Finite Group Databasebeta

← C2×C5×C7×D255 #49088056

Subgroups — C2×C5×C7×D255 #49088056

Order 35700.

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

normal subgroups only

This group has 192 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
1C5×C7×D255C212yesmaximal, direct product factor
2C2×C3×C52×C7×C17C211yesmaximal, characteristic, complemented
3C2×C5×C7×D85—31nomaximal, Hall
4C3×C52×C7×C17C2211yescharacteristic, complemented, Hall
5C2×C5×C7×D51—51nomaximal
6C2×C7×D255C511yesmaximal, characteristic, direct product factor
7C5×C7×D85—32no—
8C2×C52×C7×C17D311yescharacteristic, complemented
9C2×C5×D255C711yesmaximal, characteristic, direct product factor, Hall
10C7×D255C2×C512yesdirect product factor
11C5×C7×D51—52no—
12C2×C3×C5×C7×C17—22no—
13C2×C3×C5×C7×C17D511yescharacteristic, complemented
14C2×C3×C5×C7×C17C2×C511yescharacteristic, complemented
15C52×C7×C17C2×D311yescharacteristic, complemented, Hall
16C5×D255C2×C712yesdirect product factor
17C2×C3×C52×C17C2×C711yescharacteristic, complemented
18C2×C5×C7×D17—151no—
19C2×C7×D85—31no—
20C2×C5×C7×D15—171nomaximal, Hall
21C3×C5×C7×C17—22no—
22C3×C5×C7×C17C2×D511yescharacteristic, complemented
23C3×C5×C7×C17C22×C511yescharacteristic, complemented
24C2×C5×D85—31noHall
25C2×C7×D51—51noHall
26C3×C52×C17C22×C711yescharacteristic, complemented, Hall
27C2×C5×C7×C17—22no—
28C2×C5×C7×C17C5×D311yescharacteristic, complemented
29C2×C5×C7×C17D1511yescharacteristic, complemented
30C7×D85—32no—
31C5×C7×D17—152no—
32C2×C3×C52×C7D1711yescharacteristic, complemented
33C5×C7×D15—172no—
34C2×D255C5×C711yescharacteristic, direct product factor
35C2×C5×D51—51no—
36C2×C52×C17D3×C711yescharacteristic, complemented
37C5×D85—32no—
38C2×C3×C7×C17C5×D511yescharacteristic, complemented
39C7×D51—52no—
40C2×C5×C7×D5—511noHall
41C5×C7×C17—22no—
42C5×C7×C17C2×C5×D311yescharacteristic, complemented
43C5×C7×C17C2×D1511yescharacteristic, complemented
44C3×C52×C7C2×D1711yescharacteristic, complemented, Hall
45C2×C3×C5×C17—22no—
46C2×C3×C5×C17C7×D511yescharacteristic, complemented
47C2×C3×C5×C17C2×C5×C711yescharacteristic, complemented
48D255C2×C5×C712yesdirect product factor
49C5×D51—52no—
50C2×C7×D17—151noHall
51C52×C17C2×D3×C711yescharacteristic, complemented, Hall
52C2×C7×D15—171no—
53C2×C5×D3×C7—851no—
54C3×C7×C17C2×C5×D511yescharacteristic, complemented, Hall
55C2×C52×C7D5111yescharacteristic, complemented
56C5×C7×D5—512no—
57C2×D85—31no—
58C2×C5×D17—151no—
59C2×C5×D15—171noHall
60C3×C5×C17—22no—
61C3×C5×C17C2×C7×D511yescharacteristic, complemented
62C3×C5×C17C22×C5×C711yescharacteristic, complemented
63C2×C7×C17C5×D1511yescharacteristic, complemented
64C7×D17—152no—
65C2×C3×C5×C7—22no—
66C2×C3×C5×C7C5×D1711yescharacteristic, complemented
67C2×C3×C5×C7D8511yescharacteristic, complemented
68C7×D15—172no—
69C5×D3×C7—852no—
70C2×D51—51noHall
71C52×C7C2×D5111yescharacteristic, complemented, Hall
72C2×C5×C17—22no—
73C2×C5×C17C5×D3×C711yescharacteristic, complemented
74C2×C5×C17C7×D1511yescharacteristic, complemented
75D85—32no—
76C5×D17—152no—
77C2×C3×C52C7×D1711yescharacteristic, complemented
78C5×D15—172no—
79C22×C5×C7—2551no—
80C2×C7×D5—511no—
81C7×C17C2×C5×D1511yescharacteristic, complemented, Hall
82C3×C5×C7—22no—
83C3×C5×C7C2×C5×D1711yescharacteristic, complemented
84C3×C5×C7C2×D8511yescharacteristic, complemented
85C2×C3×C17C5×C7×D511yescharacteristic, complemented
86D51—52no—
87C2×C5×D5—511noHall
88C5×C17—22no—
89C5×C17C2×C5×D3×C711yescharacteristic, complemented
90C5×C17C2×C7×D1511yescharacteristic, complemented
91C2×D3×C7—851noHall
92C3×C52C2×C7×D1711yescharacteristic, complemented, Hall
93C2×C5×C7—22no—
94C2×C5×C7—2552no—
95C2×C5×C7C5×D5111yescharacteristic, complemented
96C2×C5×C7D25511yescharacteristic, direct product factor
97C7×D5—512no—
98C2×D17—151noHall
99C2×D15—171no—
100C2×C5×D3—851no—
101C3×C17C2×C5×C7×D511yescharacteristic, complemented, Hall
102C2×C52C7×D5111yescharacteristic, complemented
103C5×D5—512no—
104C2×C3×C7C5×D8511yescharacteristic, complemented
105D3×C7—852no—
106C5×C7—22no—
107C5×C7C2×C5×D5111yescharacteristic, complemented
108C5×C7C2×D25511yescharacteristic, direct product factor
109C2×C17C5×C7×D1511yescharacteristic, complemented
110D17—152no—
111C2×C3×C5—22no—
112C2×C3×C5C5×C7×D1711yescharacteristic, complemented
113C2×C3×C5C7×D8511yescharacteristic, complemented
114D15—172no—
115C5×D3—852no—
116C22×C7—2551noHall
117C52C2×C7×D5111yescharacteristic, complemented, Sylow
118C3×C7C2×C5×D8511yescharacteristic, complemented, Hall
119C22×C5—2551no—
120C2×D5—511no—
121C17C2×C5×C7×D1511yescharacteristic, complemented, Sylow
122C3×C5—22no—
123C3×C5C2×C7×D8511yescharacteristic, complemented
124C3×C5C2×C5×C7×D1711yescharacteristic, complemented
125C2×C7—2552no—
126C2×C7C5×D25511yescharacteristic, direct product factor
127C2×D3—851noHall
128C2×C5—22no—
129C2×C5—2552no—
130C2×C5C5×C7×D5111yescharacteristic, complemented
131C2×C5C7×D25511yescharacteristic, direct product factor
132D5—512no—
133C7C2×C5×D25511yescharacteristic, direct product factor, Sylow
134C2×C3C5×C7×D8511yescharacteristic, complemented
135D3—852no—
136C5—22no—
137C5C2×C7×D25511yescharacteristic, direct product factor
138C5C2×C5×C7×D5111yescharacteristic, complemented
139C22—2551noSylow
140C3C2×C5×C7×D8511yescharacteristic, complemented, Sylow
141C2—2552no—
142C2C5×C7×D25511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5×C7D255
commutator, cosocle, hypocenterC3×C5×C17C22×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C52×C7×C17C2
LCSG ▷ C3×C5×C17
UCSC1 ◁ C2×C5×C7

Complements

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

NH ≅ G/Ntype
1. C5×C7×D255C2direct (N × H)
2. C2×C3×C52×C7×C17C2semidirect
4. C3×C52×C7×C17C22semidirect
6. C2×C7×D255C5direct (N × H)
8. C2×C52×C7×C17D3semidirect
9. C2×C5×D255C7direct (N × H)
10. C7×D255C2×C5direct (N × H)
13. C2×C3×C5×C7×C17D5semidirect
14. C2×C3×C5×C7×C17C2×C5semidirect
15. C52×C7×C17C2×D3semidirect
16. C5×D255C2×C7direct (N × H)
17. C2×C3×C52×C17C2×C7semidirect
22. C3×C5×C7×C17C2×D5semidirect
23. C3×C5×C7×C17C22×C5semidirect
26. C3×C52×C17C22×C7semidirect
28. C2×C5×C7×C17C5×D3semidirect
29. C2×C5×C7×C17D15semidirect
32. C2×C3×C52×C7D17semidirect
34. C2×D255C5×C7direct (N × H)
36. C2×C52×C17D3×C7semidirect
38. C2×C3×C7×C17C5×D5semidirect
42. C5×C7×C17C2×C5×D3semidirect
43. C5×C7×C17C2×D15semidirect
44. C3×C52×C7C2×D17semidirect
46. C2×C3×C5×C17C7×D5semidirect
47. C2×C3×C5×C17C2×C5×C7semidirect
48. D255C2×C5×C7direct (N × H)
51. C52×C17C2×D3×C7semidirect
54. C3×C7×C17C2×C5×D5semidirect
55. C2×C52×C7D51semidirect
61. C3×C5×C17C2×C7×D5semidirect
62. C3×C5×C17C22×C5×C7semidirect
63. C2×C7×C17C5×D15semidirect
66. C2×C3×C5×C7C5×D17semidirect
67. C2×C3×C5×C7D85semidirect
71. C52×C7C2×D51semidirect
73. C2×C5×C17C5×D3×C7semidirect
74. C2×C5×C17C7×D15semidirect
77. C2×C3×C52C7×D17semidirect
81. C7×C17C2×C5×D15semidirect
83. C3×C5×C7C2×C5×D17semidirect
84. C3×C5×C7C2×D85semidirect
85. C2×C3×C17C5×C7×D5semidirect
89. C5×C17C2×C5×D3×C7semidirect
90. C5×C17C2×C7×D15semidirect
92. C3×C52C2×C7×D17semidirect
95. C2×C5×C7C5×D51semidirect
96. C2×C5×C7D255direct (N × H)
101. C3×C17C2×C5×C7×D5semidirect
102. C2×C52C7×D51semidirect
104. C2×C3×C7C5×D85semidirect
107. C5×C7C2×C5×D51semidirect
108. C5×C7C2×D255direct (N × H)
109. C2×C17C5×C7×D15semidirect
112. C2×C3×C5C5×C7×D17semidirect
113. C2×C3×C5C7×D85semidirect
117. C52C2×C7×D51semidirect
118. C3×C7C2×C5×D85semidirect
121. C17C2×C5×C7×D15semidirect
123. C3×C5C2×C7×D85semidirect
124. C3×C5C2×C5×C7×D17semidirect
126. C2×C7C5×D255direct (N × H)
130. C2×C5C5×C7×D51semidirect
131. C2×C5C7×D255direct (N × H)
133. C7C2×C5×D255direct (N × H)
134. C2×C3C5×C7×D85semidirect
137. C5C2×C7×D255direct (N × H)
138. C5C2×C5×C7×D51semidirect
140. C3C2×C5×C7×D85semidirect
142. C2C5×C7×D255direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C7×D2552
C2×C3×C52×C7×C172
C2×C5×C7×D853
C2×C5×C7×D515
C2×C7×D2555
C2×C5×D2557
C2×C5×C7×D1517