Finite Group Databasebeta

← D3×C7×D255 #36339503

Subgroups — D3×C7×D255 #36339503

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
1C3×C5×D3×C7×C17C211yesmaximal, characteristic, complemented
2C3×C7×D255C211yesmaximal, characteristic, complemented
3C7×C3⋊D255C211yesmaximal, characteristic, complemented
4C2×C7×D255—31nomaximal
5D3×C7×D85—31nomaximal
6C32×C5×C7×C17C2211yescharacteristic, complemented, Hall
7D3×C7×D51—51nomaximal, Hall
8C7×D255—31no—
9C7×D255—31no—
10C7×D255—61no—
11C7×D255D311yescharacteristic, direct product factor
12C5×D3×C7×C17D311yescharacteristic, complemented
13C3×C7×D85—31no—
14C2×C3×C5×C7×C17—31no—
15D3×D255C711yesmaximal, characteristic, direct product factor, Hall
16C2×C7×D85—91noHall
17C7×C3⋊D51—51no—
18C3×C7×D51—51no—
19C3×D3×C7×C17D511yescharacteristic, complemented
20C3×C5×C7×C17—21no—
21C3×C5×C7×C17C2×D311yescharacteristic, complemented
22C3×C5×C7×C17C2×D311yescharacteristic, complemented
23C3⋊D255C2×C711yescharacteristic, complemented
24C3×D255C2×C711yescharacteristic, complemented
25C3×C5×D3×C17C2×C711yescharacteristic, complemented
26C2×C7×D51—151no—
27D3×C7×D17—151no—
28D3×C7×D15—171nomaximal, Hall
29C2×C5×C7×C17—31no—
30C7×D85—31no—
31C7×D85—91no—
32C32×C7×C17C2×D511yescharacteristic, complemented, Hall
33C2×D255—31no—
34D3×D85—31no—
35C32×C5×C17C22×C711yescharacteristic, complemented, Hall
36C2×C3×C7×C17—31no—
37C7×D51—51no—
38C7×D51—151no—
39C7×D51—151no—
40C7×D51—301no—
41D3×C7×C17D1511yescharacteristic, complemented
42C3×C7×D17—151no—
43C7×C3⋊D15—171no—
44C3×C7×D15—171no—
45C3×C5×D3×C7D1711yescharacteristic, complemented
46D3×D51—51noHall
47C5×C7×C17D3211yescharacteristic, complemented, Hall
48C2×C3×C5×C17—31no—
49D255—31no—
50D255—31no—
51D255—61no—
52D255D3×C711yescharacteristic, direct product factor
53C5×D3×C17D3×C711yescharacteristic, complemented
54C3×D85—31no—
55C2×C7×D17—451noHall
56C2×C7×D15—511no—
57D3×C7×D5—511no—
58C3×C7×C17—21no—
59C3×C7×C17D3×D511yescharacteristic, complemented
60C3×C7×C17C2×D1511yescharacteristic, complemented
61C2×D85—91noHall
62C32×C5×C7C2×D1711yescharacteristic, complemented, Hall
63C3⋊D51—51no—
64C3×D51—51no—
65C3×D3×C17C7×D511yescharacteristic, complemented
66C3×C5×C17—21no—
67C3×C5×C17C2×D3×C711yescharacteristic, complemented
68C3×C5×C17C2×D3×C711yescharacteristic, complemented
69D32×C7—851noHall
70C2×C7×C17—31no—
71C7×D17—151no—
72C7×D17—451no—
73C2×C3×C5×C7—31no—
74C7×D15—171no—
75C7×D15—511no—
76C7×D15—511no—
77C7×D15—1021no—
78C5×D3×C7D5111yescharacteristic, complemented
79C3×C7×D5—511no—
80C2×D51—151no—
81D3×D17—151no—
82D3×D15—171noHall
83C2×C5×C17—31no—
84D85—31no—
85D85—91no—
86C32×C17C2×C7×D511yescharacteristic, complemented, Hall
87C2×C7×D5—1531noHall
88C7×C3⋊D3—851no—
89C3×D3×C7—851no—
90C3×D3×C7D8511yescharacteristic, complemented
91C7×C17D3×D1511yescharacteristic, complemented, Hall
92C3×C5×C7—21no—
93C3×C5×C7D3×D1711yescharacteristic, complemented
94C3×C5×C7C2×D5111yescharacteristic, complemented
95C2×C3×C17—31no—
96D51—51no—
97D51—151no—
98D51—151no—
99D51—301no—
100C3×D17—151no—
101D3×C17C7×D1511yescharacteristic, complemented
102C3⋊D15—171no—
103C3×D15—171no—
104C3×C5×D3C7×D1711yescharacteristic, complemented
105C5×C17D32×C711yescharacteristic, complemented, Hall
106C2×D3×C7—2551no—
107C2×D3×C7—2551no—
108C2×C5×C7—31no—
109C7×D5—511no—
110C7×D5—1531no—
111C2×D17—451noHall
112C32×C7C2×D8511yescharacteristic, complemented, Hall
113C2×D15—511no—
114D3×D5—511no—
115C3×C17—21no—
116C3×C17D3×C7×D511yescharacteristic, complemented
117C3×C17C2×C7×D1511yescharacteristic, complemented
118C32×C5C2×C7×D1711yescharacteristic, complemented, Hall
119C2×C3×C7—31no—
120C2×C3×C7—2551no—
121D3×C7—851no—
122D3×C7—5101no—
123D3×C7—2551no—
124D3×C7—2551no—
125D3×C7D25511yescharacteristic, direct product factor
126D32—851noHall
127C5×C7D3×D5111yescharacteristic, complemented, Hall
128C2×C17—31no—
129D17—151no—
130D17—451no—
131C2×C3×C5—31no—
132D15—171no—
133D15—511no—
134D15—511no—
135D15—1021no—
136C3×D5—511no—
137C5×D3C7×D5111yescharacteristic, complemented
138C22×C7—7651noHall
139C3×C7—21no—
140C3×C7D3×D8511yescharacteristic, complemented
141C3×C7C2×D25511yescharacteristic, complemented
142C2×D5—1531noHall
143C3⋊D3—851no—
144C3×D3—851no—
145C3×D3C7×D8511yescharacteristic, complemented
146C17D3×C7×D1511yescharacteristic, complemented, Sylow
147C3×C5—21no—
148C3×C5D3×C7×D1711yescharacteristic, complemented
149C3×C5C2×C7×D5111yescharacteristic, complemented
150C2×C7—31no—
151C2×C7—7651no—
152C2×C7—2551no—
153C2×D3—2551no—
154C2×D3—2551no—
155C2×C5—31no—
156D5—511no—
157D5—1531no—
158C32C2×C7×D8511yescharacteristic, complemented, Sylow
159C7D3×D25511yescharacteristic, direct product factor, Sylow
160C2×C3—31no—
161C2×C3—2551no—
162D3—851no—
163D3—5101no—
164D3—2551no—
165D3—2551no—
166D3C7×D25511yescharacteristic, direct product factor
167C5D3×C7×D5111yescharacteristic, complemented, Sylow
168C22—7651noSylow
169C3—21no—
170C3D3×C7×D8511yescharacteristic, complemented
171C3C2×C7×D25511yescharacteristic, complemented
172C2—31no—
173C2—7651no—
174C2—2551no—
subgroupG/H
center, hypercenterC7D3×D255
commutator, cosocle, hypocenterC32×C5×C17C22×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C17C22
LCSG ▷ C32×C5×C17
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C3×C5×D3×C7×C17C2semidirect
2. C3×C7×D255C2semidirect
3. C7×C3⋊D255C2semidirect
6. C32×C5×C7×C17C22semidirect
11. C7×D255D3direct (N × H)
12. C5×D3×C7×C17D3semidirect
15. D3×D255C7direct (N × H)
19. C3×D3×C7×C17D5semidirect
21. C3×C5×C7×C17C2×D3semidirect
22. C3×C5×C7×C17C2×D3semidirect
23. C3⋊D255C2×C7semidirect
24. C3×D255C2×C7semidirect
25. C3×C5×D3×C17C2×C7semidirect
32. C32×C7×C17C2×D5semidirect
35. C32×C5×C17C22×C7semidirect
41. D3×C7×C17D15semidirect
45. C3×C5×D3×C7D17semidirect
47. C5×C7×C17D32semidirect
52. D255D3×C7direct (N × H)
53. C5×D3×C17D3×C7semidirect
59. C3×C7×C17D3×D5semidirect
60. C3×C7×C17C2×D15semidirect
62. C32×C5×C7C2×D17semidirect
65. C3×D3×C17C7×D5semidirect
67. C3×C5×C17C2×D3×C7semidirect
68. C3×C5×C17C2×D3×C7semidirect
78. C5×D3×C7D51semidirect
86. C32×C17C2×C7×D5semidirect
90. C3×D3×C7D85semidirect
91. C7×C17D3×D15semidirect
93. C3×C5×C7D3×D17semidirect
94. C3×C5×C7C2×D51semidirect
101. D3×C17C7×D15semidirect
104. C3×C5×D3C7×D17semidirect
105. C5×C17D32×C7semidirect
112. C32×C7C2×D85semidirect
116. C3×C17D3×C7×D5semidirect
117. C3×C17C2×C7×D15semidirect
118. C32×C5C2×C7×D17semidirect
125. D3×C7D255direct (N × H)
127. C5×C7D3×D51semidirect
137. C5×D3C7×D51semidirect
140. C3×C7D3×D85semidirect
141. C3×C7C2×D255semidirect
145. C3×D3C7×D85semidirect
146. C17D3×C7×D15semidirect
148. C3×C5D3×C7×D17semidirect
149. C3×C5C2×C7×D51semidirect
158. C32C2×C7×D85semidirect
159. C7D3×D255direct (N × H)
166. D3C7×D255direct (N × H)
167. C5D3×C7×D51semidirect
170. C3D3×C7×D85semidirect
171. C3C2×C7×D255semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D3×C7×C172
C3×C7×D2552
C7×C3⋊D2552
C2×C7×D2553
D3×C7×D853
D3×C7×D515
D3×D2557
D3×C7×D1517