Finite Group Databasebeta

← C5×D5×D357 #49087942

Subgroups — C5×D5×D357 #49087942

Order 35700.

192 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 56 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×D5×C17C211yesmaximal, characteristic, complemented
2C52×D357C211yesmaximal, characteristic, complemented
3C5×D1785C211yesmaximal, characteristic, complemented
4C5×D5×D119—31nomaximal, Hall
5C3×C52×C7×C17C2211yescharacteristic, complemented, Hall
6C2×C5×D357—51nomaximal
7D5×D357C511yesmaximal, characteristic, direct product factor
8C5×D595—31no—
9C5×C7×D5×C17D311yescharacteristic, complemented
10C52×D119—31no—
11C5×D5×D51—71nomaximal, Hall
12D1785C2×C511yescharacteristic, complemented
13C5×D357—22no—
14C5×D357—51no—
15C5×D357D511yescharacteristic, direct product factor
16C5×D357C2×C511yescharacteristic, complemented
17C3×C7×D5×C17C2×C511yescharacteristic, complemented
18C2×C3×C5×C7×C17—51no—
19C52×C7×C17C2×D311yescharacteristic, complemented, Hall
20C5×D255—71no—
21C52×D51—71no—
22C3×C5×D5×C17D711yescharacteristic, complemented
23C2×C5×D119—151no—
24D5×D119—31no—
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
30C2×D357—51noHall
31C3×C52×C17C2×D711yescharacteristic, complemented, Hall
32C2×C5×C7×C17—51no—
33D595—31no—
34C7×D5×C17C5×D311yescharacteristic, complemented
35C5×D119—31no—
36C5×D119—31no—
37C5×D119—62no—
38C5×D119—151no—
39C5×D105—171no—
40C52×D21—171no—
41C3×C5×C7×D5D1711yescharacteristic, complemented
42C2×C5×D51—351no—
43D5×D51—71no—
44C5×D85—211no—
45C5×D5×C17D2111yescharacteristic, complemented
46C52×D17—211no—
47C2×C3×C7×C17—51no—
48D357—51no—
49D357C5×D511yescharacteristic, direct product factor
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
55C2×C3×C5×C17—51no—
56D255—71no—
57C5×D51—71no—
58C5×D51—71no—
59C5×D51—142no—
60C5×D51—351no—
61C3×D5×C17C5×D711yescharacteristic, complemented
62C2×D119—151noHall
63C52×C17C2×D2111yescharacteristic, complemented, Hall
64C2×C5×D21—851no—
65D5×D21—171no—
66C3×C7×C17C2×C5×D511yescharacteristic, complemented, Hall
67C5×D35—511no—
68C5×C7×D5D5111yescharacteristic, complemented
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
76C2×C7×C17—51no—
77D119—31no—
78D119—151no—
79C2×C3×C5×C7—51no—
80D105—171no—
81C5×D21—171no—
82C5×D21—171no—
83C5×D21—342no—
84C5×D21—851no—
85C3×C7×D5C5×D1711yescharacteristic, complemented
86C2×D51—351noHall
87C52×C7C2×D5111yescharacteristic, complemented, Hall
88C2×C5×C17—51no—
89D85—211no—
90C5×D17—211no—
91C5×D17—211no—
92C5×D17—422no—
93C5×D17—1051no—
94D5×C17C5×D2111yescharacteristic, complemented
95C5×D15—1191no—
96C52×D3—1191no—
97C3×C5×D5D11911yescharacteristic, complemented
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
104C2×C3×C17—51no—
105D51—71no—
106D51—351no—
107C2×C5×D5—3571noHall
108C5×C17—22no—
109C5×C17D5×D2111yescharacteristic, complemented
110C5×C17C2×C5×D2111yescharacteristic, complemented
111C2×D21—851noHall
112C3×C52C2×D11911yescharacteristic, complemented, Hall
113C2×C5×C7—51no—
114D35—511no—
115C5×D7—511no—
116C5×D7—511no—
117C5×D7—1022no—
118C5×D7—2551no—
119C7×D5C5×D5111yescharacteristic, complemented
120C2×D17—1051noHall
121C2×C5×D3—5951no—
122D3×D5—1191no—
123C3×C17C5×D5×D711yescharacteristic, complemented, Hall
124C2×C52—3571no—
125C5×D5—3571no—
126C5×D5D35711yescharacteristic, direct product factor
127C2×C3×C7—51no—
128D21—171no—
129D21—851no—
130C5×C7—22no—
131C5×C7D5×D5111yescharacteristic, complemented
132C5×C7C2×C5×D5111yescharacteristic, complemented
133C2×C17—51no—
134D17—211no—
135D17—1051no—
136C2×C3×C5—51no—
137D15—1191no—
138C3×D5C5×D11911yescharacteristic, complemented
139C5×D3—5951no—
140C5×D3—1191no—
141C5×D3—1191no—
142C5×D3—2382no—
143C2×D7—2551noHall
144C52C2×D35711yescharacteristic, complemented, Sylow
145C3×C7C5×D5×D1711yescharacteristic, complemented, Hall
146C22×C5—17851no—
147C2×D5—3571no—
148C17C5×D5×D2111yescharacteristic, complemented, Sylow
149C3×C5—22no—
150C3×C5D5×D11911yescharacteristic, complemented
151C3×C5C2×C5×D11911yescharacteristic, complemented
152C2×C7—51no—
153D7—511no—
154D7—2551no—
155C2×D3—5951noHall
156C2×C5—51no—
157C2×C5—3571no—
158C2×C5—3571no—
159C2×C5—7142no—
160C2×C5—17851no—
161D5—3571no—
162D5C5×D35711yescharacteristic, direct product factor
163C7C5×D5×D5111yescharacteristic, complemented, Sylow
164C2×C3—51no—
165D3—5951no—
166D3—1191no—
167C5—22no—
168C5D5×D35711yescharacteristic, direct product factor
169C5C2×C5×D35711yescharacteristic, complemented
170C22—17851noSylow
171C3C5×D5×D11911yescharacteristic, complemented, Sylow
172C2—51no—
173C2—3571no—
174C2—17851no—
subgroupG/H
center, hypercenterC5D5×D357
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×D5×C17C2semidirect
2. C52×D357C2semidirect
3. C5×D1785C2semidirect
5. C3×C52×C7×C17C22semidirect
7. D5×D357C5direct (N × H)
9. C5×C7×D5×C17D3semidirect
12. D1785C2×C5semidirect
15. C5×D357D5direct (N × H)
16. C5×D357C2×C5semidirect
17. C3×C7×D5×C17C2×C5semidirect
19. C52×C7×C17C2×D3semidirect
22. C3×C5×D5×C17D7semidirect
27. C3×C5×C7×C17C2×D5semidirect
28. C3×C5×C7×C17C22×C5semidirect
31. C3×C52×C17C2×D7semidirect
34. C7×D5×C17C5×D3semidirect
41. C3×C5×C7×D5D17semidirect
45. C5×D5×C17D21semidirect
49. D357C5×D5direct (N × H)
52. C5×C7×C17D3×D5semidirect
53. C5×C7×C17C2×C5×D3semidirect
54. C3×C52×C7C2×D17semidirect
61. C3×D5×C17C5×D7semidirect
63. C52×C17C2×D21semidirect
66. C3×C7×C17C2×C5×D5semidirect
68. C5×C7×D5D51semidirect
74. C3×C5×C17D5×D7semidirect
75. C3×C5×C17C2×C5×D7semidirect
85. C3×C7×D5C5×D17semidirect
87. C52×C7C2×D51semidirect
94. D5×C17C5×D21semidirect
97. C3×C5×D5D119semidirect
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×C52C2×D119semidirect
119. C7×D5C5×D51semidirect
123. C3×C17C5×D5×D7semidirect
126. C5×D5D357direct (N × H)
131. C5×C7D5×D51semidirect
132. C5×C7C2×C5×D51semidirect
138. C3×D5C5×D119semidirect
144. C52C2×D357semidirect
145. C3×C7C5×D5×D17semidirect
148. C17C5×D5×D21semidirect
150. C3×C5D5×D119semidirect
151. C3×C5C2×C5×D119semidirect
162. D5C5×D357direct (N × H)
163. C7C5×D5×D51semidirect
168. C5D5×D357direct (N × H)
169. C5C2×C5×D357semidirect
171. C3C5×D5×D119semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C7×D5×C172
C52×D3572
C5×D17852
C5×D5×D1193
C2×C5×D3575
D5×D3575
C5×D5×D517
C5×D5×D2117