C2×C5×C7×C19—31no—
29C5×C7×D19—31no—
30C5×C7×D19—91no—
31C5×D32×C7—191nomaximal, Hall
32C32×C7×C19C22×C511yescharacteristic, complemented, Hall
33C2×C5×D57—31no—
34C5×D3×D19—31no—
35C32×C5×C19C22×C711yescharacteristic, complemented, Hall
36C2×C3×C7×C19—31no—
37C7×D57—31no—
38C7×D57—31no—
39C7×D57—61no—
40C7×D57C5×D311yescharacteristic, direct product factor
41D3×C7×C19C5×D311yescharacteristic, complemented
42C3×C7×D19—31no—
43D3×D57C5×C711yescharacteristic, direct product factor, Hall
44C5×C7×C19D3211yescharacteristic, complemented, Hall
45C5×C7×C3⋊D3—191no—
46C3×C5×D3×C7—191no—
47C3×C5×D3×C7D1911yescharacteristic, complemented
48C2×C3×C5×C19—31no—
49C5×D57—31no—
50C5×D57—31no—
51C5×D57—61no—
52C5×D57D3×C711yescharacteristic, direct product factor
53C5×D3×C19D3×C711yescharacteristic, complemented
54C3×C5×D19—31no—
55C2×C7×D19—91noHall
56C2×C5×D3×C7—571no—
57C2×C5×D3×C7—571no—
58C3×C7×C19—21no—
59C3×C7×C19C2×C5×D311yescharacteristic, complemented
60C3×C7×C19C2×C5×D311yescharacteristic, complemented
61C2×C5×D19—91noHall
62C3⋊D57C2×C5×C711yescharacteristic, complemented
63C3×D57C2×C5×C711yescharacteristic, complemented
64C3×D3×C19C2×C5×C711yescharacteristic, complemented
65C32×C5×C7C2×D1911yescharacteristic, complemented, Hall
66C3×C5×C19—21no—
67C3×C5×C19C2×D3×C711yescharacteristic, complemented
68C3×C5×C19C2×D3×C711yescharacteristic, complemented
69C2×C7×C19—31no—
70C7×D19—31no—
71C7×D19—91no—
72D32×C7—191noHall
73C2×D57—31no—
74D3×D19—31no—
75C2×C3×C5×C7—31no—
76C2×C3×C5×C7—571no—
77C5×D3×C7—191no—
78C5×D3×C7—571no—
79C5×D3×C7—571no—
80C5×D3×C7—1141no—
81C5×D3×C7D5711yescharacteristic, direct product factor
82C2×C5×C19—31no—
83C5×D19—31no—
84C5×D19—91no—
85C5×D32—191noHall
86C32×C19C22×C5×C711yescharacteristic, complemented, Hall
87C22×C5×C7—1711noHall
88C7×C19C5×D3211yescharacteristic, complemented, Hall
89C7×C3⋊D3—191no—
90C3×D3×C7—191no—
91C3×D3×C7C5×D1911yescharacteristic, complemented
92C2×C3×C19—31no—
93D57—31no—
94D57—31no—
95D57—61no—
96D57C5×D3×C711yescharacteristic, direct product factor
97C3×D19—31no—
98D3×C19C5×D3×C711yescharacteristic, complemented
99C3×C5×C7—21no—
100C3×C5×C7D3×D1911yescharacteristic, complemented
101C3×C5×C7C2×D5711yescharacteristic, complemented
102C5×C19D32×C711yescharacteristic, complemented, Hall
103C5×C3⋊D3—191no—
104C3×C5×D3—191no—
105C3×C5×D3C7×D1911yescharacteristic, complemented
106C2×D3×C7—571no—
107C2×D3×C7—571no—
108C2×D19—91noHall
109C2×C5×C7—31no—
110C2×C5×C7—571no—
111C2×C5×C7—1711no—
112C32×C7C2×C5×D1911yescharacteristic, complemented, Hall
113C2×C5×D3—571no—
114C2×C5×D3—571no—
115C3×C19—21no—
116C3×C19C2×C5×D3×C711yescharacteristic, complemented
117C3×C19C2×C5×D3×C711yescharacteristic, complemented
118C32×C5C2×C7×D1911yescharacteristic, complemented, Hall
119C2×C3×C7—31no—
120C2×C3×C7—571no—
121D3×C7—191no—
122D3×C7—571no—
123D3×C7—571no—
124D3×C7—1141no—
125D3×C7C5×D5711yescharacteristic, direct product factor
126C2×C19—31no—
127D19—31no—
128D19—91no—
129D32—191noHall
130C5×C7D3×D5711yescharacteristic, direct product factor, Hall
131C2×C3×C5—31no—
132C2×C3×C5—571no—
133C5×D3—191no—
134C5×D3—571no—
135C5×D3—571no—
136C5×D3—1141no—
137C5×D3C7×D5711yescharacteristic, direct product factor
138C22×C7—1711noHall
139C3×C7—21no—
140C3×C7C5×D3×D1911yescharacteristic, complemented
141C3×C7C2×C5×D5711yescharacteristic, complemented
142C22×C5—1711noHall
143C19C5×D32×C711yescharacteristic, complemented, Sylow
144C3⋊D3—191no—
145C3×D3—191no—
146C3×D3C5×C7×D1911yescharacteristic, complemented
147C3×C5—21no—
148C3×C5D3×C7×D1911yescharacteristic, complemented
149C3×C5C2×C7×D5711yescharacteristic, complemented
150C2×C7—31no—
151C2×C7—571no—
152C2×C7—1711no—
153C2×D3—571no—
154C2×D3—571no—
155C2×C5—31no—
156C2×C5—571no—
157C2×C5—1711no—
158C32C2×C5×C7×D1911yescharacteristic, complemented, Sylow
159C7C5×D3×D5711yescharacteristic, direct product factor, Sylow
160C2×C3—31no—
161C2×C3—571no—
162D3—191no—
163D3—571no—
164D3—571no—
165D3—1141no—
166D3C5×C7×D5711yescharacteristic, direct product factor
167C5D3×C7×D5711yescharacteristic, direct product factor, Sylow
168C22—1711noSylow
169C3—21no—
170C3C5×D3×C7×D1911yescharacteristic, complemented
171C3C2×C5×C7×D5711yescharacteristic, complemented
172C2—31no—
173C2—571no—
174C2—1711no—
subgroupG/H
center, hypercenterC5×C7D3×D57
commutator, cosocle, hypocenterC32×C19C22×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C19C22
LCSG ▷ C32×C19
UCSC1 ◁ C5×C7

Complements

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

NH ≅ G/Ntype
1. C3×C5×D3×C7×C19C2semidirect
2. C3×C5×C7×D57C2semidirect
3. C5×C7×C3⋊D57C2semidirect
6. C32×C5×C7×C19C22semidirect
7. D3×C7×D57C5direct (N × H)
11. C5×C7×D57D3direct (N × H)
12. C5×D3×C7×C19D3semidirect
15. C5×D3×D57C7direct (N × H)
17. C7×C3⋊D57C2×C5semidirect
18. C3×C7×D57C2×C5semidirect
19. C3×D3×C7×C19C2×C5semidirect
21. C3×C5×C7×C19C2×D3semidirect
22. C3×C5×C7×C19C2×D3semidirect
23. C5×C3⋊D57C2×C7semidirect
24. C3×C5×D57C2×C7semidirect
25. C3×C5×D3×C19C2×C7semidirect
32. C32×C7×C19C22×C5semidirect
35. C32×C5×C19C22×C7semidirect
40. C7×D57C5×D3direct (N × H)
41. D3×C7×C19C5×D3semidirect
43. D3×D57C5×C7direct (N × H)
44. C5×C7×C19D32semidirect
47. C3×C5×D3×C7D19semidirect
52. C5×D57D3×C7direct (N × H)
53. C5×D3×C19D3×C7semidirect
59. C3×C7×C19C2×C5×D3semidirect
60. C3×C7×C19C2×C5×D3semidirect
62. C3⋊D57C2×C5×C7semidirect
63. C3×D57C2×C5×C7semidirect
64. C3×D3×C19C2×C5×C7semidirect
65. C32×C5×C7C2×D19semidirect
67. C3×C5×C19C2×D3×C7semidirect
68. C3×C5×C19C2×D3×C7semidirect
81. C5×D3×C7D57direct (N × H)
86. C32×C19C22×C5×C7semidirect
88. C7×C19C5×D32semidirect
91. C3×D3×C7C5×D19semidirect
96. D57C5×D3×C7direct (N × H)
98. D3×C19C5×D3×C7semidirect
100. C3×C5×C7D3×D19semidirect
101. C3×C5×C7C2×D57semidirect
102. C5×C19D32×C7semidirect
105. C3×C5×D3C7×D19semidirect
112. C32×C7C2×C5×D19semidirect
116. C3×C19C2×C5×D3×C7semidirect
117. C3×C19C2×C5×D3×C7semidirect
118. C32×C5C2×C7×D19semidirect
125. D3×C7C5×D57direct (N × H)
130. C5×C7D3×D57direct (N × H)
137. C5×D3C7×D57direct (N × H)
140. C3×C7C5×D3×D19semidirect
141. C3×C7C2×C5×D57semidirect
143. C19C5×D32×C7semidirect
146. C3×D3C5×C7×D19semidirect
148. C3×C5D3×C7×D19semidirect
149. C3×C5C2×C7×D57semidirect
158. C32C2×C5×C7×D19semidirect
159. C7C5×D3×D57direct (N × H)
166. D3C5×C7×D57direct (N × H)
167. C5D3×C7×D57direct (N × H)
170. C3C5×D3×C7×D19semidirect
171. C3C2×C5×C7×D57semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D3×C7×C192
C3×C5×C7×D572
C5×C7×C3⋊D572
C2×C5×C7×D573
C5×D3×C7×D193
D3×C7×D575
C5×D3×D577
C5×D32×C719