Finite Group Databasebeta

← D35⋊D255 #49087982

Subgroups — D35⋊D255 #49087982

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×C17×D35C211yesmaximal, characteristic, complemented
2C5×D1785C211yesmaximal, characteristic, complemented
3C7×C3⋊(C5⋊D85)C211yesmaximal, characteristic, complemented
4D35⋊D85—31nomaximal, Hall
5C3×C52×C7×C17C2211yescharacteristic, complemented, Hall
6D35⋊D51—51nomaximal
7D7×D255—51nomaximal
8C7×C5⋊D85—31no—
9C5×D595—31no—
10C5×C17×D35D311yescharacteristic, complemented
11D5×D255—71nomaximal, Hall
12D1785D511yescharacteristic, complemented
13C7×D255—51no—
14C7×D255—51no—
15C7×D255—102no—
16C5×D357—51no—
17C3×C17×D35D511yescharacteristic, complemented
18C3×C5×D7×C17—51no—
19C52×C7×C17C2×D311yescharacteristic, complemented, Hall
20C3⋊(C5⋊D85)D711yescharacteristic, complemented
21C5×D255—71no—
22C3×C5×D5×C17—71no—
23D35⋊D17—151no—
24D7×D85—151no—
25D35⋊D15—171nomaximal, Hall
26C3×C5×C7×C17—22no—
27C3×C5×C7×C17C2×D511yescharacteristic, complemented
28C3×C5×C7×C17C2×D511yescharacteristic, complemented
29D5×D85—211noHall
30D7×D51—251noHall
31C3×C52×C17C2×D711yescharacteristic, complemented, Hall
32D595—31no—
33C17×D35D1511yescharacteristic, complemented
34C7×D85—151no—
35C7×D85—151no—
36C7×D85—302no—
37C5×D119—151no—
38C5×D7×C17—51no—
39C7×C3⋊(C5⋊D5)—171no—
40C5×D105—171no—
41C3×C5×D35D1711yescharacteristic, complemented
42C2×D255—351no—
43D5×D51—351no—
44C5⋊D85—31no—
45C5×D85—211no—
46C5×D5×C17—71no—
47D357—51no—
48C7×D51—251no—
49C3×D7×C17—51no—
50(C5⋊D5)⋊D7—511noHall
51C5×C7×C17—22no—
52C5×C7×C17D3×D511yescharacteristic, complemented
53C5×C7×C17C2×D1511yescharacteristic, complemented
54C3×C52×C7C2×D1711yescharacteristic, complemented, Hall
55C2×C3×C5×C17—351no—
56D255—51no—
57D255—51no—
58D255—71no—
59D255—102no—
60C5×D51—351no—
61C3×D5×C17—71no—
62D7×D17—751noHall
63C52×C17D3×D711yescharacteristic, complemented, Hall
64D15⋊D7—851no—
65D7×D15—851no—
66C3×C7×C17D5211yescharacteristic, complemented, Hall
67C7×C5⋊D5—511no—
68C5×D35—511no—
69C5×D35D5111yescharacteristic, complemented
70C2×D85—1051no—
71D5×D17—1051no—
72D5×D15—1191noHall
73C3×C5×C17—22no—
74C3×C5×C17D5×D711yescharacteristic, complemented
75C3×C5×C17D5×D711yescharacteristic, complemented
76D119—151no—
77C7×D17—751no—
78D7×C17—51no—
79D105—171no—
80C7×D15—851no—
81C7×D15—851no—
82C7×D15—1702no—
83C5×D21—851no—
84C3×D35D8511yescharacteristic, complemented
85C3×C5×D7—51no—
86C2×D51—1751noHall
87C52×C7C2×D5111yescharacteristic, complemented, Hall
88C2×C5×C17—351no—
89D85—151no—
90D85—151no—
91D85—211no—
92D85—302no—
93C5×D17—1051no—
94D5×C17—71no—
95C3⋊(C5⋊D5)—171no—
96C5×D15—1191no—
97C3×C5×D5—71no—
98D5×D7—2551no—
99D5×D7—2551no—
100C7×C17D5×D1511yescharacteristic, complemented, Hall
101C3×C5×C7—22no—
102C3×C5×C7D5×D1711yescharacteristic, complemented
103C3×C5×C7C2×D8511yescharacteristic, complemented
104C2×C3×C17—351no—
105D51—251no—
106D51—351no—
107D52—3571noHall
108C5×C17—22no—
109C5×C17D7×D1511yescharacteristic, complemented
110C5×C17D15⋊D711yescharacteristic, complemented
111D3×D7—4251noHall
112C3×C52D7×D1711yescharacteristic, complemented, Hall
113D35—511no—
114D35D25511yescharacteristic, complemented
115C5×D7—51no—
116C5×D7—2551no—
117C7×D5—5102no—
118C7×D5—2551no—
119C7×D5—2551no—
120C2×D17—5251noHall
121C2×D15—5951no—
122D3×D5—5951no—
123C3×C17(C5⋊D5)⋊D711yescharacteristic, complemented, Hall
124C5⋊D5—511no—
125C5×D5—71no—
126C5×D5—3571no—
127D21—851no—
128C3×D7—51no—
129D3×C7—4251no—
130C5×C7—22no—
131C5×C7D5×D5111yescharacteristic, complemented
132C5×C7C2×D25511yescharacteristic, complemented
133C2×C17—351no—
134D17—751no—
135D17—1051no—
136C2×C3×C5—351no—
137D15—851no—
138D15—851no—
139D15—1191no—
140D15—1702no—
141C3×D5—71no—
142C5×D3—5951no—
143C2×D7—12751noHall
144C52D7×D5111yescharacteristic, complemented, Sylow
145C3×C7D5×D8511yescharacteristic, complemented, Hall
146C2×D5—17851no—
147C2×D5—17851no—
148C17D35⋊D1511yescharacteristic, complemented, Sylow
149C3×C5—22no—
150C3×C5D7×D8511yescharacteristic, complemented
151C3×C5D35⋊D1711yescharacteristic, complemented
152C2×C7—12751no—
153D7—51no—
154D7—2551no—
155C2×D3—29751noHall
156C2×C5—351no—
157C2×C5—17851no—
158D5—71no—
159D5—3571no—
160D5—5102no—
161D5—2551no—
162D5—2551no—
163C7D5×D25511yescharacteristic, complemented, Sylow
164C2×C3—351no—
165D3—5951no—
166D3—4251no—
167C5—22no—
168C5D7×D25511yescharacteristic, complemented
169C5D35⋊D5111yescharacteristic, complemented
170C22—89251noSylow
171C3D35⋊D8511yescharacteristic, complemented, Sylow
172C2—351no—
173C2—17851no—
174C2—12751no—
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×C17×D35C2semidirect
2. C5×D1785C2semidirect
3. C7×C3⋊(C5⋊D85)C2semidirect
5. C3×C52×C7×C17C22semidirect
10. C5×C17×D35D3semidirect
12. D1785D5semidirect
17. C3×C17×D35D5semidirect
19. C52×C7×C17C2×D3semidirect
20. C3⋊(C5⋊D85)D7semidirect
27. C3×C5×C7×C17C2×D5semidirect
28. C3×C5×C7×C17C2×D5semidirect
31. C3×C52×C17C2×D7semidirect
33. C17×D35D15semidirect
41. C3×C5×D35D17semidirect
52. C5×C7×C17D3×D5semidirect
53. C5×C7×C17C2×D15semidirect
54. C3×C52×C7C2×D17semidirect
63. C52×C17D3×D7semidirect
66. C3×C7×C17D52semidirect
69. C5×D35D51semidirect
74. C3×C5×C17D5×D7semidirect
75. C3×C5×C17D5×D7semidirect
84. C3×D35D85semidirect
87. C52×C7C2×D51semidirect
100. C7×C17D5×D15semidirect
102. C3×C5×C7D5×D17semidirect
103. C3×C5×C7C2×D85semidirect
109. C5×C17D7×D15semidirect
110. C5×C17D15⋊D7semidirect
112. C3×C52D7×D17semidirect
114. D35D255semidirect
123. C3×C17(C5⋊D5)⋊D7semidirect
131. C5×C7D5×D51semidirect
132. C5×C7C2×D255semidirect
144. C52D7×D51semidirect
145. C3×C7D5×D85semidirect
148. C17D35⋊D15semidirect
150. C3×C5D7×D85semidirect
151. C3×C5D35⋊D17semidirect
163. C7D5×D255semidirect
168. C5D7×D255semidirect
169. C5D35⋊D51semidirect
171. C3D35⋊D85semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C17×D352
C5×D17852
C7×C3⋊(C5⋊D85)2
D35⋊D853
D35⋊D515
D7×D2555
D5×D2557
D35⋊D1517