Finite Group Databasebeta

← C3×D7×D255 #36339473

Subgroups — C3×D7×D255 #36339473

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×C5×D7×C17C211yesmaximal, characteristic, complemented
2C3×C7×D255C211yesmaximal, characteristic, complemented
3C3×D1785C211yesmaximal, characteristic, complemented
4D7×D255C311yesmaximal, characteristic, direct product factor
5C3×D7×D85—31nomaximal
6C32×C5×C7×C17C2211yescharacteristic, complemented, Hall
7C3×D7×D51—51nomaximal, Hall
8D1785C2×C311yescharacteristic, complemented
9C7×D255C2×C311yescharacteristic, complemented
10C3×D595—31no—
11C3×C7×D85—31no—
12C3×C5×D7×C17—21no—
13C3×C5×D7×C17D311yescharacteristic, complemented
14C3×C5×D7×C17C2×C311yescharacteristic, complemented
15C2×C3×D255—71nomaximal, Hall
16D7×D85—31noHall
17C3×D357—51no—
18C3×C7×D51—51no—
19C32×D7×C17D511yescharacteristic, complemented
20C3×C5×C7×C17—21no—
21C3×C5×C7×C17C2×D311yescharacteristic, complemented
22C3×C5×C7×C17C22×C311yescharacteristic, complemented
23C2×C32×C5×C17—71no—
24C3×D255—71no—
25C3×D255D711yescharacteristic, direct product factor
26D7×D51—51no—
27C3×D7×D17—151no—
28C3×D7×D15—171nomaximal, Hall
29D595—31no—
30C7×D85—31no—
31C5×D7×C17C3×D311yescharacteristic, complemented
32C32×C7×C17C2×D511yescharacteristic, complemented, Hall
33C2×D255—71no—
34C2×C3×D85—211no—
35C32×C5×C17C2×D711yescharacteristic, complemented, Hall
36D357—51no—
37C7×D51—51no—
38C3×D119—151no—
39C3×D7×C17—21no—
40C3×D7×C17C3×D511yescharacteristic, complemented
41C3×D7×C17D1511yescharacteristic, complemented
42C3×C7×D17—151no—
43C3×D105—171no—
44C3×C7×D15—171no—
45C32×C5×D7D1711yescharacteristic, complemented
46C2×C3×D51—351noHall
47C5×C7×C17C2×C3×D311yescharacteristic, complemented, Hall
48C2×C3×C5×C17—71no—
49C2×C3×C5×C17—71no—
50C2×C3×C5×C17—141no—
51D255—71no—
52D255C3×D711yescharacteristic, direct product factor
53C3×D85—31no—
54C3×D85—211no—
55D7×D17—151noHall
56D7×D15—171no—
57C3×D5×D7—511no—
58C3×C7×C17—21no—
59C3×C7×C17C2×C3×D511yescharacteristic, complemented
60C3×C7×C17C2×D1511yescharacteristic, complemented
61C2×D85—211noHall
62C32×C5×C7C2×D1711yescharacteristic, complemented, Hall
63C2×C32×C17—71no—
64C3×D51—51no—
65C3×D51—351no—
66C3×C5×C17—21no—
67C3×C5×C17D3×D711yescharacteristic, complemented
68C3×C5×C17C2×C3×D711yescharacteristic, complemented
69C3×D3×D7—851noHall
70D119—151no—
71C7×D17—151no—
72D7×C17C3×D1511yescharacteristic, complemented
73D105—171no—
74C7×D15—171no—
75C3×D35—511no—
76C3×C7×D5—511no—
77C3×C5×D7—21no—
78C3×C5×D7C3×D1711yescharacteristic, complemented
79C3×C5×D7D5111yescharacteristic, complemented
80C2×D51—351no—
81C2×C3×D17—1051no—
82C2×C3×D15—1191noHall
83C2×C5×C17—71no—
84D85—31no—
85D85—211no—
86C32×C17D5×D711yescharacteristic, complemented, Hall
87D5×D7—511noHall
88C3×D21—851no—
89C3×D3×C7—851no—
90C32×D7D8511yescharacteristic, complemented
91C7×C17C2×C3×D1511yescharacteristic, complemented, Hall
92C3×C5×C7—21no—
93C3×C5×C7C2×C3×D1711yescharacteristic, complemented
94C3×C5×C7C2×D5111yescharacteristic, complemented
95C2×C3×C17—71no—
96C2×C3×C17—71no—
97C2×C3×C17—141no—
98D51—51no—
99D51—351no—
100C3×D17—151no—
101C3×D17—1051no—
102C2×C32×C5—71no—
103C3×D15—171no—
104C3×D15—1191no—
105C5×C17C3×D3×D711yescharacteristic, complemented, Hall
106C2×C3×D7—2551no—
107D3×D7—851no—
108D35—511no—
109C5×D7C3×D5111yescharacteristic, complemented
110C7×D5—511no—
111C2×D17—1051noHall
112C32×C7C2×D8511yescharacteristic, complemented, Hall
113C2×D15—1191no—
114C2×C3×D5—3571no—
115C3×C17—21no—
116C3×C17C3×D5×D711yescharacteristic, complemented
117C3×C17D7×D1511yescharacteristic, complemented
118C32×C5D7×D1711yescharacteristic, complemented, Hall
119C2×C3×C7—2551no—
120D21—851no—
121C3×D7—21no—
122C3×D7—2551no—
123C3×D7C3×D8511yescharacteristic, complemented
124C3×D7D25511yescharacteristic, direct product factor
125D3×C7—851no—
126C2×C3×D3—5951noHall
127C5×C7C2×C3×D5111yescharacteristic, complemented, Hall
128C2×C17—71no—
129D17—151no—
130D17—1051no—
131C2×C3×C5—71no—
132C2×C3×C5—71no—
133C2×C3×C5—141no—
134D15—171no—
135D15—1191no—
136C3×D5—511no—
137C3×D5—3571no—
138C2×D7—2551noHall
139C3×C7—21no—
140C3×C7C2×C3×D8511yescharacteristic, complemented
141C3×C7C2×D25511yescharacteristic, complemented
142C2×D5—3571noHall
143C2×C32—71no—
144C3×D3—5951no—
145C3×D3—851no—
146C17C3×D7×D1511yescharacteristic, complemented, Sylow
147C3×C5—21no—
148C3×C5C3×D7×D1711yescharacteristic, complemented
149C3×C5D7×D5111yescharacteristic, complemented
150C2×C7—2551no—
151D7—2551no—
152D7C3×D25511yescharacteristic, direct product factor
153C22×C3—17851no—
154C2×D3—5951no—
155C2×C5—71no—
156D5—511no—
157D5—3571no—
158C32D7×D8511yescharacteristic, complemented, Sylow
159C7C2×C3×D25511yescharacteristic, complemented, Sylow
160C2×C3—71no—
161C2×C3—71no—
162C2×C3—141no—
163C2×C3—17851no—
164C2×C3—2551no—
165D3—5951no—
166D3—851no—
167C5C3×D7×D5111yescharacteristic, complemented, Sylow
168C22—17851noSylow
169C3—21no—
170C3C3×D7×D8511yescharacteristic, complemented
171C3D7×D25511yescharacteristic, direct product factor
172C2—71no—
173C2—17851no—
174C2—2551no—
subgroupG/H
center, hypercenterC3D7×D255
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×C5×D7×C17C2semidirect
2. C3×C7×D255C2semidirect
3. C3×D1785C2semidirect
4. D7×D255C3direct (N × H)
6. C32×C5×C7×C17C22semidirect
8. D1785C2×C3semidirect
9. C7×D255C2×C3semidirect
13. C3×C5×D7×C17D3semidirect
14. C3×C5×D7×C17C2×C3semidirect
19. C32×D7×C17D5semidirect
21. C3×C5×C7×C17C2×D3semidirect
22. C3×C5×C7×C17C22×C3semidirect
25. C3×D255D7direct (N × H)
31. C5×D7×C17C3×D3semidirect
32. C32×C7×C17C2×D5semidirect
35. C32×C5×C17C2×D7semidirect
40. C3×D7×C17C3×D5semidirect
41. C3×D7×C17D15semidirect
45. C32×C5×D7D17semidirect
47. C5×C7×C17C2×C3×D3semidirect
52. D255C3×D7direct (N × H)
59. C3×C7×C17C2×C3×D5semidirect
60. C3×C7×C17C2×D15semidirect
62. C32×C5×C7C2×D17semidirect
67. C3×C5×C17D3×D7semidirect
68. C3×C5×C17C2×C3×D7semidirect
72. D7×C17C3×D15semidirect
78. C3×C5×D7C3×D17semidirect
79. C3×C5×D7D51semidirect
86. C32×C17D5×D7semidirect
90. C32×D7D85semidirect
91. C7×C17C2×C3×D15semidirect
93. C3×C5×C7C2×C3×D17semidirect
94. C3×C5×C7C2×D51semidirect
105. C5×C17C3×D3×D7semidirect
109. C5×D7C3×D51semidirect
112. C32×C7C2×D85semidirect
116. C3×C17C3×D5×D7semidirect
117. C3×C17D7×D15semidirect
118. C32×C5D7×D17semidirect
123. C3×D7C3×D85semidirect
124. C3×D7D255direct (N × H)
127. C5×C7C2×C3×D51semidirect
140. C3×C7C2×C3×D85semidirect
141. C3×C7C2×D255semidirect
146. C17C3×D7×D15semidirect
148. C3×C5C3×D7×D17semidirect
149. C3×C5D7×D51semidirect
152. D7C3×D255direct (N × H)
158. C32D7×D85semidirect
159. C7C2×C3×D255semidirect
167. C5C3×D7×D51semidirect
170. C3C3×D7×D85semidirect
171. C3D7×D255direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×D7×C172
C3×C7×D2552
C3×D17852
D7×D2553
C3×D7×D853
C3×D7×D515
C2×C3×D2557
C3×D7×D1517