Finite Group Databasebeta

← D5×C3⋊D399 #37561609

Subgroups — D5×C3⋊D399 #37561609

Order 23940.

240 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 76 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×D5×C19C211yesmaximal, characteristic, complemented
2C5×C3⋊D399C211yesmaximal, characteristic, complemented
3C3⋊D1995C211yesmaximal, characteristic, complemented
4D5×D399—34nomaximal
5C32×C5×C7×C19C2211yescharacteristic, complemented, Hall
6C2×C3⋊D399—51nomaximal, Hall
7D1995—34no—
8C5×D399—34no—
9C3×C7×D5×C19D314yescomplemented
10D5×C3⋊D57—71nomaximal, Hall
11D5×D133—91noHall
12C3⋊D399—51no—
13C3⋊D399D511yescharacteristic, direct product factor
14C2×C32×C7×C19—51no—
15C3×C5×C7×C19C2×D314yescomplemented
16C3⋊D285—71no—
17C5×C3⋊D57—71no—
18C32×D5×C19D711yescharacteristic, complemented
19C2×D399—154no—
20D665—91no—
21C7×D5×C19C3⋊D311yescharacteristic, complemented
22C5×D133—91no—
23D5×C3⋊D21—191nomaximal, Hall
24C32×C7×C19C2×D511yescharacteristic, complemented, Hall
25D5×D57—214no—
26C32×C5×C19C2×D711yescharacteristic, complemented, Hall
27C2×C3×C7×C19—54no—
28D399—34no—
29D399—154no—
30C2×C3⋊D57—351noHall
31C5×C7×C19C2×C3⋊D311yescharacteristic, complemented, Hall
32C3⋊D105—191no—
33C5×C3⋊D21—191no—
34C32×C7×D5D1911yescharacteristic, complemented
35D285—214no—
36C5×D57—214no—
37C3×D5×C19D2114yescomplemented
38C2×D133—451noHall
39D5×D21—574no—
40C3×C7×C19D3×D514yescomplemented
41D5×D19—631noHall
42C2×C32×C19—51no—
43C3⋊D57—71no—
44C3⋊D57—351no—
45C32×C5×C7C2×D1911yescharacteristic, complemented, Hall
46C3×C5×C19C2×D2114yescomplemented
47C2×C7×C19—51no—
48D133—91no—
49D133—451no—
50C2×C3⋊D21—951noHall
51C2×D57—1054no—
52D105—574no—
53C5×D21—574no—
54C3×C7×D5D5714yescomplemented
55D95—631no—
56C5×D19—631no—
57D5×C19C3⋊D2111yescharacteristic, complemented
58D5×C3⋊D3—1331noHall
59C32×C19D5×D711yescharacteristic, complemented, Hall
60D5×D7—1711noHall
61C7×C19D5×C3⋊D311yescharacteristic, complemented, Hall
62C2×C32×C7—51no—
63C3⋊D21—191no—
64C3⋊D21—951no—
65C2×C3×C19—54no—
66D57—214no—
67D57—1054no—
68C3×C5×C7C2×D5714yescomplemented
69C5×C19C2×C3⋊D2111yescharacteristic, complemented, Hall
70C3⋊D15—1331no—
71C5×C3⋊D3—1331no—
72C32×D5D13311yescharacteristic, complemented
73C2×D21—2854no—
74C2×D19—3151noHall
75D35—1711no—
76C5×D7—1711no—
77C7×D5C3⋊D5711yescharacteristic, complemented
78C32×C7D5×D1911yescharacteristic, complemented, Hall
79D3×D5—3994no—
80C3×C19D5×D2114yescomplemented
81C32×C5C2×D13311yescharacteristic, complemented, Hall
82C2×C3×C7—54no—
83D21—2854no—
84D21—574no—
85C2×C19—51no—
86D19—3151no—
87D19—631no—
88C2×C3⋊D3—6651noHall
89C5×C7C2×C3⋊D5711yescharacteristic, complemented, Hall
90D15—3994no—
91C3×D5D39914yescomplemented
92C5×D3—3994no—
93C2×D7—8551noHall
94C3×C7D5×D5714yescomplemented
95C2×D5—11971noHall
96C19D5×C3⋊D2111yescharacteristic, complemented, Sylow
97C2×C32—51no—
98C3⋊D3—1331no—
99C3⋊D3—6651no—
100C3×C5C2×D39914yescomplemented
101C2×C7—51no—
102D7—8551no—
103D7—1711no—
104C2×D3—19954no—
105C2×C5—11971no—
106D5—11971no—
107D5C3⋊D39911yescharacteristic, direct product factor
108C32D5×D13311yescharacteristic, complemented, Sylow
109C7D5×C3⋊D5711yescharacteristic, complemented, Sylow
110C2×C3—54no—
111D3—3994no—
112D3—19954no—
113C5C2×C3⋊D39911yescharacteristic, complemented, Sylow
114C22—59851noSylow
115C3D5×D39914yescomplemented
116C2—51no—
117C2—59851no—
118C2—11971no—
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. C32×C7×D5×C19C2semidirect
2. C5×C3⋊D399C2semidirect
3. C3⋊D1995C2semidirect
5. C32×C5×C7×C19C22semidirect
9. C3×C7×D5×C19D3semidirect
13. C3⋊D399D5direct (N × H)
15. C3×C5×C7×C19C2×D3semidirect
18. C32×D5×C19D7semidirect
21. C7×D5×C19C3⋊D3semidirect
24. C32×C7×C19C2×D5semidirect
26. C32×C5×C19C2×D7semidirect
31. C5×C7×C19C2×C3⋊D3semidirect
34. C32×C7×D5D19semidirect
37. C3×D5×C19D21semidirect
40. C3×C7×C19D3×D5semidirect
45. C32×C5×C7C2×D19semidirect
46. C3×C5×C19C2×D21semidirect
54. C3×C7×D5D57semidirect
57. D5×C19C3⋊D21semidirect
59. C32×C19D5×D7semidirect
61. C7×C19D5×C3⋊D3semidirect
68. C3×C5×C7C2×D57semidirect
69. C5×C19C2×C3⋊D21semidirect
72. C32×D5D133semidirect
77. C7×D5C3⋊D57semidirect
78. C32×C7D5×D19semidirect
80. C3×C19D5×D21semidirect
81. C32×C5C2×D133semidirect
89. C5×C7C2×C3⋊D57semidirect
91. C3×D5D399semidirect
94. C3×C7D5×D57semidirect
96. C19D5×C3⋊D21semidirect
100. C3×C5C2×D399semidirect
107. D5C3⋊D399direct (N × H)
108. C32D5×D133semidirect
109. C7D5×C3⋊D57semidirect
113. C5C2×C3⋊D399semidirect
115. C3D5×D399semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D5×C192
C5×C3⋊D3992
C3⋊D19952
D5×D3993
C2×C3⋊D3995
D5×C3⋊D577
D5×C3⋊D2119