Finite Group Databasebeta

← C3×C7×D15⋊D19 #37561539

Subgroups — C3×C7×D15⋊D19 #37561539

Order 23940.

176 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C32×C7×D95C211yesmaximal, characteristic, complemented
2C3×C5×C7×D57C211yesmaximal, characteristic, complemented
3C3×C7×C19×D15C211yesmaximal, characteristic, complemented
4C7×D15⋊D19C311yesmaximal, characteristic, direct product factor
5C3×C7×D5×D19—31nomaximal
6C32×C5×C7×C19C2211yescharacteristic, complemented, Hall
7C3×D3×C7×D19—51nomaximal, Hall
8C7×C19×D15C2×C311yescharacteristic, complemented
9C5×C7×D57C2×C311yescharacteristic, complemented
10C3×C7×D95—21no—
11C3×C7×D95D311yescharacteristic, complemented
12C3×C7×D95C2×C311yescharacteristic, complemented
13C3×C7×D5×C19—31no—
14C3×C5×C7×D19—31no—
15C3×D15⋊D19C711yesmaximal, characteristic, direct product factor, Hall
16C7×D5×D19—31noHall
17C3×C7×D57D511yescharacteristic, complemented
18C3×D3×C7×C19—51no—
19C32×C7×D19—51no—
20C3×C5×C7×C19—21no—
21C3×C5×C7×C19C2×D311yescharacteristic, complemented
22C3×C5×C7×C19C22×C311yescharacteristic, complemented
23C3×C19×D15C2×C711yescharacteristic, complemented
24C3×C5×D57C2×C711yescharacteristic, complemented
25C32×D95C2×C711yescharacteristic, complemented
26C2×C3×C7×D19—151no—
27D3×C7×D19—51no—
28C7×D95C3×D311yescharacteristic, complemented
29C7×D5×C19—31no—
30C5×C7×D19—31no—
31C3×D3×C7×D5—191nomaximal, Hall
32C32×C7×C19C2×D511yescharacteristic, complemented, Hall
33D15⋊D19C3×C711yescharacteristic, direct product factor
34C3×D5×D19—31no—
35C32×C5×C19C22×C711yescharacteristic, complemented, Hall
36C2×C3×C7×C19—151no—
37C7×D57C3×D511yescharacteristic, complemented
38D3×C7×C19—51no—
39C3×C7×D19—31no—
40C3×C7×D19—51no—
41C3×C7×D19—51no—
42C3×C7×D19—101no—
43C3×D3×D19—51noHall
44C5×C7×C19C2×C3×D311yescharacteristic, complemented, Hall
45C3×C7×D15D1911yescharacteristic, complemented
46C3×C5×D3×C7—191no—
47C32×C7×D5—191no—
48C19×D15C2×C3×C711yescharacteristic, complemented
49C5×D57C2×C3×C711yescharacteristic, complemented
50C3×D95—21no—
51C3×D95D3×C711yescharacteristic, complemented
52C3×D95C2×C3×C711yescharacteristic, complemented
53C3×D5×C19—31no—
54C3×C5×D19—31no—
55C2×C7×D19—151noHall
56C2×C3×C7×D5—571no—
57D3×C7×D5—191no—
58C3×C7×C19—21no—
59C3×C7×C19D3×D511yescharacteristic, complemented
60C3×C7×C19C2×C3×D511yescharacteristic, complemented
61D5×D19—31noHall
62C3×D57C7×D511yescharacteristic, complemented
63C3×D3×C19—51no—
64C32×D19—51no—
65C32×C5×C7C2×D1911yescharacteristic, complemented, Hall
66C3×C5×C19—21no—
67C3×C5×C19C2×D3×C711yescharacteristic, complemented
68C3×C5×C19C22×C3×C711yescharacteristic, complemented
69C2×C7×C19—151no—
70C7×D19—31no—
71C7×D19—51no—
72C2×C3×D3×C7—951noHall
73C2×C3×D19—151no—
74D3×D19—51no—
75C2×C3×C5×C7—571no—
76C7×D15C3×D1911yescharacteristic, complemented
77C5×D3×C7—191no—
78C3×C7×D5—31no—
79C3×C7×D5—191no—
80C3×C7×D5—191no—
81C3×C7×D5—381no—
82D95C3×D3×C711yescharacteristic, complemented
83C5×D19—31no—
84D5×C19—31no—
85C3×D3×D5—191noHall
86C32×C19C2×C7×D511yescharacteristic, complemented, Hall
87C2×C7×D5—571noHall
88C7×C19C3×D3×D511yescharacteristic, complemented, Hall
89C2×C32×C7—951no—
90C3×D3×C7—51no—
91C3×D3×C7—191no—
92C2×C3×C19—151no—
93D57C3×C7×D511yescharacteristic, complemented
94C3×D19—31no—
95C3×D19—51no—
96C3×D19—51no—
97C3×D19—101no—
98D3×C19—51no—
99C3×C5×C7—21no—
100C3×C5×C7D3×D1911yescharacteristic, complemented
101C3×C5×C7C2×C3×D1911yescharacteristic, complemented
102C5×C19C2×C3×D3×C711yescharacteristic, complemented, Hall
103C3×D15C7×D1911yescharacteristic, complemented
104C3×C5×D3—191no—
105C32×D5—191no—
106C22×C3×C7—2851no—
107C2×D3×C7—951no—
108C2×D19—151noHall
109C2×C5×C7—571no—
110C7×D5—31no—
111C7×D5—191no—
112C32×C7D5×D1911yescharacteristic, complemented, Hall
113C2×C3×D5—571no—
114D3×D5—191no—
115C3×C19—21no—
116C3×C19D3×C7×D511yescharacteristic, complemented
117C3×C19C2×C3×C7×D511yescharacteristic, complemented
118C32×C5C2×C7×D1911yescharacteristic, complemented, Hall
119C2×C3×C7—151no—
120C2×C3×C7—571no—
121C2×C3×C7—951no—
122C2×C3×C7—951no—
123C2×C3×C7—1901no—
124D3×C7—51no—
125D3×C7—191no—
126C2×C19—151no—
127D19—31no—
128D19—51no—
129C2×C3×D3—951noHall
130C5×C7C3×D3×D1911yescharacteristic, complemented, Hall
131C2×C3×C5—571no—
132D15C3×C7×D1911yescharacteristic, complemented
133C3×D5—31no—
134C3×D5—191no—
135C3×D5—191no—
136C3×D5—381no—
137C5×D3—191no—
138C22×C7—2851noHall
139C3×C7—21no—
140C3×C7C3×D5×D1911yescharacteristic, complemented
141C3×C7D15⋊D1911yescharacteristic, direct product factor
142C2×D5—571noHall
143C19C3×D3×C7×D511yescharacteristic, complemented, Sylow
144C2×C32—951no—
145C3×D3—51no—
146C3×D3—191no—
147C3×C5—21no—
148C3×C5D3×C7×D1911yescharacteristic, complemented
149C3×C5C2×C3×C7×D1911yescharacteristic, complemented
150C2×C7—151no—
151C2×C7—571no—
152C2×C7—951no—
153C22×C3—2851no—
154C2×D3—951no—
155C2×C5—571no—
156D5—31no—
157D5—191no—
158C32C7×D5×D1911yescharacteristic, complemented, Sylow
159C7C3×D15⋊D1911yescharacteristic, direct product factor, Sylow
160C2×C3—151no—
161C2×C3—571no—
162C2×C3—951no—
163C2×C3—951no—
164C2×C3—1901no—
165D3—51no—
166D3—191no—
167C5C3×D3×C7×D1911yescharacteristic, complemented, Sylow
168C22—2851noSylow
169C3—21no—
170C3C3×C7×D5×D1911yescharacteristic, complemented
171C3C7×D15⋊D1911yescharacteristic, direct product factor
172C2—151no—
173C2—571no—
174C2—951no—
subgroupG/H
center, hypercenterC3×C7D15⋊D19
commutator, cosocle, hypocenterC3×C5×C19C22×C3×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C19C22
LCSG ▷ C3×C5×C19
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
1. C32×C7×D95C2semidirect
2. C3×C5×C7×D57C2semidirect
3. C3×C7×C19×D15C2semidirect
4. C7×D15⋊D19C3direct (N × H)
6. C32×C5×C7×C19C22semidirect
8. C7×C19×D15C2×C3semidirect
9. C5×C7×D57C2×C3semidirect
11. C3×C7×D95D3semidirect
12. C3×C7×D95C2×C3semidirect
15. C3×D15⋊D19C7direct (N × H)
17. C3×C7×D57D5semidirect
21. C3×C5×C7×C19C2×D3semidirect
22. C3×C5×C7×C19C22×C3semidirect
23. C3×C19×D15C2×C7semidirect
24. C3×C5×D57C2×C7semidirect
25. C32×D95C2×C7semidirect
28. C7×D95C3×D3semidirect
32. C32×C7×C19C2×D5semidirect
33. D15⋊D19C3×C7direct (N × H)
35. C32×C5×C19C22×C7semidirect
37. C7×D57C3×D5semidirect
44. C5×C7×C19C2×C3×D3semidirect
45. C3×C7×D15D19semidirect
48. C19×D15C2×C3×C7semidirect
49. C5×D57C2×C3×C7semidirect
51. C3×D95D3×C7semidirect
52. C3×D95C2×C3×C7semidirect
59. C3×C7×C19D3×D5semidirect
60. C3×C7×C19C2×C3×D5semidirect
62. C3×D57C7×D5semidirect
65. C32×C5×C7C2×D19semidirect
67. C3×C5×C19C2×D3×C7semidirect
68. C3×C5×C19C22×C3×C7semidirect
76. C7×D15C3×D19semidirect
82. D95C3×D3×C7semidirect
86. C32×C19C2×C7×D5semidirect
88. C7×C19C3×D3×D5semidirect
93. D57C3×C7×D5semidirect
100. C3×C5×C7D3×D19semidirect
101. C3×C5×C7C2×C3×D19semidirect
102. C5×C19C2×C3×D3×C7semidirect
103. C3×D15C7×D19semidirect
112. C32×C7D5×D19semidirect
116. C3×C19D3×C7×D5semidirect
117. C3×C19C2×C3×C7×D5semidirect
118. C32×C5C2×C7×D19semidirect
130. C5×C7C3×D3×D19semidirect
132. D15C3×C7×D19semidirect
140. C3×C7C3×D5×D19semidirect
141. C3×C7D15⋊D19direct (N × H)
143. C19C3×D3×C7×D5semidirect
148. C3×C5D3×C7×D19semidirect
149. C3×C5C2×C3×C7×D19semidirect
158. C32C7×D5×D19semidirect
159. C7C3×D15⋊D19direct (N × H)
167. C5C3×D3×C7×D19semidirect
170. C3C3×C7×D5×D19semidirect
171. C3C7×D15⋊D19direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C7×D952
C3×C5×C7×D572
C3×C7×C19×D152
C7×D15⋊D193
C3×C7×D5×D193
C3×D3×C7×D195
C3×D15⋊D197
C3×D3×C7×D519