Finite Group Databasebeta

← (C3⋊D3)⋊D665 #37561587

Subgroups — (C3⋊D3)⋊D665 #37561587

Order 23940.

176 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 45 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×D1995C212yesmaximal, complemented
2C5×C7×C3⋊D3×C19C211yesmaximal, characteristic, complemented
3D3×D665—32nomaximal
4C32×C5×C7×C19C2211yescharacteristic, complemented, Hall
5(C3⋊D3)⋊D133—51nomaximal, Hall
6D1995D312yescomplemented
7C5×D3×C7×C19—32no—
8C5×D3×C7×C19—61no—
9C3×D665—32no—
10(C3⋊D3)⋊D95—71nomaximal, Hall
11C2×D665—91noHall
12C7×C3⋊D3×C19D511yescharacteristic, complemented
13C3×D399—52no—
14C3×C5×C7×C19—21no—
15C3×C5×C7×C19C2×D312yescomplemented
16C5×C3⋊D3×C19D711yescharacteristic, complemented
17C3×D285—72no—
18D3×D133—152no—
19C2×C5×C7×C19—91no—
20D665—32no—
21(C3⋊D3)⋊D35—191nomaximal, Hall
22C32×C7×C19C2×D511yescharacteristic, complemented, Hall
23D3×D95—212no—
24C32×C5×C19C2×D711yescharacteristic, complemented, Hall
25D399—52no—
26D3×C7×C19—32no—
27D3×C7×C19—61no—
28C3×D133—152no—
29(C3⋊D3)⋊D19—351noHall
30C5×C7×C19D3211yescharacteristic, complemented, Hall
31C5×C7×C3⋊D3D1911yescharacteristic, complemented
32C3×D105—192no—
33D285—72no—
34C5×D3×C19—32no—
35C5×D3×C19—61no—
36C3×D95—212no—
37C2×D133—451noHall
38D3×D35—572no—
39C3×C7×C19—21no—
40C3×C7×C19D3×D512yescomplemented
41C2×D95—631noHall
42C3⋊D3×C19D3511yescharacteristic, complemented
43C3×D57—352no—
44C32×C5×C7C2×D1911yescharacteristic, complemented, Hall
45C3×C5×C19—21no—
46C3×C5×C19D3×D712yescomplemented
47C2×C7×C19—91no—
48D133—152no—
49(C3⋊D3)⋊D7—951noHall
50D3×D19—1052no—
51D105—192no—
52C5×D3×C7—32no—
53C5×D3×C7—61no—
54C3×D35—572no—
55C2×C5×C19—91no—
56D95—212no—
57(C3⋊D3)⋊D5—1331noHall
58C32×C19C2×D3511yescharacteristic, complemented, Hall
59C2×D35—1711noHall
60C7×C19(C3⋊D3)⋊D511yescharacteristic, complemented, Hall
61C7×C3⋊D3D9511yescharacteristic, complemented
62C3×D21—952no—
63D57—352no—
64C3×D19—1052no—
65D3×C19—32no—
66D3×C19—61no—
67C3×C5×C7—21no—
68C3×C5×C7D3×D1912yescomplemented
69C5×C19(C3⋊D3)⋊D711yescharacteristic, complemented, Hall
70C5×C3⋊D3D13311yescharacteristic, complemented
71C3×D15—1332no—
72D3×D7—2852no—
73C2×D19—3151noHall
74C2×C5×C7—91no—
75D35—572no—
76C32×C7C2×D9511yescharacteristic, complemented, Hall
77D3×D5—3992no—
78C3×C19—21no—
79C3×C19D3×D3512yescomplemented
80C32×C5C2×D13311yescharacteristic, complemented, Hall
81D21—952no—
82C3×D7—2852no—
83D3×C7—32no—
84D3×C7—61no—
85C2×C19—91no—
86D19—1052no—
87D32—6651noHall
88C5×C7(C3⋊D3)⋊D1911yescharacteristic, complemented, Hall
89D15—1332no—
90C3×D5—3992no—
91C5×D3—32no—
92C5×D3—61no—
93C2×D7—8551noHall
94C3×C7—21no—
95C3×C7D3×D9512yescomplemented
96C2×D5—11971noHall
97C19(C3⋊D3)⋊D3511yescharacteristic, complemented, Sylow
98C3⋊D3D66511yescharacteristic, complemented
99C3×D3—6652no—
100C3×C5—21no—
101C3×C5D3×D13312yescomplemented
102C2×C7—91no—
103D7—2852no—
104C2×D3—19952no—
105C2×C5—91no—
106D5—3992no—
107C32C2×D66511yescharacteristic, complemented, Sylow
108C7(C3⋊D3)⋊D9511yescharacteristic, complemented, Sylow
109C2×C3—19952no—
110D3—32no—
111D3—61no—
112D3—6652no—
113C5(C3⋊D3)⋊D13311yescharacteristic, complemented, Sylow
114C22—59851noSylow
115C3—21no—
116C3D3×D66512yescomplemented
117C2—91no—
118C2—19952no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C19C22
LCSG ▷ C32×C5×C7×C19
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×D1995C2semidirect
2. C5×C7×C3⋊D3×C19C2semidirect
4. C32×C5×C7×C19C22semidirect
6. D1995D3semidirect
12. C7×C3⋊D3×C19D5semidirect
15. C3×C5×C7×C19C2×D3semidirect
16. C5×C3⋊D3×C19D7semidirect
22. C32×C7×C19C2×D5semidirect
24. C32×C5×C19C2×D7semidirect
30. C5×C7×C19D32semidirect
31. C5×C7×C3⋊D3D19semidirect
40. C3×C7×C19D3×D5semidirect
42. C3⋊D3×C19D35semidirect
44. C32×C5×C7C2×D19semidirect
46. C3×C5×C19D3×D7semidirect
58. C32×C19C2×D35semidirect
60. C7×C19(C3⋊D3)⋊D5semidirect
61. C7×C3⋊D3D95semidirect
68. C3×C5×C7D3×D19semidirect
69. C5×C19(C3⋊D3)⋊D7semidirect
70. C5×C3⋊D3D133semidirect
76. C32×C7C2×D95semidirect
79. C3×C19D3×D35semidirect
80. C32×C5C2×D133semidirect
88. C5×C7(C3⋊D3)⋊D19semidirect
95. C3×C7D3×D95semidirect
97. C19(C3⋊D3)⋊D35semidirect
98. C3⋊D3D665semidirect
101. C3×C5D3×D133semidirect
107. C32C2×D665semidirect
108. C7(C3⋊D3)⋊D95semidirect
113. C5(C3⋊D3)⋊D133semidirect
116. C3D3×D665semidirect

Maximal subgroups

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

subgroupindex
C3×D19952
C5×C7×C3⋊D3×C192
D3×D6653
(C3⋊D3)⋊D1335
(C3⋊D3)⋊D957
(C3⋊D3)⋊D3519