Finite Group Databasebeta

← C5×D3×C22⋊D7 #13132683

Subgroups — C5×D3×C22⋊D7 #13132683

Order 1680.

216 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C22×C5×D3×C7C211yesmaximal, characteristic, complemented
2C2×C5×D3×D7C211yesmaximal, characteristic, complemented
3C5×#4268C211yesmaximal, characteristic, complemented
4C3×C5×C22⋊D7C211yesmaximal, characteristic, complemented
5C5×#4247C211yesmaximal, characteristic, complemented
6C5×#4245C211yesmaximal, characteristic, complemented
7C5×D3×Dic7C211yesmaximal, characteristic, complemented
8C2×C5×C22⋊D7—31nomaximal, Hall
9C22×C3×C5×C7C2211yescharacteristic, complemented
10C2×C5×D21C2211yescharacteristic, complemented
11C2×C5×D3×C7—22no—
12C2×C5×D3×C7C2211yescharacteristic
13C2×C5×D3×C7C2211yescharacteristic, complemented
14C2×C3×C5×D7C2211yescharacteristic, complemented
15C5×D3×D7—22no—
16C5×Dic21C2211yescharacteristic, complemented
17C3×C5×Dic7C2211yescharacteristic, complemented
18D3×C22⋊D7C511yesmaximal, characteristic, direct product factor, Hall
19C23×C5×C7—31no—
20C22×C5×D7—31no—
21C5×C22⋊D7—31no—
22C5×C22⋊D7—31no—
23C5×C22⋊D7—31no—
24C5×C22⋊D7D311yescharacteristic, direct product factor
25C2×C5×Dic7—31no—
26C5×D3×D4—71nomaximal, Hall
27C2×C3×C5×C7—21no—
28C2×C3×C5×C7C2311yescharacteristic
29C5×D21—21no—
30C5×D3×C7—21no—
31C5×D3×C7D412yescomplemented
32C3×C5×D7—21no—
33C22×D3×C7C2×C511yescharacteristic, complemented
34C2×D3×D7C2×C511yescharacteristic, complemented
35#4268C2×C511yescharacteristic, complemented
36C3×C22⋊D7C2×C511yescharacteristic, complemented
37#4247C2×C511yescharacteristic, complemented
38#4245C2×C511yescharacteristic, complemented
39D3×Dic7C2×C511yescharacteristic, complemented
40C22×C5×C7—31no—
41C22×C5×C7—31no—
42C22×C5×C7—62no—
43C22×C5×C7C2×D311yescharacteristic, complemented
44C2×C5×D7—31no—
45C2×C5×D7—62no—
46C2×C5×D7C2×D311yescharacteristic, complemented
47C5×Dic7—31no—
48C5×Dic7C2×D311yescharacteristic, complemented
49C22×C5×D3—71no—
50C22×C5×D3D711yescharacteristic, complemented
51C3×C5×D4—71no—
52C5×#67—71no—
53C5×#67—71no—
54C5×D12—71no—
55C4×C5×D3—71no—
56C2×C22⋊D7—31noHall
57C3×C5×C7C2×D411yescharacteristic, complemented, Hall
58C22×C3×C7C22×C511yescharacteristic, complemented
59C2×D21C22×C511yescharacteristic, complemented
60C2×D3×C7—22no—
61C2×D3×C7C22×C511yescharacteristic
62C2×D3×C7C22×C511yescharacteristic, complemented
63C2×C3×D7C22×C511yescharacteristic, complemented
64D3×D7—22no—
65Dic21C22×C511yescharacteristic, complemented
66C3×Dic7C22×C511yescharacteristic, complemented
67C2×C5×D4—211noHall
68C2×C5×C7—21no—
69C2×C5×C7—32no—
70C2×C5×C7—61no—
71C2×C5×C7C22×D311yescharacteristic
72C5×D7—21no—
73C5×D7—61no—
74C22×C3×C5—71no—
75C22×C3×C5C2×D711yescharacteristic, complemented
76C2×C5×D3—22no—
77C2×C5×D3—71no—
78C2×C5×D3—142no—
79C2×C5×D3C2×D711yescharacteristic
80C2×C5×D3C2×D711yescharacteristic, complemented
81C3×C4×C5—71no—
82C5×Dic3—71no—
83C23×C7—31no—
84C22×D7—31no—
85C22⋊D7—31no—
86C22⋊D7—31no—
87C22⋊D7—31no—
88C22⋊D7C5×D311yescharacteristic, direct product factor
89C2×Dic7—31no—
90D3×D4—71noHall
91C2×C3×C7—21no—
92C2×C3×C7C23×C511yescharacteristic
93D21—21no—
94C3×D7—21no—
95D3×C7—21no—
96D3×C7C5×D412yescomplemented
97C23×C5—31no—
98C23×C5—211no—
99C5×D4—71no—
100C5×D4—211no—
101C5×D4—211no—
102C5×D4—211no—
103C2×C4×C5—211no—
104C5×C7D3×D411yescharacteristic, complemented, Hall
105C2×C3×C5—21no—
106C2×C3×C5—141no—
107C2×C3×C5C22×D711yescharacteristic
108C5×D3—21no—
109C5×D3—141no—
110C5×D3C22⋊D712yesdirect product factor
111C22×C7—31no—
112C22×C7—31no—
113C22×C7—62no—
114C22×C7C2×C5×D311yescharacteristic, complemented
115C2×D7—31no—
116C2×D7—62no—
117C2×D7C2×C5×D311yescharacteristic, complemented
118Dic7—31no—
119Dic7C2×C5×D311yescharacteristic, complemented
120C22×D3—71no—
121C22×D3C5×D711yescharacteristic, complemented
122C3×D4—71no—
123#67—71no—
124#67—71no—
125D12—71no—
126C4×D3—71no—
127C3×C7C2×C5×D411yescharacteristic, complemented, Hall
128C22×C5—31no—
129C22×C5—31no—
130C22×C5—62no—
131C22×C5—71no—
132C22×C5—211no—
133C22×C5—422no—
134C22×C5D3×D711yescharacteristic, complemented
135C4×C5—71no—
136C4×C5—211no—
137C2×D4—211noSylow
138C3×C5C2×C22⋊D711yescharacteristic, complemented, Hall
139C2×C7—21no—
140C2×C7—32no—
141C2×C7—61no—
142C2×C7C22×C5×D311yescharacteristic
143D7—21no—
144D7—61no—
145C22×C3—71no—
146C22×C3C2×C5×D711yescharacteristic, complemented
147C2×D3—22no—
148C2×D3—71no—
149C2×D3—142no—
150C2×D3C2×C5×D711yescharacteristic
151C2×D3C2×C5×D711yescharacteristic, complemented
152C3×C4—71no—
153Dic3—71no—
154C2×C5—21no—
155C2×C5—32no—
156C2×C5—61no—
157C2×C5—141no—
158C2×C5—421no—
159C2×C5C2×D3×D711yescharacteristic
160C23—31no—
161C23—211no—
162D4—71no—
163D4—211no—
164D4—211no—
165D4—211no—
166C2×C4—211no—
167C7C5×D3×D411yescharacteristic, complemented, Sylow
168C2×C3—21no—
169C2×C3—141no—
170C2×C3C22×C5×D711yescharacteristic
171D3—21no—
172D3—141no—
173D3C5×C22⋊D712yesdirect product factor
174C5D3×C22⋊D711yescharacteristic, direct product factor, Sylow
175C22—31no—
176C22—31no—
177C22—62no—
178C22—71no—
179C22—211no—
180C22—422no—
181C22C5×D3×D711yescharacteristic, complemented
182C4—71no—
183C4—211no—
184C3C2×C5×C22⋊D711yescharacteristic, complemented, Sylow
185C2—21no—
186C2—32no—
187C2—61no—
188C2—141no—
189C2—421no—
190C2C2×C5×D3×D711yescharacteristic
subgroupG/H
centerC2×C5C2×D3×D7
commutator, cosocleC2×C3×C7C23×C5
FrattiniC2C2×C5×D3×D7
FittingC22×C3×C5×C7C22
socleC2×C3×C5×C7C23
hypercenterC22×C5D3×D7
hypocenterC3×C7C2×C5×D4
LCSG ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2×C5 ◁ C22×C5

Complements

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

NH ≅ G/Ntype
1. C22×C5×D3×C7C2semidirect
2. C2×C5×D3×D7C2semidirect
3. C5×#4268C2semidirect
4. C3×C5×C22⋊D7C2semidirect
5. C5×#4247C2semidirect
6. C5×#4245C2semidirect
7. C5×D3×Dic7C2semidirect
9. C22×C3×C5×C7C22semidirect
10. C2×C5×D21C22semidirect
13. C2×C5×D3×C7C22semidirect
14. C2×C3×C5×D7C22semidirect
16. C5×Dic21C22semidirect
17. C3×C5×Dic7C22semidirect
18. D3×C22⋊D7C5direct (N × H)
24. C5×C22⋊D7D3direct (N × H)
31. C5×D3×C7D4semidirect
33. C22×D3×C7C2×C5semidirect
34. C2×D3×D7C2×C5semidirect
35. #4268C2×C5semidirect
36. C3×C22⋊D7C2×C5semidirect
37. #4247C2×C5semidirect
38. #4245C2×C5semidirect
39. D3×Dic7C2×C5semidirect
43. C22×C5×C7C2×D3semidirect
46. C2×C5×D7C2×D3semidirect
48. C5×Dic7C2×D3semidirect
50. C22×C5×D3D7semidirect
57. C3×C5×C7C2×D4semidirect
58. C22×C3×C7C22×C5semidirect
59. C2×D21C22×C5semidirect
62. C2×D3×C7C22×C5semidirect
63. C2×C3×D7C22×C5semidirect
65. Dic21C22×C5semidirect
66. C3×Dic7C22×C5semidirect
75. C22×C3×C5C2×D7semidirect
80. C2×C5×D3C2×D7semidirect
88. C22⋊D7C5×D3direct (N × H)
96. D3×C7C5×D4semidirect
104. C5×C7D3×D4semidirect
110. C5×D3C22⋊D7direct (N × H)
114. C22×C7C2×C5×D3semidirect
117. C2×D7C2×C5×D3semidirect
119. Dic7C2×C5×D3semidirect
121. C22×D3C5×D7semidirect
127. C3×C7C2×C5×D4semidirect
134. C22×C5D3×D7semidirect
138. C3×C5C2×C22⋊D7semidirect
146. C22×C3C2×C5×D7semidirect
151. C2×D3C2×C5×D7semidirect
167. C7C5×D3×D4semidirect
173. D3C5×C22⋊D7direct (N × H)
174. C5D3×C22⋊D7direct (N × H)
181. C22C5×D3×D7semidirect
184. C3C2×C5×C22⋊D7semidirect

Maximal subgroups

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

subgroupindex
C22×C5×D3×C72
C2×C5×D3×D72
C5×#42682
C3×C5×C22⋊D72
C5×#42472
C5×#42452
C5×D3×Dic72
C2×C5×C22⋊D73
D3×C22⋊D75
C5×D3×D47