Finite Group Databasebeta

← C7×D19×C3⋊D15 #37561598

Subgroups — C7×D19×C3⋊D15 #37561598

Order 23940.

240 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 80 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×C5×C7×D19C211yesmaximal, characteristic, complemented
2C7×C19×C3⋊D15C211yesmaximal, characteristic, complemented
3C7×C3⋊D285C211yesmaximal, characteristic, complemented
4C7×D15×D19—34nomaximal
5C32×C5×C7×C19C2211yescharacteristic, complemented, Hall
6C7×C3⋊D3×D19—51nomaximal, Hall
7C7×D285—34no—
8C7×C19×D15—34no—
9C3×C5×C7×D19D314yescomplemented
10D19×C3⋊D15C711yesmaximal, characteristic, direct product factor, Hall
11C7×D5×D19—91noHall
12C7×C3⋊D57—51no—
13C7×C3⋊D3×C19—51no—
14C32×C7×D19D511yescharacteristic, complemented
15C3×C5×C7×C19C2×D314yescomplemented
16C3⋊D285C2×C711yescharacteristic, complemented
17C19×C3⋊D15C2×C711yescharacteristic, complemented
18C32×C5×D19C2×C711yescharacteristic, complemented
19D3×C7×D19—154no—
20C7×D95—91no—
21C7×D5×C19—91no—
22C5×C7×D19C3⋊D311yescharacteristic, complemented
23C2×C7×C3⋊D15—191nomaximal, Hall
24C32×C7×C19C2×D511yescharacteristic, complemented, Hall
25D15×D19—34no—
26C32×C5×C19C22×C711yescharacteristic, complemented, Hall
27C7×D57—154no—
28D3×C7×C19—154no—
29C3×C7×D19D1514yescomplemented
30C3⋊D3×D19—51noHall
31C5×C7×C19C2×C3⋊D311yescharacteristic, complemented, Hall
32C2×C32×C5×C7—191no—
33C7×C3⋊D15—191no—
34C7×C3⋊D15D1911yescharacteristic, direct product factor
35D285—34no—
36C19×D15—34no—
37C3×C5×D19D3×C714yescomplemented
38C2×C7×D19—451noHall
39C2×C7×D15—574no—
40C3×C7×C19C2×D1514yescomplemented
41D5×D19—91noHall
42C3⋊D57—51no—
43C3⋊D3×C19—51no—
44C32×D19C7×D511yescharacteristic, complemented
45C32×C5×C7C2×D1911yescharacteristic, complemented, Hall
46C3×C5×C19C2×D3×C714yescomplemented
47C2×C7×C19—451no—
48C7×D19—451no—
49C7×D19C3⋊D1511yescharacteristic, direct product factor
50C2×C7×C3⋊D3—951noHall
51D3×D19—154no—
52C2×C3×C5×C7—194no—
53C7×D15—34no—
54C7×D15—574no—
55D95—91no—
56C5×D19C7×C3⋊D311yescharacteristic, complemented
57D5×C19—91no—
58C2×C3⋊D15—191noHall
59C32×C19C2×C7×D511yescharacteristic, complemented, Hall
60C2×C7×D5—1711noHall
61C7×C19C2×C3⋊D1511yescharacteristic, complemented, Hall
62C2×C32×C7—191no—
63C7×C3⋊D3—51no—
64C7×C3⋊D3—951no—
65D57—154no—
66C3×D19C7×D1514yescomplemented
67D3×C19—154no—
68C3×C5×C7D3×D1914yescomplemented
69C5×C19C2×C7×C3⋊D311yescharacteristic, complemented, Hall
70C2×C32×C5—191no—
71C3⋊D15—191no—
72C3⋊D15C7×D1911yescharacteristic, direct product factor
73C2×D3×C7—2854no—
74C2×D19—451noHall
75C2×C5×C7—191no—
76C7×D5—91no—
77C7×D5—1711no—
78C32×C7D5×D1911yescharacteristic, complemented, Hall
79C2×D15—574no—
80C3×C19C2×C7×D1514yescomplemented
81C32×C5C2×C7×D1911yescharacteristic, complemented, Hall
82C2×C3×C7—194no—
83D3×C7—154no—
84D3×C7—2854no—
85C2×C19—451no—
86D19—451no—
87D19C7×C3⋊D1511yescharacteristic, direct product factor
88C2×C3⋊D3—951noHall
89C5×C7C3⋊D3×D1911yescharacteristic, complemented, Hall
90C2×C3×C5—194no—
91D15—34no—
92D15—574no—
93C22×C7—8551noHall
94C3×C7D15×D1914yescomplemented
95C2×D5—1711noHall
96C19C2×C7×C3⋊D1511yescharacteristic, complemented, Sylow
97C2×C32—191no—
98C3⋊D3—51no—
99C3⋊D3—951no—
100C3×C5D3×C7×D1914yescomplemented
101C2×C7—191no—
102C2×C7—451no—
103C2×C7—8551no—
104C2×D3—2854no—
105C2×C5—191no—
106D5—91no—
107D5—1711no—
108C32C7×D5×D1911yescharacteristic, complemented, Sylow
109C7D19×C3⋊D1511yescharacteristic, direct product factor, Sylow
110C2×C3—194no—
111D3—154no—
112D3—2854no—
113C5C7×C3⋊D3×D1911yescharacteristic, complemented, Sylow
114C22—8551noSylow
115C3C7×D15×D1914yescomplemented
116C2—191no—
117C2—451no—
118C2—8551no—
subgroupG/H
center, hypercenterC7D19×C3⋊D15
commutator, cosocle, hypocenterC32×C5×C19C22×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C19C22
LCSG ▷ C32×C5×C19
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C32×C5×C7×D19C2semidirect
2. C7×C19×C3⋊D15C2semidirect
3. C7×C3⋊D285C2semidirect
5. C32×C5×C7×C19C22semidirect
9. C3×C5×C7×D19D3semidirect
10. D19×C3⋊D15C7direct (N × H)
14. C32×C7×D19D5semidirect
15. C3×C5×C7×C19C2×D3semidirect
16. C3⋊D285C2×C7semidirect
17. C19×C3⋊D15C2×C7semidirect
18. C32×C5×D19C2×C7semidirect
22. C5×C7×D19C3⋊D3semidirect
24. C32×C7×C19C2×D5semidirect
26. C32×C5×C19C22×C7semidirect
29. C3×C7×D19D15semidirect
31. C5×C7×C19C2×C3⋊D3semidirect
34. C7×C3⋊D15D19direct (N × H)
37. C3×C5×D19D3×C7semidirect
40. C3×C7×C19C2×D15semidirect
44. C32×D19C7×D5semidirect
45. C32×C5×C7C2×D19semidirect
46. C3×C5×C19C2×D3×C7semidirect
49. C7×D19C3⋊D15direct (N × H)
56. C5×D19C7×C3⋊D3semidirect
59. C32×C19C2×C7×D5semidirect
61. C7×C19C2×C3⋊D15semidirect
66. C3×D19C7×D15semidirect
68. C3×C5×C7D3×D19semidirect
69. C5×C19C2×C7×C3⋊D3semidirect
72. C3⋊D15C7×D19direct (N × H)
78. C32×C7D5×D19semidirect
80. C3×C19C2×C7×D15semidirect
81. C32×C5C2×C7×D19semidirect
87. D19C7×C3⋊D15direct (N × H)
89. C5×C7C3⋊D3×D19semidirect
94. C3×C7D15×D19semidirect
96. C19C2×C7×C3⋊D15semidirect
100. C3×C5D3×C7×D19semidirect
108. C32C7×D5×D19semidirect
109. C7D19×C3⋊D15direct (N × H)
113. C5C7×C3⋊D3×D19semidirect
115. C3C7×D15×D19semidirect

Maximal subgroups

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

subgroupindex
C32×C5×C7×D192
C7×C19×C3⋊D152
C7×C3⋊D2852
C7×D15×D193
C7×C3⋊D3×D195
D19×C3⋊D157
C2×C7×C3⋊D1519