Finite Group Databasebeta

← C3×D5×D357 #36339481

Subgroups — C3×D5×D357 #36339481

Order 21420.

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

normal subgroups only

This group has 176 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
1C32×C7×D5×C17C211yesmaximal, characteristic, complemented
2C3×C5×D357C211yesmaximal, characteristic, complemented
3C3×D1785C211yesmaximal, characteristic, complemented
4D5×D357C311yesmaximal, characteristic, direct product factor
5C3×D5×D119—31nomaximal
6C32×C5×C7×C17C2211yescharacteristic, complemented, Hall
7C2×C3×D357—51nomaximal, Hall
8D1785C2×C311yescharacteristic, complemented
9C5×D357C2×C311yescharacteristic, complemented
10C3×D595—31no—
11C3×C7×D5×C17—21no—
12C3×C7×D5×C17D311yescharacteristic, complemented
13C3×C7×D5×C17C2×C311yescharacteristic, complemented
14C3×C5×D119—31no—
15C3×D5×D51—71nomaximal, Hall
16D5×D119—31noHall
17C3×D357—51no—
18C3×D357D511yescharacteristic, direct product factor
19C2×C32×C7×C17—51no—
20C3×C5×C7×C17—21no—
21C3×C5×C7×C17C2×D311yescharacteristic, complemented
22C3×C5×C7×C17C22×C311yescharacteristic, complemented
23C3×D255—71no—
24C3×C5×D51—71no—
25C32×D5×C17D711yescharacteristic, complemented
26C2×D357—51no—
27C2×C3×D119—151no—
28C3×D5×D21—171nomaximal, Hall
29D595—31no—
30C7×D5×C17C3×D311yescharacteristic, complemented
31C5×D119—31no—
32C32×C7×C17C2×D511yescharacteristic, complemented, Hall
33D5×D51—71no—
34C3×D5×D17—211no—
35C32×C5×C17C2×D711yescharacteristic, complemented, Hall
36C2×C3×C7×C17—51no—
37C2×C3×C7×C17—51no—
38C2×C3×C7×C17—101no—
39D357—51no—
40D357C3×D511yescharacteristic, direct product factor
41C3×D119—31no—
42C3×D119—151no—
43C3×D105—171no—
44C3×C5×D21—171no—
45C32×C7×D5D1711yescharacteristic, complemented
46C2×C3×D51—351noHall
47C5×C7×C17C2×C3×D311yescharacteristic, complemented, Hall
48D255—71no—
49C5×D51—71no—
50C3×D85—211no—
51C3×D5×C17—21no—
52C3×D5×C17C3×D711yescharacteristic, complemented
53C3×D5×C17D2111yescharacteristic, complemented
54C3×C5×D17—211no—
55C2×D119—151noHall
56D5×D21—171no—
57C3×D5×D7—511no—
58C3×C7×C17—21no—
59C3×C7×C17D3×D511yescharacteristic, complemented
60C3×C7×C17C2×C3×D511yescharacteristic, complemented
61D5×D17—211noHall
62C32×C5×C7C2×D1711yescharacteristic, complemented, Hall
63C2×C32×C17—51no—
64C3×D51—71no—
65C3×D51—351no—
66C3×C5×C17—21no—
67C3×C5×C17C2×C3×D711yescharacteristic, complemented
68C3×C5×C17C2×D2111yescharacteristic, complemented
69C2×C3×D21—851noHall
70C2×C7×C17—51no—
71D119—31no—
72D119—151no—
73D105—171no—
74C5×D21—171no—
75C3×D35—511no—
76C3×C7×D5—21no—
77C3×C7×D5C3×D1711yescharacteristic, complemented
78C3×C7×D5D5111yescharacteristic, complemented
79C3×C5×D7—511no—
80C2×D51—351no—
81C2×C3×D17—1051no—
82C3×D3×D5—1191noHall
83D85—211no—
84C5×D17—211no—
85D5×C17C3×D2111yescharacteristic, complemented
86C32×C17D5×D711yescharacteristic, complemented, Hall
87D5×D7—511noHall
88C2×C32×C7—51no—
89C3×D21—171no—
90C3×D21—851no—
91C7×C17C3×D3×D511yescharacteristic, complemented, Hall
92C3×C5×C7—21no—
93C3×C5×C7C2×C3×D1711yescharacteristic, complemented
94C3×C5×C7C2×D5111yescharacteristic, complemented
95C2×C3×C17—51no—
96C2×C3×C17—51no—
97C2×C3×C17—101no—
98D51—71no—
99D51—351no—
100C3×D17—211no—
101C3×D17—1051no—
102C3×D15—1191no—
103C3×C5×D3—1191no—
104C32×D5D11911yescharacteristic, complemented
105C5×C17C2×C3×D2111yescharacteristic, complemented, Hall
106C2×D21—851no—
107C2×C3×D7—2551no—
108D35—511no—
109C5×D7—511no—
110C7×D5C3×D5111yescharacteristic, complemented
111C2×D17—1051noHall
112C32×C7D5×D1711yescharacteristic, complemented, Hall
113C2×C3×D5—3571no—
114D3×D5—1191no—
115C3×C17—21no—
116C3×C17C3×D5×D711yescharacteristic, complemented
117C3×C17D5×D2111yescharacteristic, complemented
118C32×C5C2×D11911yescharacteristic, complemented, Hall
119C2×C3×C7—51no—
120C2×C3×C7—51no—
121C2×C3×C7—101no—
122D21—171no—
123D21—851no—
124C3×D7—511no—
125C3×D7—2551no—
126C2×C3×D3—5951noHall
127C5×C7C2×C3×D5111yescharacteristic, complemented, Hall
128C2×C17—51no—
129D17—211no—
130D17—1051no—
131C2×C3×C5—3571no—
132D15—1191no—
133C3×D5—21no—
134C3×D5—3571no—
135C3×D5C3×D11911yescharacteristic, complemented
136C3×D5D35711yescharacteristic, direct product factor
137C5×D3—1191no—
138C2×D7—2551noHall
139C3×C7—21no—
140C3×C7C3×D5×D1711yescharacteristic, complemented
141C3×C7D5×D5111yescharacteristic, complemented
142C2×D5—3571noHall
143C2×C32—51no—
144C3×D3—5951no—
145C3×D3—1191no—
146C17C3×D5×D2111yescharacteristic, complemented, Sylow
147C3×C5—21no—
148C3×C5C2×C3×D11911yescharacteristic, complemented
149C3×C5C2×D35711yescharacteristic, complemented
150C2×C7—51no—
151D7—511no—
152D7—2551no—
153C22×C3—17851no—
154C2×D3—5951no—
155C2×C5—3571no—
156D5—3571no—
157D5C3×D35711yescharacteristic, direct product factor
158C32D5×D11911yescharacteristic, complemented, Sylow
159C7C3×D5×D5111yescharacteristic, complemented, Sylow
160C2×C3—51no—
161C2×C3—51no—
162C2×C3—101no—
163C2×C3—3571no—
164C2×C3—17851no—
165D3—5951no—
166D3—1191no—
167C5C2×C3×D35711yescharacteristic, complemented, Sylow
168C22—17851noSylow
169C3—21no—
170C3C3×D5×D11911yescharacteristic, complemented
171C3D5×D35711yescharacteristic, direct product factor
172C2—51no—
173C2—3571no—
174C2—17851no—
subgroupG/H
center, hypercenterC3D5×D357
commutator, cosocle, hypocenterC3×C5×C7×C17C22×C3
FrattiniC1G
Fitting, socleC32×C5×C7×C17C22
LCSG ▷ C3×C5×C7×C17
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C7×D5×C17C2semidirect
2. C3×C5×D357C2semidirect
3. C3×D1785C2semidirect
4. D5×D357C3direct (N × H)
6. C32×C5×C7×C17C22semidirect
8. D1785C2×C3semidirect
9. C5×D357C2×C3semidirect
12. C3×C7×D5×C17D3semidirect
13. C3×C7×D5×C17C2×C3semidirect
18. C3×D357D5direct (N × H)
21. C3×C5×C7×C17C2×D3semidirect
22. C3×C5×C7×C17C22×C3semidirect
25. C32×D5×C17D7semidirect
30. C7×D5×C17C3×D3semidirect
32. C32×C7×C17C2×D5semidirect
35. C32×C5×C17C2×D7semidirect
40. D357C3×D5direct (N × H)
45. C32×C7×D5D17semidirect
47. C5×C7×C17C2×C3×D3semidirect
52. C3×D5×C17C3×D7semidirect
53. C3×D5×C17D21semidirect
59. C3×C7×C17D3×D5semidirect
60. C3×C7×C17C2×C3×D5semidirect
62. C32×C5×C7C2×D17semidirect
67. C3×C5×C17C2×C3×D7semidirect
68. C3×C5×C17C2×D21semidirect
77. C3×C7×D5C3×D17semidirect
78. C3×C7×D5D51semidirect
85. D5×C17C3×D21semidirect
86. C32×C17D5×D7semidirect
91. C7×C17C3×D3×D5semidirect
93. C3×C5×C7C2×C3×D17semidirect
94. C3×C5×C7C2×D51semidirect
104. C32×D5D119semidirect
105. C5×C17C2×C3×D21semidirect
110. C7×D5C3×D51semidirect
112. C32×C7D5×D17semidirect
116. C3×C17C3×D5×D7semidirect
117. C3×C17D5×D21semidirect
118. C32×C5C2×D119semidirect
127. C5×C7C2×C3×D51semidirect
135. C3×D5C3×D119semidirect
136. C3×D5D357direct (N × H)
140. C3×C7C3×D5×D17semidirect
141. C3×C7D5×D51semidirect
146. C17C3×D5×D21semidirect
148. C3×C5C2×C3×D119semidirect
149. C3×C5C2×D357semidirect
157. D5C3×D357direct (N × H)
158. C32D5×D119semidirect
159. C7C3×D5×D51semidirect
167. C5C2×C3×D357semidirect
170. C3C3×D5×D119semidirect
171. C3D5×D357direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C7×D5×C172
C3×C5×D3572
C3×D17852
D5×D3573
C3×D5×D1193
C2×C3×D3575
C3×D5×D517
C3×D5×D2117