Finite Group Databasebeta

← C2×C3×C5×C7×D91 #50304512

Subgroups — C2×C3×C5×C7×D91 #50304512

Order 38220.

208 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 88 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×C7×D91C212yesmaximal, direct product factor
2C2×C3×C5×C72×C13C211yesmaximal, characteristic, complemented
3C2×C5×C7×D91C311yesmaximal, characteristic, direct product factor, Hall
4C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
5C2×C3×C7×D91C511yesmaximal, characteristic, direct product factor, Hall
6C5×C7×D91C2×C312yesdirect product factor
7C2×C5×C72×C13C2×C311yescharacteristic, complemented
8C2×C3×C5×D91C711yesmaximal, characteristic, direct product factor
9C2×C3×C5×C7×D13—71nomaximal
10C3×C7×D91C2×C512yesdirect product factor
11C2×C3×C72×C13C2×C511yescharacteristic, complemented
12C5×C72×C13C22×C311yescharacteristic, complemented, Hall
13C2×C3×C5×C7×D7—131nomaximal, Hall
14C3×C5×D91C2×C712yesdirect product factor
15C3×C5×C7×D13—72no—
16C2×C3×C5×C7×C13—23no—
17C2×C3×C5×C7×C13D711yescharacteristic, complemented
18C2×C3×C5×C7×C13C2×C711yescharacteristic, complemented
19C2×C7×D91C3×C511yescharacteristic, direct product factor, Hall
20C3×C72×C13C22×C511yescharacteristic, complemented, Hall
21C2×C5×D91C3×C711yescharacteristic, direct product factor
22C2×C5×C7×D13—71no—
23C2×C3×C5×C72D1311yescharacteristic, complemented
24C3×C5×C7×D7—132no—
25C3×C5×C7×C13—23no—
26C3×C5×C7×C13C2×D711yescharacteristic, complemented
27C3×C5×C7×C13C22×C711yescharacteristic, complemented
28C2×C72×C13C2×C3×C511yescharacteristic, complemented
29C7×D91C2×C3×C512yesdirect product factor
30C2×C3×D91C5×C711yescharacteristic, direct product factor
31C2×C3×C7×D13—71no—
32C2×C5×C7×D7—131noHall
33C2×C5×C7×C13—23no—
34C2×C5×C7×C13C3×D711yescharacteristic, complemented
35C2×C5×C7×C13C2×C3×C711yescharacteristic, complemented
36C5×D91C2×C3×C712yesdirect product factor
37C5×C7×D13—72no—
38C2×C3×C5×D13—71noHall
39C3×C5×C72C2×D1311yescharacteristic, complemented, Hall
40C72×C13C22×C3×C511yescharacteristic, complemented, Hall
41C2×C3×C7×D7—131noHall
42C2×C3×C7×C13—23no—
43C2×C3×C7×C13C5×D711yescharacteristic, complemented
44C2×C3×C7×C13C2×C5×C711yescharacteristic, complemented
45C3×D91C2×C5×C712yesdirect product factor
46C3×C7×D13—72no—
47C2×C5×C72C3×D1311yescharacteristic, complemented
48C5×C7×D7—132no—
49C5×C7×C13—23no—
50C5×C7×C13C2×C3×D711yescharacteristic, complemented
51C5×C7×C13C22×C3×C711yescharacteristic, complemented
52C22×C3×C5×C7—911no—
53C2×C3×C5×D7—131no—
54C2×C3×C5×C13C7×D711yescharacteristic, complemented
55C3×C5×D13—72no—
56C2×D91C3×C5×C711yescharacteristic, direct product factor
57C2×C7×D13—71no—
58C2×C3×C72C5×D1311yescharacteristic, complemented
59C3×C7×D7—132no—
60C3×C7×C13—23no—
61C3×C7×C13C2×C5×D711yescharacteristic, complemented
62C3×C7×C13C22×C5×C711yescharacteristic, complemented
63C2×C5×D13—71noHall
64C5×C72C2×C3×D1311yescharacteristic, complemented, Hall
65C2×C3×C5×C7—23no—
66C2×C3×C5×C7—912no—
67C2×C3×C5×C7C7×D1311yescharacteristic, complemented
68C2×C3×C5×C7D9111yescharacteristic, direct product factor
69C3×C5×D7—132no—
70C2×C7×D7—131noHall
71C3×C5×C13C2×C7×D711yescharacteristic, complemented, Hall
72C2×C7×C13—23no—
73C2×C7×C13C3×C5×D711yescharacteristic, complemented
74C2×C7×C13C2×C3×C5×C711yescharacteristic, complemented
75D91C2×C3×C5×C712yesdirect product factor
76C7×D13—72no—
77C2×C3×D13—71noHall
78C3×C72C2×C5×D1311yescharacteristic, complemented, Hall
79C22×C5×C7—911no—
80C2×C5×D7—131no—
81C2×C5×C13C3×C7×D711yescharacteristic, complemented
82C5×D13—72no—
83C3×C5×C7—23no—
84C3×C5×C7C2×C7×D1311yescharacteristic, complemented
85C3×C5×C7C2×D9111yescharacteristic, direct product factor
86C2×C72C3×C5×D1311yescharacteristic, complemented
87C7×D7—132no—
88C7×C13—23no—
89C7×C13C2×C3×C5×D711yescharacteristic, complemented
90C7×C13C22×C3×C5×C711yescharacteristic, complemented
91C22×C3×C7—911no—
92C2×C3×D7—131no—
93C2×C3×C13C5×C7×D711yescharacteristic, complemented
94C3×D13—72no—
95C2×C5×C7—23no—
96C2×C5×C7—912no—
97C2×C5×C7C3×C7×D1311yescharacteristic, complemented
98C2×C5×C7C3×D9111yescharacteristic, direct product factor
99C5×D7—132no—
100C5×C13C2×C3×C7×D711yescharacteristic, complemented, Hall
101C22×C3×C5—911noHall
102C2×D13—71noHall
103C72C2×C3×C5×D1311yescharacteristic, complemented, Sylow
104C2×C3×C7—23no—
105C2×C3×C7—912no—
106C2×C3×C7C5×C7×D1311yescharacteristic, complemented
107C2×C3×C7C5×D9111yescharacteristic, direct product factor
108C3×D7—132no—
109C3×C13C2×C5×C7×D711yescharacteristic, complemented, Hall
110C5×C7—23no—
111C5×C7C2×C3×C7×D1311yescharacteristic, complemented
112C5×C7C2×C3×D9111yescharacteristic, direct product factor
113C2×C3×C5—912no—
114C2×C3×C5C7×D9111yescharacteristic, direct product factor
115C22×C7—911no—
116C2×D7—131no—
117C2×C13C3×C5×C7×D711yescharacteristic, complemented
118D13—72no—
119C3×C7—23no—
120C3×C7C2×C5×C7×D1311yescharacteristic, complemented
121C3×C7C2×C5×D9111yescharacteristic, direct product factor
122C22×C5—911noHall
123C3×C5C2×C7×D9111yescharacteristic, direct product factor, Hall
124C2×C7—23no—
125C2×C7—912no—
126C2×C7C3×C5×C7×D1311yescharacteristic, complemented
127C2×C7C3×C5×D9111yescharacteristic, direct product factor
128D7—132no—
129C13C2×C3×C5×C7×D711yescharacteristic, complemented, Sylow
130C22×C3—911noHall
131C2×C5—912no—
132C2×C5C3×C7×D9111yescharacteristic, direct product factor
133C7—23no—
134C7C2×C3×C5×C7×D1311yescharacteristic, complemented
135C7C2×C3×C5×D9111yescharacteristic, direct product factor
136C2×C3—912no—
137C2×C3C5×C7×D9111yescharacteristic, direct product factor
138C5C2×C3×C7×D9111yescharacteristic, direct product factor, Sylow
139C22—911noSylow
140C3C2×C5×C7×D9111yescharacteristic, direct product factor, Sylow
141C2—912no—
142C2C3×C5×C7×D9111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C5×C7D91
commutator, cosocle, hypocenterC7×C13C22×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C72×C13C2
LCSG ▷ C7×C13
UCSC1 ◁ C2×C3×C5×C7

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D91C2direct (N × H)
2. C2×C3×C5×C72×C13C2semidirect
3. C2×C5×C7×D91C3direct (N × H)
4. C3×C5×C72×C13C22semidirect
5. C2×C3×C7×D91C5direct (N × H)
6. C5×C7×D91C2×C3direct (N × H)
7. C2×C5×C72×C13C2×C3semidirect
8. C2×C3×C5×D91C7direct (N × H)
10. C3×C7×D91C2×C5direct (N × H)
11. C2×C3×C72×C13C2×C5semidirect
12. C5×C72×C13C22×C3semidirect
14. C3×C5×D91C2×C7direct (N × H)
17. C2×C3×C5×C7×C13D7semidirect
18. C2×C3×C5×C7×C13C2×C7semidirect
19. C2×C7×D91C3×C5direct (N × H)
20. C3×C72×C13C22×C5semidirect
21. C2×C5×D91C3×C7direct (N × H)
23. C2×C3×C5×C72D13semidirect
26. C3×C5×C7×C13C2×D7semidirect
27. C3×C5×C7×C13C22×C7semidirect
28. C2×C72×C13C2×C3×C5semidirect
29. C7×D91C2×C3×C5direct (N × H)
30. C2×C3×D91C5×C7direct (N × H)
34. C2×C5×C7×C13C3×D7semidirect
35. C2×C5×C7×C13C2×C3×C7semidirect
36. C5×D91C2×C3×C7direct (N × H)
39. C3×C5×C72C2×D13semidirect
40. C72×C13C22×C3×C5semidirect
43. C2×C3×C7×C13C5×D7semidirect
44. C2×C3×C7×C13C2×C5×C7semidirect
45. C3×D91C2×C5×C7direct (N × H)
47. C2×C5×C72C3×D13semidirect
50. C5×C7×C13C2×C3×D7semidirect
51. C5×C7×C13C22×C3×C7semidirect
54. C2×C3×C5×C13C7×D7semidirect
56. C2×D91C3×C5×C7direct (N × H)
58. C2×C3×C72C5×D13semidirect
61. C3×C7×C13C2×C5×D7semidirect
62. C3×C7×C13C22×C5×C7semidirect
64. C5×C72C2×C3×D13semidirect
67. C2×C3×C5×C7C7×D13semidirect
68. C2×C3×C5×C7D91direct (N × H)
71. C3×C5×C13C2×C7×D7semidirect
73. C2×C7×C13C3×C5×D7semidirect
74. C2×C7×C13C2×C3×C5×C7semidirect
75. D91C2×C3×C5×C7direct (N × H)
78. C3×C72C2×C5×D13semidirect
81. C2×C5×C13C3×C7×D7semidirect
84. C3×C5×C7C2×C7×D13semidirect
85. C3×C5×C7C2×D91direct (N × H)
86. C2×C72C3×C5×D13semidirect
89. C7×C13C2×C3×C5×D7semidirect
90. C7×C13C22×C3×C5×C7semidirect
93. C2×C3×C13C5×C7×D7semidirect
97. C2×C5×C7C3×C7×D13semidirect
98. C2×C5×C7C3×D91direct (N × H)
100. C5×C13C2×C3×C7×D7semidirect
103. C72C2×C3×C5×D13semidirect
106. C2×C3×C7C5×C7×D13semidirect
107. C2×C3×C7C5×D91direct (N × H)
109. C3×C13C2×C5×C7×D7semidirect
111. C5×C7C2×C3×C7×D13semidirect
112. C5×C7C2×C3×D91direct (N × H)
114. C2×C3×C5C7×D91direct (N × H)
117. C2×C13C3×C5×C7×D7semidirect
120. C3×C7C2×C5×C7×D13semidirect
121. C3×C7C2×C5×D91direct (N × H)
123. C3×C5C2×C7×D91direct (N × H)
126. C2×C7C3×C5×C7×D13semidirect
127. C2×C7C3×C5×D91direct (N × H)
129. C13C2×C3×C5×C7×D7semidirect
132. C2×C5C3×C7×D91direct (N × H)
134. C7C2×C3×C5×C7×D13semidirect
135. C7C2×C3×C5×D91direct (N × H)
137. C2×C3C5×C7×D91direct (N × H)
138. C5C2×C3×C7×D91direct (N × H)
140. C3C2×C5×C7×D91direct (N × H)
142. C2C3×C5×C7×D91direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C7×D912
C2×C3×C5×C72×C132
C2×C5×C7×D913
C2×C3×C7×D915
C2×C3×C5×D917
C2×C3×C5×C7×D137
C2×C3×C5×C7×D713