Finite Group Databasebeta

← C5×D21⋊D51 #36339500

Subgroups — C5×D21⋊D51 #36339500

Order 21420.

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

normal subgroups only

This group has 176 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×C17×D21C211yesmaximal, characteristic, complemented
2C3×C5×D357C211yesmaximal, characteristic, complemented
3C5×C7×C3⋊D51C211yesmaximal, characteristic, complemented
4C5×D21⋊D17—31nomaximal
5C5×D7×D51—31nomaximal
6C32×C5×C7×C17C2211yescharacteristic, complemented, Hall
7D21⋊D51C511yesmaximal, characteristic, direct product factor, Hall
8C5×D357D311yescharacteristic, complemented
9C5×C17×D21D311yescharacteristic, complemented
10C5×C7×D51—31no—
11C5×C7×D51—31no—
12C5×C7×D51—61no—
13C3×C5×D119—31no—
14C3×C5×D7×C17—31no—
15C5×D3×D51—71nomaximal, Hall
16C5×D7×D17—91noHall
17C7×C3⋊D51C2×C511yescharacteristic, complemented
18C3×D357C2×C511yescharacteristic, complemented
19C3×C17×D21C2×C511yescharacteristic, complemented
20C3×C5×C7×C17—21no—
21C3×C5×C7×C17C2×D311yescharacteristic, complemented
22C3×C5×C7×C17C2×D311yescharacteristic, complemented
23C5×C3⋊D51D711yescharacteristic, complemented
24C3×C5×D51—71no—
25C3×C5×D3×C17—71no—
26D21⋊D17—31no—
27D7×D51—31no—
28C5×(C3⋊D3)⋊D7—171nomaximal, Hall
29C5×D119—31no—
30C5×D7×C17—31no—
31C5×C7×D17—91no—
32C32×C7×C17C22×C511yescharacteristic, complemented, Hall
33C2×C5×D51—211no—
34C5×D3×D17—211no—
35C32×C5×C17C2×D711yescharacteristic, complemented, Hall
36D357C5×D311yescharacteristic, complemented
37C17×D21C5×D311yescharacteristic, complemented
38C7×D51—31no—
39C7×D51—31no—
40C7×D51—61no—
41C3×D119—31no—
42C3×D7×C17—31no—
43C5×C7×C3⋊D3—171no—
44C3×C5×D21—171no—
45C3×C5×D21D1711yescharacteristic, complemented
46D3×D51—71noHall
47C5×C7×C17D3211yescharacteristic, complemented, Hall
48C2×C3×C5×C17—211no—
49C5×D51—31no—
50C5×D51—31no—
51C5×D51—61no—
52C5×D51—71no—
53C5×D3×C17—71no—
54C3×C5×D17—211no—
55D7×D17—91noHall
56C5×D3×D7—511no—
57C5×D3×D7—511no—
58C3×C7×C17—21no—
59C3×C7×C17C2×C5×D311yescharacteristic, complemented
60C3×C7×C17C2×C5×D311yescharacteristic, complemented
61C2×C5×D17—631noHall
62C32×C5×C7C2×D1711yescharacteristic, complemented, Hall
63C3⋊D51C5×D711yescharacteristic, complemented
64C3×D51—71no—
65C3×D3×C17—71no—
66C3×C5×C17—21no—
67C3×C5×C17D3×D711yescharacteristic, complemented
68C3×C5×C17D3×D711yescharacteristic, complemented
69(C3⋊D3)⋊D7—171noHall
70D119—31no—
71C7×D17—91no—
72D7×C17—31no—
73C5×D21—171no—
74C5×D21D5111yescharacteristic, complemented
75C5×D3×C7—511no—
76C5×D3×C7—511no—
77C5×D3×C7—1021no—
78C3×C5×D7—31no—
79C3×C5×D7—511no—
80C2×D51—211no—
81D3×D17—211no—
82C5×D32—1191noHall
83C2×C5×C17—211no—
84C5×D17—91no—
85C5×D17—211no—
86C32×C17C2×C5×D711yescharacteristic, complemented, Hall
87C2×C5×D7—1531noHall
88C7×C3⋊D3—171no—
89C3×D21—171no—
90C3×D21C5×D1711yescharacteristic, complemented
91C7×C17C5×D3211yescharacteristic, complemented, Hall
92C3×C5×C7—21no—
93C3×C5×C7D3×D1711yescharacteristic, complemented
94C3×C5×C7C2×D5111yescharacteristic, complemented
95C2×C3×C17—211no—
96D51—31no—
97D51—31no—
98D51—61no—
99D51—71no—
100C3×D17—211no—
101D3×C17—71no—
102C5×C3⋊D3—171no—
103C3×C5×D3—71no—
104C3×C5×D3—1191no—
105C5×C17(C3⋊D3)⋊D711yescharacteristic, complemented, Hall
106D3×D7—511no—
107D3×D7—511no—
108C2×C5×C7—1531no—
109C5×D7—31no—
110C5×D7—511no—
111C2×D17—631noHall
112C32×C7C2×C5×D1711yescharacteristic, complemented, Hall
113C2×C5×D3—3571no—
114C2×C5×D3—3571no—
115C3×C17—21no—
116C3×C17C5×D3×D711yescharacteristic, complemented
117C3×C17C5×D3×D711yescharacteristic, complemented
118C32×C5D7×D1711yescharacteristic, complemented, Hall
119D21—171no—
120D21C5×D5111yescharacteristic, complemented
121C3×D7—31no—
122C3×D7—511no—
123D3×C7—511no—
124D3×C7—511no—
125D3×C7—1021no—
126D32—1191noHall
127C5×C7D3×D5111yescharacteristic, complemented, Hall
128C2×C17—211no—
129D17—91no—
130D17—211no—
131C2×C3×C5—211no—
132C2×C3×C5—3571no—
133C5×D3—71no—
134C5×D3—511no—
135C5×D3—511no—
136C5×D3—1021no—
137C5×D3—1191no—
138C2×D7—1531noHall
139C3×C7—21no—
140C3×C7C5×D3×D1711yescharacteristic, complemented
141C3×C7C2×C5×D5111yescharacteristic, complemented
142C22×C5—10711noHall
143C3⋊D3—171no—
144C3×D3—71no—
145C3×D3—1191no—
146C17C5×(C3⋊D3)⋊D711yescharacteristic, complemented, Sylow
147C3×C5—21no—
148C3×C5D7×D5111yescharacteristic, complemented
149C3×C5D21⋊D1711yescharacteristic, complemented
150C2×C7—1531no—
151D7—31no—
152D7—511no—
153C2×D3—3571no—
154C2×D3—3571no—
155C2×C5—211no—
156C2×C5—3571no—
157C2×C5—1531no—
158C32C5×D7×D1711yescharacteristic, complemented, Sylow
159C7C5×D3×D5111yescharacteristic, complemented, Sylow
160C2×C3—211no—
161C2×C3—3571no—
162D3—71no—
163D3—511no—
164D3—511no—
165D3—1021no—
166D3—1191no—
167C5D21⋊D5111yescharacteristic, direct product factor, Sylow
168C22—10711noSylow
169C3—21no—
170C3C5×D7×D5111yescharacteristic, complemented
171C3C5×D21⋊D1711yescharacteristic, complemented
172C2—211no—
173C2—3571no—
174C2—1531no—
subgroupG/H
center, hypercenterC5D21⋊D51
commutator, cosocle, hypocenterC32×C7×C17C22×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C17C22
LCSG ▷ C32×C7×C17
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×C17×D21C2semidirect
2. C3×C5×D357C2semidirect
3. C5×C7×C3⋊D51C2semidirect
6. C32×C5×C7×C17C22semidirect
7. D21⋊D51C5direct (N × H)
8. C5×D357D3semidirect
9. C5×C17×D21D3semidirect
17. C7×C3⋊D51C2×C5semidirect
18. C3×D357C2×C5semidirect
19. C3×C17×D21C2×C5semidirect
21. C3×C5×C7×C17C2×D3semidirect
22. C3×C5×C7×C17C2×D3semidirect
23. C5×C3⋊D51D7semidirect
32. C32×C7×C17C22×C5semidirect
35. C32×C5×C17C2×D7semidirect
36. D357C5×D3semidirect
37. C17×D21C5×D3semidirect
45. C3×C5×D21D17semidirect
47. C5×C7×C17D32semidirect
59. C3×C7×C17C2×C5×D3semidirect
60. C3×C7×C17C2×C5×D3semidirect
62. C32×C5×C7C2×D17semidirect
63. C3⋊D51C5×D7semidirect
67. C3×C5×C17D3×D7semidirect
68. C3×C5×C17D3×D7semidirect
74. C5×D21D51semidirect
86. C32×C17C2×C5×D7semidirect
90. C3×D21C5×D17semidirect
91. C7×C17C5×D32semidirect
93. C3×C5×C7D3×D17semidirect
94. C3×C5×C7C2×D51semidirect
105. C5×C17(C3⋊D3)⋊D7semidirect
112. C32×C7C2×C5×D17semidirect
116. C3×C17C5×D3×D7semidirect
117. C3×C17C5×D3×D7semidirect
118. C32×C5D7×D17semidirect
120. D21C5×D51semidirect
127. C5×C7D3×D51semidirect
140. C3×C7C5×D3×D17semidirect
141. C3×C7C2×C5×D51semidirect
146. C17C5×(C3⋊D3)⋊D7semidirect
148. C3×C5D7×D51semidirect
149. C3×C5D21⋊D17semidirect
158. C32C5×D7×D17semidirect
159. C7C5×D3×D51semidirect
167. C5D21⋊D51direct (N × H)
170. C3C5×D7×D51semidirect
171. C3C5×D21⋊D17semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C17×D212
C3×C5×D3572
C5×C7×C3⋊D512
C5×D21⋊D173
C5×D7×D513
D21⋊D515
C5×D3×D517
C5×(C3⋊D3)⋊D717