Finite Group Databasebeta

← D85⋊D105 #49087976

Subgroups — D85⋊D105 #49087976

Order 35700.

192 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 45 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×D85C211yesmaximal, characteristic, complemented
2C5×D1785C211yesmaximal, characteristic, complemented
3C17×C3⋊(C5⋊D35)C211yesmaximal, characteristic, complemented
4D85⋊D35—31nomaximal, Hall
5C3×C52×C7×C17C2211yescharacteristic, complemented, Hall
6D85⋊D21—51nomaximal
7D17×D105—51nomaximal
8C17×C5⋊D35—31no—
9C5×D595—31no—
10C5×C7×D85D311yescharacteristic, complemented
11D85⋊D15—71nomaximal, Hall
12D1785D511yescharacteristic, complemented
13C17×D105—51no—
14C17×D105—51no—
15C17×D105—102no—
16C5×D357—51no—
17C3×C7×D85D511yescharacteristic, complemented
18C3×C5×C7×D17—51no—
19C52×C7×C17C2×D311yescharacteristic, complemented, Hall
20C17×C3⋊(C5⋊D5)—71no—
21C5×D255—71no—
22C3×C5×D85D711yescharacteristic, complemented
23D35⋊D17—151no—
24D17×D35—151no—
25D5×D105—171nomaximal, Hall
26C3×C5×C7×C17—22no—
27C3×C5×C7×C17C2×D511yescharacteristic, complemented
28C3×C5×C7×C17C2×D511yescharacteristic, complemented
29(C5⋊D5)⋊D17—211noHall
30D17×D21—251noHall
31C3×C52×C17C2×D711yescharacteristic, complemented, Hall
32D595—31no—
33C17×D35—151no—
34C17×D35—151no—
35C17×D35—302no—
36C7×D85D1511yescharacteristic, complemented
37C5×D119—151no—
38C5×C7×D17—51no—
39C3⋊(C5⋊D35)D1711yescharacteristic, complemented
40C5×D105—171no—
41C3×C5×C7×D5—171no—
42D15⋊D17—351no—
43D15×D17—351no—
44C17×C5⋊D5—211no—
45C5×D85—211no—
46C5×D85D2111yescharacteristic, complemented
47D357—51no—
48C17×D21—251no—
49C3×C7×D17—51no—
50D5×D35—511noHall
51C5×C7×C17—22no—
52C5×C7×C17D3×D511yescharacteristic, complemented
53C5×C7×C17C2×D1511yescharacteristic, complemented
54C3×C52×C7C2×D1711yescharacteristic, complemented, Hall
55D255—71no—
56C17×D15—351no—
57C17×D15—351no—
58C17×D15—702no—
59C5×D51—351no—
60C3×D85D3511yescharacteristic, complemented
61C3×C5×D17—51no—
62D7×D17—751noHall
63C52×C17C2×D2111yescharacteristic, complemented, Hall
64C2×D105—851no—
65D5×D21—851no—
66C3×C7×C17D5211yescharacteristic, complemented, Hall
67C5⋊D35—31no—
68C5×D35—511no—
69C5×C7×D5—171no—
70D5×D17—1051no—
71D5×D17—1051no—
72D5×D15—1191noHall
73C3×C5×C17—22no—
74C3×C5×C17D5×D711yescharacteristic, complemented
75C3×C5×C17C2×D3511yescharacteristic, complemented
76D119—151no—
77C7×D17—51no—
78D7×C17—751no—
79C2×C3×C5×C7—851no—
80D105—51no—
81D105—51no—
82D105—102no—
83D105—171no—
84C5×D21—851no—
85C3×C7×D5—171no—
86D3×D17—1751noHall
87C52×C7D3×D1711yescharacteristic, complemented, Hall
88D85—211no—
89D85D10511yescharacteristic, complemented
90C5×D17—51no—
91C5×D17—1051no—
92D5×C17—1051no—
93D5×C17—1051no—
94D5×C17—2102no—
95C3⋊(C5⋊D5)—71no—
96C5×D15—1191no—
97C3×C5×D5—171no—
98C2×D35—2551no—
99D5×D7—2551no—
100C7×C17D5×D1511yescharacteristic, complemented, Hall
101C3×C5×C7—22no—
102C3×C5×C7D5×D1711yescharacteristic, complemented
103C3×C5×C7D5×D1711yescharacteristic, complemented
104D51—351no—
105C3×D17—51no—
106D3×C17—1751no—
107D52—3571noHall
108C5×C17—22no—
109C5×C17D5×D2111yescharacteristic, complemented
110C5×C17C2×D10511yescharacteristic, complemented
111C2×D21—4251noHall
112C3×C52D7×D1711yescharacteristic, complemented, Hall
113C2×C5×C7—851no—
114D35—151no—
115D35—151no—
116D35—302no—
117D35—511no—
118C5×D7—2551no—
119C7×D5—171no—
120C2×D17—5251noHall
121C2×D15—5951no—
122D3×D5—5951no—
123C3×C17D5×D3511yescharacteristic, complemented, Hall
124C5⋊D5—211no—
125C5×D5—171no—
126C5×D5—3571no—
127C2×C3×C7—851no—
128D21—251no—
129D21—851no—
130C5×C7—22no—
131C5×C7D15×D1711yescharacteristic, complemented
132C5×C7D15⋊D1711yescharacteristic, complemented
133C2×C17—5251no—
134D17—51no—
135D17—1051no—
136C2×C3×C5—851no—
137D15—351no—
138D15—351no—
139D15—702no—
140D15—1191no—
141C3×D5—171no—
142C5×D3—5951no—
143C2×D7—12751noHall
144C52D17×D2111yescharacteristic, complemented, Sylow
145C3×C7(C5⋊D5)⋊D1711yescharacteristic, complemented, Hall
146C2×D5—17851no—
147C2×D5—17851no—
148C17D5×D10511yescharacteristic, complemented, Sylow
149C3×C5—22no—
150C3×C5D17×D3511yescharacteristic, complemented
151C3×C5D35⋊D1711yescharacteristic, complemented
152C2×C7—851no—
153D7—751no—
154D7—2551no—
155C2×D3—29751noHall
156C2×C5—851no—
157C2×C5—17851no—
158D5—171no—
159D5—3571no—
160D5—1051no—
161D5—1051no—
162D5—2102no—
163C7D85⋊D1511yescharacteristic, complemented, Sylow
164C2×C3—851no—
165D3—5951no—
166D3—1751no—
167C5—22no—
168C5D17×D10511yescharacteristic, complemented
169C5D85⋊D2111yescharacteristic, complemented
170C22—89251noSylow
171C3D85⋊D3511yescharacteristic, complemented, Sylow
172C2—5251no—
173C2—851no—
174C2—17851no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C7×C17C22
LCSG ▷ C3×C52×C7×C17
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D85C2semidirect
2. C5×D1785C2semidirect
3. C17×C3⋊(C5⋊D35)C2semidirect
5. C3×C52×C7×C17C22semidirect
10. C5×C7×D85D3semidirect
12. D1785D5semidirect
17. C3×C7×D85D5semidirect
19. C52×C7×C17C2×D3semidirect
22. C3×C5×D85D7semidirect
27. C3×C5×C7×C17C2×D5semidirect
28. C3×C5×C7×C17C2×D5semidirect
31. C3×C52×C17C2×D7semidirect
36. C7×D85D15semidirect
39. C3⋊(C5⋊D35)D17semidirect
46. C5×D85D21semidirect
52. C5×C7×C17D3×D5semidirect
53. C5×C7×C17C2×D15semidirect
54. C3×C52×C7C2×D17semidirect
60. C3×D85D35semidirect
63. C52×C17C2×D21semidirect
66. C3×C7×C17D52semidirect
74. C3×C5×C17D5×D7semidirect
75. C3×C5×C17C2×D35semidirect
87. C52×C7D3×D17semidirect
89. D85D105semidirect
100. C7×C17D5×D15semidirect
102. C3×C5×C7D5×D17semidirect
103. C3×C5×C7D5×D17semidirect
109. C5×C17D5×D21semidirect
110. C5×C17C2×D105semidirect
112. C3×C52D7×D17semidirect
123. C3×C17D5×D35semidirect
131. C5×C7D15×D17semidirect
132. C5×C7D15⋊D17semidirect
144. C52D17×D21semidirect
145. C3×C7(C5⋊D5)⋊D17semidirect
148. C17D5×D105semidirect
150. C3×C5D17×D35semidirect
151. C3×C5D35⋊D17semidirect
163. C7D85⋊D15semidirect
168. C5D17×D105semidirect
169. C5D85⋊D21semidirect
171. C3D85⋊D35semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C7×D852
C5×D17852
C17×C3⋊(C5⋊D35)2
D85⋊D353
D85⋊D215
D17×D1055
D85⋊D157
D5×D10517