Finite Group Databasebeta

← C2×C3×C5×D399 #37561639

Subgroups — C2×C3×C5×D399 #37561639

Order 23940.

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

normal subgroups only

This group has 176 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
1C3×C5×D399C212yesmaximal, direct product factor
2C2×C32×C5×C7×C19C211yesmaximal, characteristic, complemented
3C2×C3×C5×D133—31nomaximal
4C2×C5×D399C311yesmaximal, characteristic, direct product factor
5C32×C5×C7×C19C2211yescharacteristic, complemented, Hall
6C2×C3×D399C511yesmaximal, characteristic, direct product factor, Hall
7C5×D399C2×C312yesdirect product factor
8C3×C5×D133—32no—
9C2×C3×C5×C7×C19—21no—
10C2×C3×C5×C7×C19D311yescharacteristic, complemented
11C2×C3×C5×C7×C19C2×C311yescharacteristic, complemented
12C2×C3×C5×D57—71nomaximal, Hall
13C2×C5×D133—31noHall
14C3×D399C2×C512yesdirect product factor
15C2×C32×C7×C19C2×C511yescharacteristic, complemented
16C3×C5×C7×C19—21no—
17C3×C5×C7×C19C2×D311yescharacteristic, complemented
18C3×C5×C7×C19C22×C311yescharacteristic, complemented
19C2×C32×C5×C19D711yescharacteristic, complemented
20C3×C5×D57—72no—
21C2×D399C3×C511yescharacteristic, direct product factor
22C2×C3×D133—31no—
23C2×C5×C7×C19C3×D311yescharacteristic, complemented
24C5×D133—32no—
25C2×C3×C5×D21—191nomaximal, Hall
26C32×C7×C19C22×C511yescharacteristic, complemented, Hall
27C2×C5×D57—71no—
28C2×C3×C5×D19—211no—
29C32×C5×C19C2×D711yescharacteristic, complemented, Hall
30C2×C3×C7×C19—21no—
31C2×C3×C7×C19C5×D311yescharacteristic, complemented
32C2×C3×C7×C19C2×C3×C511yescharacteristic, complemented
33D399C2×C3×C512yesdirect product factor
34C3×D133—32no—
35C2×C3×D57—71noHall
36C5×C7×C19C2×C3×D311yescharacteristic, complemented, Hall
37C2×C32×C5×C7D1911yescharacteristic, complemented
38C3×C5×D21—192no—
39C2×C3×C5×C19—21no—
40C2×C3×C5×C19C3×D711yescharacteristic, complemented
41C2×C3×C5×C19D2111yescharacteristic, complemented
42C5×D57—72no—
43C3×C5×D19—212no—
44C2×D133—31noHall
45C2×C5×D21—191no—
46C2×C3×C5×D7—571no—
47C3×C7×C19—21no—
48C3×C7×C19C2×C5×D311yescharacteristic, complemented
49C3×C7×C19C22×C3×C511yescharacteristic, complemented
50C2×C5×D19—211noHall
51C2×C32×C19C5×D711yescharacteristic, complemented
52C3×D57—72no—
53C32×C5×C7C2×D1911yescharacteristic, complemented, Hall
54C3×C5×C19—21no—
55C3×C5×C19C2×C3×D711yescharacteristic, complemented
56C3×C5×C19C2×D2111yescharacteristic, complemented
57C2×C7×C19C3×C5×D311yescharacteristic, complemented
58D133—32no—
59C2×C3×D21—191noHall
60C2×D57—71no—
61C2×C3×D19—211no—
62C2×C3×C5×C7—21no—
63C2×C3×C5×C7C3×D1911yescharacteristic, complemented
64C2×C3×C5×C7D5711yescharacteristic, complemented
65C5×D21—192no—
66C3×C5×D7—572no—
67C2×C5×C19C3×D2111yescharacteristic, complemented
68C5×D19—212no—
69C2×C3×C5×D3—1331noHall
70C32×C19C2×C5×D711yescharacteristic, complemented, Hall
71C2×C5×D7—571noHall
72C7×C19C2×C3×C5×D311yescharacteristic, complemented, Hall
73C2×C32×C7C5×D1911yescharacteristic, complemented
74C3×D21—192no—
75C2×C3×C19—21no—
76C2×C3×C19C3×C5×D711yescharacteristic, complemented
77C2×C3×C19C5×D2111yescharacteristic, complemented
78D57—72no—
79C3×D19—212no—
80C3×C5×C7—21no—
81C3×C5×C7C2×C3×D1911yescharacteristic, complemented
82C3×C5×C7C2×D5711yescharacteristic, complemented
83C5×C19C2×C3×D2111yescharacteristic, complemented, Hall
84C2×C32×C5D13311yescharacteristic, complemented
85C3×C5×D3—1332no—
86C2×D21—191no—
87C2×C3×D7—571no—
88C2×D19—211noHall
89C2×C5×C7C3×D5711yescharacteristic, complemented
90C5×D7—572no—
91C32×C7C2×C5×D1911yescharacteristic, complemented, Hall
92C22×C3×C5—3991no—
93C2×C5×D3—1331no—
94C3×C19—21no—
95C3×C19C2×C3×C5×D711yescharacteristic, complemented
96C3×C19C2×C5×D2111yescharacteristic, complemented
97C32×C5C2×D13311yescharacteristic, complemented, Hall
98C2×C3×C7—21no—
99C2×C3×C7C3×C5×D1911yescharacteristic, complemented
100C2×C3×C7C5×D5711yescharacteristic, complemented
101D21—192no—
102C3×D7—572no—
103C2×C19C3×C5×D2111yescharacteristic, complemented
104D19—212no—
105C2×C3×D3—1331noHall
106C5×C7C2×C3×D5711yescharacteristic, complemented, Hall
107C2×C3×C5—21no—
108C2×C3×C5—3992no—
109C2×C3×C5C3×D13311yescharacteristic, complemented
110C2×C3×C5D39911yescharacteristic, direct product factor
111C5×D3—1332no—
112C2×D7—571noHall
113C3×C7—21no—
114C3×C7C2×C3×C5×D1911yescharacteristic, complemented
115C3×C7C2×C5×D5711yescharacteristic, complemented
116C22×C5—3991noHall
117C19C2×C3×C5×D2111yescharacteristic, complemented, Sylow
118C2×C32C5×D13311yescharacteristic, complemented
119C3×D3—1332no—
120C3×C5—21no—
121C3×C5C2×C3×D13311yescharacteristic, complemented
122C3×C5C2×D39911yescharacteristic, direct product factor
123C2×C7C3×C5×D5711yescharacteristic, complemented
124D7—572no—
125C22×C3—3991no—
126C2×D3—1331no—
127C2×C5—3992no—
128C2×C5C3×D39911yescharacteristic, direct product factor
129C32C2×C5×D13311yescharacteristic, complemented, Sylow
130C7C2×C3×C5×D5711yescharacteristic, complemented, Sylow
131C2×C3—21no—
132C2×C3—3992no—
133C2×C3C3×C5×D13311yescharacteristic, complemented
134C2×C3C5×D39911yescharacteristic, direct product factor
135D3—1332no—
136C5C2×C3×D39911yescharacteristic, direct product factor, Sylow
137C22—3991noSylow
138C3—21no—
139C3C2×C5×D39911yescharacteristic, direct product factor
140C3C2×C3×C5×D13311yescharacteristic, complemented
141C2—3992no—
142C2C3×C5×D39911yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C5D399
commutator, cosocle, hypocenterC3×C7×C19C22×C3×C5
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C19C2
LCSG ▷ C3×C7×C19
UCSC1 ◁ C2×C3×C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×D399C2direct (N × H)
2. C2×C32×C5×C7×C19C2semidirect
4. C2×C5×D399C3direct (N × H)
5. C32×C5×C7×C19C22semidirect
6. C2×C3×D399C5direct (N × H)
7. C5×D399C2×C3direct (N × H)
10. C2×C3×C5×C7×C19D3semidirect
11. C2×C3×C5×C7×C19C2×C3semidirect
14. C3×D399C2×C5direct (N × H)
15. C2×C32×C7×C19C2×C5semidirect
17. C3×C5×C7×C19C2×D3semidirect
18. C3×C5×C7×C19C22×C3semidirect
19. C2×C32×C5×C19D7semidirect
21. C2×D399C3×C5direct (N × H)
23. C2×C5×C7×C19C3×D3semidirect
26. C32×C7×C19C22×C5semidirect
29. C32×C5×C19C2×D7semidirect
31. C2×C3×C7×C19C5×D3semidirect
32. C2×C3×C7×C19C2×C3×C5semidirect
33. D399C2×C3×C5direct (N × H)
36. C5×C7×C19C2×C3×D3semidirect
37. C2×C32×C5×C7D19semidirect
40. C2×C3×C5×C19C3×D7semidirect
41. C2×C3×C5×C19D21semidirect
48. C3×C7×C19C2×C5×D3semidirect
49. C3×C7×C19C22×C3×C5semidirect
51. C2×C32×C19C5×D7semidirect
53. C32×C5×C7C2×D19semidirect
55. C3×C5×C19C2×C3×D7semidirect
56. C3×C5×C19C2×D21semidirect
57. C2×C7×C19C3×C5×D3semidirect
63. C2×C3×C5×C7C3×D19semidirect
64. C2×C3×C5×C7D57semidirect
67. C2×C5×C19C3×D21semidirect
70. C32×C19C2×C5×D7semidirect
72. C7×C19C2×C3×C5×D3semidirect
73. C2×C32×C7C5×D19semidirect
76. C2×C3×C19C3×C5×D7semidirect
77. C2×C3×C19C5×D21semidirect
81. C3×C5×C7C2×C3×D19semidirect
82. C3×C5×C7C2×D57semidirect
83. C5×C19C2×C3×D21semidirect
84. C2×C32×C5D133semidirect
89. C2×C5×C7C3×D57semidirect
91. C32×C7C2×C5×D19semidirect
95. C3×C19C2×C3×C5×D7semidirect
96. C3×C19C2×C5×D21semidirect
97. C32×C5C2×D133semidirect
99. C2×C3×C7C3×C5×D19semidirect
100. C2×C3×C7C5×D57semidirect
103. C2×C19C3×C5×D21semidirect
106. C5×C7C2×C3×D57semidirect
109. C2×C3×C5C3×D133semidirect
110. C2×C3×C5D399direct (N × H)
114. C3×C7C2×C3×C5×D19semidirect
115. C3×C7C2×C5×D57semidirect
117. C19C2×C3×C5×D21semidirect
118. C2×C32C5×D133semidirect
121. C3×C5C2×C3×D133semidirect
122. C3×C5C2×D399direct (N × H)
123. C2×C7C3×C5×D57semidirect
128. C2×C5C3×D399direct (N × H)
129. C32C2×C5×D133semidirect
130. C7C2×C3×C5×D57semidirect
133. C2×C3C3×C5×D133semidirect
134. C2×C3C5×D399direct (N × H)
136. C5C2×C3×D399direct (N × H)
139. C3C2×C5×D399direct (N × H)
140. C3C2×C3×C5×D133semidirect
142. C2C3×C5×D399direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×D3992
C2×C32×C5×C7×C192
C2×C3×C5×D1333
C2×C5×D3993
C2×C3×D3995
C2×C3×C5×D577
C2×C3×C5×D2119