Finite Group Databasebeta

← C2×C5×C17×D105 #49088057

Subgroups — C2×C5×C17×D105 #49088057

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×C17×D105C212yesmaximal, direct product factor
2C2×C3×C52×C7×C17C211yesmaximal, characteristic, complemented
3C2×C5×C17×D35—31nomaximal, Hall
4C3×C52×C7×C17C2211yescharacteristic, complemented, Hall
5C2×C5×C17×D21—51nomaximal
6C2×C17×D105C511yesmaximal, characteristic, direct product factor
7C5×C17×D35—32no—
8C2×C52×C7×C17D311yescharacteristic, complemented
9C2×C5×C17×D15—71nomaximal, Hall
10C17×D105C2×C512yesdirect product factor
11C5×C17×D21—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×C17×D15—72no—
17C2×C3×C52×C17D711yescharacteristic, complemented
18C2×C5×D7×C17—151no—
19C2×C17×D35—31no—
20C2×C5×D105C1711yesmaximal, characteristic, direct product factor, Hall
21C3×C5×C7×C17—22no—
22C3×C5×C7×C17C2×D511yescharacteristic, complemented
23C3×C5×C7×C17C22×C511yescharacteristic, complemented
24C2×C5×D5×C17—211noHall
25C2×C17×D21—51noHall
26C3×C52×C17C2×D711yescharacteristic, complemented, Hall
27C2×C5×C7×C17—22no—
28C2×C5×C7×C17C5×D311yescharacteristic, complemented
29C2×C5×C7×C17D1511yescharacteristic, complemented
30C17×D35—32no—
31C5×D7×C17—152no—
32C2×C3×C52×C7C2×C1711yescharacteristic, complemented
33C5×D105C2×C1712yesdirect product factor
34C2×C17×D15—71no—
35C2×C5×D3×C17—351no—
36C2×C52×C17D2111yescharacteristic, complemented
37C5×D5×C17—212no—
38C2×C3×C7×C17C5×D511yescharacteristic, complemented
39C17×D21—52no—
40C2×C5×D35—31noHall
41C5×C7×C17—22no—
42C5×C7×C17C2×C5×D311yescharacteristic, complemented
43C5×C7×C17C2×D1511yescharacteristic, complemented
44C3×C52×C7C22×C1711yescharacteristic, complemented, Hall
45C2×C3×C5×C17—22no—
46C2×C3×C5×C17C5×D711yescharacteristic, complemented
47C2×C3×C5×C17D3511yescharacteristic, complemented
48C17×D15—72no—
49C5×D3×C17—352no—
50C2×D7×C17—151noHall
51C52×C17C2×D2111yescharacteristic, complemented, Hall
52C2×D105C5×C1711yescharacteristic, direct product factor
53C2×C5×D21—51no—
54C3×C7×C17C2×C5×D511yescharacteristic, complemented, Hall
55C2×C52×C7D3×C1711yescharacteristic, complemented
56C5×D35—32no—
57C22×C5×C17—1051no—
58C2×D5×C17—211no—
59C2×C5×D15—71noHall
60C3×C5×C17—22no—
61C3×C5×C17C2×C5×D711yescharacteristic, complemented
62C3×C5×C17C2×D3511yescharacteristic, complemented
63C2×C7×C17C5×D1511yescharacteristic, complemented
64D7×C17—152no—
65C2×C3×C5×C7—22no—
66C2×C3×C5×C7D5×C1711yescharacteristic, complemented
67C2×C3×C5×C7C2×C5×C1711yescharacteristic, complemented
68D105C2×C5×C1712yesdirect product factor
69C5×D21—52no—
70C2×D3×C17—351noHall
71C52×C7C2×D3×C1711yescharacteristic, complemented, Hall
72C2×C5×C17—22no—
73C2×C5×C17—1052no—
74C2×C5×C17C5×D2111yescharacteristic, complemented
75C2×C5×C17D10511yescharacteristic, direct product factor
76D5×C17—212no—
77C2×C3×C52D7×C1711yescharacteristic, complemented
78C5×D15—72no—
79C2×D35—31no—
80C2×C5×D7—151no—
81C7×C17C2×C5×D1511yescharacteristic, complemented, Hall
82C3×C5×C7—22no—
83C3×C5×C7C2×D5×C1711yescharacteristic, complemented
84C3×C5×C7C22×C5×C1711yescharacteristic, complemented
85C2×C3×C17C5×D3511yescharacteristic, complemented
86D3×C17—352no—
87C2×C5×D5—211noHall
88C5×C17—22no—
89C5×C17C2×C5×D2111yescharacteristic, complemented
90C5×C17C2×D10511yescharacteristic, direct product factor
91C2×D21—51noHall
92C3×C52C2×D7×C1711yescharacteristic, complemented, Hall
93C2×C5×C7—22no—
94C2×C5×C7C5×D3×C1711yescharacteristic, complemented
95C2×C5×C7C17×D1511yescharacteristic, complemented
96D35—32no—
97C5×D7—152no—
98C22×C17—1051noHall
99C2×D15—71no—
100C2×C5×D3—351no—
101C3×C17C2×C5×D3511yescharacteristic, complemented, Hall
102C2×C52C17×D2111yescharacteristic, complemented
103C5×D5—212no—
104C2×C3×C7C5×D5×C1711yescharacteristic, complemented
105D21—52no—
106C5×C7—22no—
107C5×C7C2×C5×D3×C1711yescharacteristic, complemented
108C5×C7C2×C17×D1511yescharacteristic, complemented
109C2×C17—1052no—
110C2×C17C5×D10511yescharacteristic, direct product factor
111C2×C3×C5—22no—
112C2×C3×C5C5×D7×C1711yescharacteristic, complemented
113C2×C3×C5C17×D3511yescharacteristic, complemented
114D15—72no—
115C5×D3—352no—
116C2×D7—151noHall
117C52C2×C17×D2111yescharacteristic, complemented, Sylow
118C3×C7C2×C5×D5×C1711yescharacteristic, complemented, Hall
119C22×C5—1051no—
120C2×D5—211no—
121C17C2×C5×D10511yescharacteristic, direct product factor, Sylow
122C3×C5—22no—
123C3×C5C2×C17×D3511yescharacteristic, complemented
124C3×C5C2×C5×D7×C1711yescharacteristic, complemented
125C2×C7C5×C17×D1511yescharacteristic, complemented
126D7—152no—
127C2×D3—351noHall
128C2×C5—22no—
129C2×C5—1052no—
130C2×C5C5×C17×D2111yescharacteristic, complemented
131C2×C5C17×D10511yescharacteristic, direct product factor
132D5—212no—
133C7C2×C5×C17×D1511yescharacteristic, complemented, Sylow
134C2×C3C5×C17×D3511yescharacteristic, complemented
135D3—352no—
136C5—22no—
137C5C2×C17×D10511yescharacteristic, direct product factor
138C5C2×C5×C17×D2111yescharacteristic, complemented
139C22—1051noSylow
140C3C2×C5×C17×D3511yescharacteristic, complemented, Sylow
141C2—1052no—
142C2C5×C17×D10511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5×C17D105
commutator, cosocle, hypocenterC3×C5×C7C22×C5×C17
FrattiniC1G
Fitting, socleC2×C3×C52×C7×C17C2
LCSG ▷ C3×C5×C7
UCSC1 ◁ C2×C5×C17

Complements

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

NH ≅ G/Ntype
1. C5×C17×D105C2direct (N × H)
2. C2×C3×C52×C7×C17C2semidirect
4. C3×C52×C7×C17C22semidirect
6. C2×C17×D105C5direct (N × H)
8. C2×C52×C7×C17D3semidirect
10. C17×D105C2×C5direct (N × H)
13. C2×C3×C5×C7×C17D5semidirect
14. C2×C3×C5×C7×C17C2×C5semidirect
15. C52×C7×C17C2×D3semidirect
17. C2×C3×C52×C17D7semidirect
20. C2×C5×D105C17direct (N × H)
22. C3×C5×C7×C17C2×D5semidirect
23. C3×C5×C7×C17C22×C5semidirect
26. C3×C52×C17C2×D7semidirect
28. C2×C5×C7×C17C5×D3semidirect
29. C2×C5×C7×C17D15semidirect
32. C2×C3×C52×C7C2×C17semidirect
33. C5×D105C2×C17direct (N × H)
36. C2×C52×C17D21semidirect
38. C2×C3×C7×C17C5×D5semidirect
42. C5×C7×C17C2×C5×D3semidirect
43. C5×C7×C17C2×D15semidirect
44. C3×C52×C7C22×C17semidirect
46. C2×C3×C5×C17C5×D7semidirect
47. C2×C3×C5×C17D35semidirect
51. C52×C17C2×D21semidirect
52. C2×D105C5×C17direct (N × H)
54. C3×C7×C17C2×C5×D5semidirect
55. C2×C52×C7D3×C17semidirect
61. C3×C5×C17C2×C5×D7semidirect
62. C3×C5×C17C2×D35semidirect
63. C2×C7×C17C5×D15semidirect
66. C2×C3×C5×C7D5×C17semidirect
67. C2×C3×C5×C7C2×C5×C17semidirect
68. D105C2×C5×C17direct (N × H)
71. C52×C7C2×D3×C17semidirect
74. C2×C5×C17C5×D21semidirect
75. C2×C5×C17D105direct (N × H)
77. C2×C3×C52D7×C17semidirect
81. C7×C17C2×C5×D15semidirect
83. C3×C5×C7C2×D5×C17semidirect
84. C3×C5×C7C22×C5×C17semidirect
85. C2×C3×C17C5×D35semidirect
89. C5×C17C2×C5×D21semidirect
90. C5×C17C2×D105direct (N × H)
92. C3×C52C2×D7×C17semidirect
94. C2×C5×C7C5×D3×C17semidirect
95. C2×C5×C7C17×D15semidirect
101. C3×C17C2×C5×D35semidirect
102. C2×C52C17×D21semidirect
104. C2×C3×C7C5×D5×C17semidirect
107. C5×C7C2×C5×D3×C17semidirect
108. C5×C7C2×C17×D15semidirect
110. C2×C17C5×D105direct (N × H)
112. C2×C3×C5C5×D7×C17semidirect
113. C2×C3×C5C17×D35semidirect
117. C52C2×C17×D21semidirect
118. C3×C7C2×C5×D5×C17semidirect
121. C17C2×C5×D105direct (N × H)
123. C3×C5C2×C17×D35semidirect
124. C3×C5C2×C5×D7×C17semidirect
125. C2×C7C5×C17×D15semidirect
130. C2×C5C5×C17×D21semidirect
131. C2×C5C17×D105direct (N × H)
133. C7C2×C5×C17×D15semidirect
134. C2×C3C5×C17×D35semidirect
137. C5C2×C17×D105direct (N × H)
138. C5C2×C5×C17×D21semidirect
140. C3C2×C5×C17×D35semidirect
142. C2C5×C17×D105direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C17×D1052
C2×C3×C52×C7×C172
C2×C5×C17×D353
C2×C5×C17×D215
C2×C17×D1055
C2×C5×C17×D157
C2×C5×D10517