Finite Group Databasebeta

← C5×D85⋊D21 #49087944

Subgroups — C5×D85⋊D21 #49087944

Order 35700.

192 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 50 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
2C52×D357C211yesmaximal, characteristic, complemented
3C5×C17×D105C211yesmaximal, characteristic, complemented
4C5×D35⋊D17—31nomaximal, Hall
5C3×C52×C7×C17C2211yescharacteristic, complemented, Hall
6D85⋊D21C511yesmaximal, characteristic, direct product factor
7C5×D17×D21—51nomaximal
8C5×C17×D35—31no—
9C5×C7×D85D311yescharacteristic, complemented
10C52×D119—31no—
11C5×D15⋊D17—71nomaximal, Hall
12C17×D105C2×C511yescharacteristic, complemented
13C5×D357—22no—
14C5×D357D511yescharacteristic, complemented
15C5×D357C2×C511yescharacteristic, complemented
16C5×C17×D21—51no—
17C3×C7×D85C2×C511yescharacteristic, complemented
18C3×C5×C7×D17—51no—
19C52×C7×C17C2×D311yescharacteristic, complemented, Hall
20C5×C17×D15—71no—
21C52×D51—71no—
22C3×C5×D85D711yescharacteristic, complemented
23D35⋊D17—31no—
24C5×D7×D17—151no—
25C5×D5×D21—171nomaximal, Hall
26C3×C5×C7×C17—22no—
27C3×C5×C7×C17C2×D511yescharacteristic, complemented
28C3×C5×C7×C17C22×C511yescharacteristic, complemented
29C5×D5×D17—211noHall
30D17×D21—51noHall
31C3×C52×C17C2×D711yescharacteristic, complemented, Hall
32C17×D35—31no—
33C7×D85C5×D311yescharacteristic, complemented
34C5×D119—31no—
35C5×D119—31no—
36C5×D119—62no—
37C5×D7×C17—151no—
38C5×C7×D17—51no—
39C5×D105D1711yescharacteristic, complemented
40C52×D21—171no—
41C3×C5×C7×D5—171no—
42D15⋊D17—71no—
43C5×D3×D17—351no—
44C5×D85D2111yescharacteristic, complemented
45C5×D5×C17—211no—
46C52×D17—211no—
47D357C5×D511yescharacteristic, complemented
48C17×D21—51no—
49C3×C7×D17—51no—
50C5×D5×D7—511noHall
51C5×C7×C17—22no—
52C5×C7×C17D3×D511yescharacteristic, complemented
53C5×C7×C17C2×C5×D311yescharacteristic, complemented
54C3×C52×C7C2×D1711yescharacteristic, complemented, Hall
55C17×D15—71no—
56C5×D51—71no—
57C5×D51—71no—
58C5×D51—142no—
59C5×D3×C17—351no—
60C3×D85C5×D711yescharacteristic, complemented
61C3×C5×D17—51no—
62D7×D17—151noHall
63C52×C17C2×D2111yescharacteristic, complemented, Hall
64C2×C5×D21—851no—
65D5×D21—171no—
66C3×C7×C17C2×C5×D511yescharacteristic, complemented, Hall
67C5×D35—31no—
68C5×C7×D5—171no—
69C52×D7—511no—
70C2×C5×D17—1051no—
71D5×D17—211no—
72C5×D3×D5—1191noHall
73C3×C5×C17—22no—
74C3×C5×C17D5×D711yescharacteristic, complemented
75C3×C5×C17C2×C5×D711yescharacteristic, complemented
76D119—31no—
77C7×D17—51no—
78D7×C17—151no—
79C2×C3×C5×C7—851no—
80D105C5×D1711yescharacteristic, complemented
81C5×D21—51no—
82C5×D21—171no—
83C5×D21—171no—
84C5×D21—342no—
85C3×C7×D5—171no—
86D3×D17—351noHall
87C52×C7D3×D1711yescharacteristic, complemented, Hall
88C2×C5×C17—1051no—
89D85C5×D2111yescharacteristic, complemented
90C5×D17—51no—
91C5×D17—211no—
92C5×D17—211no—
93C5×D17—422no—
94D5×C17—211no—
95C5×D15—71no—
96C52×D3—1191no—
97C3×C5×D5—171no—
98C2×C5×D7—2551no—
99D5×D7—511no—
100C7×C17C5×D3×D511yescharacteristic, complemented, Hall
101C3×C5×C7—22no—
102C3×C5×C7D5×D1711yescharacteristic, complemented
103C3×C5×C7C2×C5×D1711yescharacteristic, complemented
104D51—71no—
105C3×D17—51no—
106D3×C17—351no—
107C2×C5×D5—3571noHall
108C5×C17—22no—
109C5×C17D5×D2111yescharacteristic, complemented
110C5×C17C2×C5×D2111yescharacteristic, complemented
111C2×D21—851noHall
112C3×C52D7×D1711yescharacteristic, complemented, Hall
113C2×C5×C7—851no—
114D35—31no—
115C5×D7—151no—
116C5×D7—511no—
117C5×D7—511no—
118C5×D7—1022no—
119C7×D5—171no—
120C2×D17—1051noHall
121C2×C5×D3—5951no—
122D3×D5—1191no—
123C3×C17C5×D5×D711yescharacteristic, complemented, Hall
124C2×C52—3571no—
125C5×D5—171no—
126C5×D5—211no—
127C2×C3×C7—851no—
128D21—51no—
129D21—171no—
130C5×C7—22no—
131C5×C7C5×D3×D1711yescharacteristic, complemented
132C5×C7D15⋊D1711yescharacteristic, complemented
133C2×C17—1051no—
134D17—51no—
135D17—211no—
136C2×C3×C5—851no—
137D15—71no—
138C3×D5—171no—
139C5×D3—351no—
140C5×D3—1191no—
141C5×D3—1191no—
142C5×D3—2382no—
143C2×D7—2551noHall
144C52D17×D2111yescharacteristic, complemented, Sylow
145C3×C7C5×D5×D1711yescharacteristic, complemented, Hall
146C22×C5—17851no—
147C2×D5—3571no—
148C17C5×D5×D2111yescharacteristic, complemented, Sylow
149C3×C5—22no—
150C3×C5C5×D7×D1711yescharacteristic, complemented
151C3×C5D35⋊D1711yescharacteristic, complemented
152C2×C7—851no—
153D7—151no—
154D7—511no—
155C2×D3—5951noHall
156C2×C5—851no—
157C2×C5—3571no—
158C2×C5—3571no—
159C2×C5—1051no—
160C2×C5—7142no—
161D5—171no—
162D5—211no—
163C7C5×D15⋊D1711yescharacteristic, complemented, Sylow
164C2×C3—851no—
165D3—351no—
166D3—1191no—
167C5—22no—
168C5C5×D17×D2111yescharacteristic, complemented
169C5D85⋊D2111yescharacteristic, direct product factor
170C22—17851noSylow
171C3C5×D35⋊D1711yescharacteristic, complemented, Sylow
172C2—851no—
173C2—3571no—
174C2—1051no—
subgroupG/H
center, hypercenterC5D85⋊D21
commutator, cosocle, hypocenterC3×C5×C7×C17C22×C5
FrattiniC1G
Fitting, socleC3×C52×C7×C17C22
LCSG ▷ C3×C5×C7×C17
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D85C2semidirect
2. C52×D357C2semidirect
3. C5×C17×D105C2semidirect
5. C3×C52×C7×C17C22semidirect
6. D85⋊D21C5direct (N × H)
9. C5×C7×D85D3semidirect
12. C17×D105C2×C5semidirect
14. C5×D357D5semidirect
15. C5×D357C2×C5semidirect
17. C3×C7×D85C2×C5semidirect
19. C52×C7×C17C2×D3semidirect
22. C3×C5×D85D7semidirect
27. C3×C5×C7×C17C2×D5semidirect
28. C3×C5×C7×C17C22×C5semidirect
31. C3×C52×C17C2×D7semidirect
33. C7×D85C5×D3semidirect
39. C5×D105D17semidirect
44. C5×D85D21semidirect
47. D357C5×D5semidirect
52. C5×C7×C17D3×D5semidirect
53. C5×C7×C17C2×C5×D3semidirect
54. C3×C52×C7C2×D17semidirect
60. C3×D85C5×D7semidirect
63. C52×C17C2×D21semidirect
66. C3×C7×C17C2×C5×D5semidirect
74. C3×C5×C17D5×D7semidirect
75. C3×C5×C17C2×C5×D7semidirect
80. D105C5×D17semidirect
87. C52×C7D3×D17semidirect
89. D85C5×D21semidirect
100. C7×C17C5×D3×D5semidirect
102. C3×C5×C7D5×D17semidirect
103. C3×C5×C7C2×C5×D17semidirect
109. C5×C17D5×D21semidirect
110. C5×C17C2×C5×D21semidirect
112. C3×C52D7×D17semidirect
123. C3×C17C5×D5×D7semidirect
131. C5×C7C5×D3×D17semidirect
132. C5×C7D15⋊D17semidirect
144. C52D17×D21semidirect
145. C3×C7C5×D5×D17semidirect
148. C17C5×D5×D21semidirect
150. C3×C5C5×D7×D17semidirect
151. C3×C5D35⋊D17semidirect
163. C7C5×D15⋊D17semidirect
168. C5C5×D17×D21semidirect
169. C5D85⋊D21direct (N × H)
171. C3C5×D35⋊D17semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C7×D852
C52×D3572
C5×C17×D1052
C5×D35⋊D173
D85⋊D215
C5×D17×D215
C5×D15⋊D177
C5×D5×D2117