Finite Group Databasebeta

← C3×D5×C22⋊D7 #13132656

Subgroups — C3×D5×C22⋊D7 #13132656

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×C3×C7×D5C211yesmaximal, characteristic, complemented
2C2×C3×D5×D7C211yesmaximal, characteristic, complemented
3C3×C22⋊D35C211yesmaximal, characteristic, complemented
4C3×C5×C22⋊D7C211yesmaximal, characteristic, complemented
5C3×#63307C211yesmaximal, characteristic, complemented
6C3×#63305C211yesmaximal, characteristic, complemented
7C3×D5×Dic7C211yesmaximal, characteristic, complemented
8D5×C22⋊D7C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×C7C2211yescharacteristic, complemented
10C2×C3×D35C2211yescharacteristic, complemented
11C2×C3×C7×D5—22no—
12C2×C3×C7×D5C2211yescharacteristic
13C2×C3×C7×D5C2211yescharacteristic, complemented
14C2×C3×C5×D7C2211yescharacteristic, complemented
15C3×D5×D7—22no—
16C3×Dic35C2211yescharacteristic, complemented
17C3×C5×Dic7C2211yescharacteristic, complemented
18C2×C3×C22⋊D7—51nomaximal, Hall
19C22×C7×D5C2×C311yescharacteristic, complemented
20C2×D5×D7C2×C311yescharacteristic, complemented
21C22⋊D35C2×C311yescharacteristic, complemented
22C5×C22⋊D7C2×C311yescharacteristic, complemented
23#63307C2×C311yescharacteristic, complemented
24#63305C2×C311yescharacteristic, complemented
25D5×Dic7C2×C311yescharacteristic, complemented
26C3×D4×D5—71nomaximal, Hall
27C2×C3×C5×C7—21no—
28C2×C3×C5×C7C2311yescharacteristic
29C3×D35—21no—
30C3×C7×D5—21no—
31C3×C7×D5D412yescomplemented
32C3×C5×D7—21no—
33C23×C3×C7—51no—
34C22×C3×D7—51no—
35C3×C22⋊D7—51no—
36C3×C22⋊D7—51no—
37C3×C22⋊D7—51no—
38C3×C22⋊D7D511yescharacteristic, direct product factor
39C2×C3×Dic7—51no—
40C22×C5×C7C22×C311yescharacteristic, complemented
41C2×D35C22×C311yescharacteristic, complemented
42C2×C7×D5—22no—
43C2×C7×D5C22×C311yescharacteristic
44C2×C7×D5C22×C311yescharacteristic, complemented
45C2×C5×D7C22×C311yescharacteristic, complemented
46D5×D7—22no—
47Dic35C22×C311yescharacteristic, complemented
48C5×Dic7C22×C311yescharacteristic, complemented
49C22×C3×D5—71no—
50C22×C3×D5D711yescharacteristic, complemented
51C3×C5×D4—71no—
52C3×C22⋊D5—71no—
53C3×C22⋊D5—71no—
54C3×D20—71no—
55C3×C4×D5—71no—
56C2×C22⋊D7—51noHall
57C3×C5×C7C2×D411yescharacteristic, complemented, Hall
58C22×C3×C7—51no—
59C22×C3×C7—51no—
60C22×C3×C7—102no—
61C22×C3×C7C2×D511yescharacteristic, complemented
62C2×C3×D7—51no—
63C2×C3×D7—102no—
64C2×C3×D7C2×D511yescharacteristic, complemented
65C3×Dic7—51no—
66C3×Dic7C2×D511yescharacteristic, complemented
67D4×D5—71noHall
68C2×C5×C7—21no—
69C2×C5×C7C23×C311yescharacteristic
70D35—21no—
71C5×D7—21no—
72C7×D5—21no—
73C7×D5C3×D412yescomplemented
74C22×C3×C5—71no—
75C22×C3×C5C2×D711yescharacteristic, complemented
76C2×C3×D5—22no—
77C2×C3×D5—71no—
78C2×C3×D5—142no—
79C2×C3×D5C2×D711yescharacteristic
80C2×C3×D5C2×D711yescharacteristic, complemented
81C3×C4×C5—71no—
82C3×Dic5—71no—
83C23×C7—51no—
84C22×D7—51no—
85C22⋊D7—51no—
86C22⋊D7—51no—
87C22⋊D7—51no—
88C22⋊D7C3×D511yescharacteristic, direct product factor
89C2×Dic7—51no—
90C2×C3×D4—351noHall
91C2×C3×C7—21no—
92C2×C3×C7—52no—
93C2×C3×C7—101no—
94C2×C3×C7C22×D511yescharacteristic
95C3×D7—21no—
96C3×D7—101no—
97C22×D5—71no—
98C22×D5C3×D711yescharacteristic, complemented
99C5×D4—71no—
100C22⋊D5—71no—
101C22⋊D5—71no—
102D20—71no—
103C4×D5—71no—
104C5×C7C2×C3×D411yescharacteristic, complemented, Hall
105C2×C3×C5—21no—
106C2×C3×C5—141no—
107C2×C3×C5C22×D711yescharacteristic
108C3×D5—21no—
109C3×D5—141no—
110C3×D5C22⋊D712yesdirect product factor
111C22×C7—51no—
112C22×C7—51no—
113C22×C7—102no—
114C22×C7C2×C3×D511yescharacteristic, complemented
115C2×D7—51no—
116C2×D7—102no—
117C2×D7C2×C3×D511yescharacteristic, complemented
118Dic7—51no—
119Dic7C2×C3×D511yescharacteristic, complemented
120C23×C3—51no—
121C23×C3—351no—
122C3×D4—71no—
123C3×D4—351no—
124C3×D4—351no—
125C3×D4—351no—
126C2×C3×C4—351no—
127C3×C7D4×D511yescharacteristic, complemented, Hall
128C22×C5—71no—
129C22×C5C2×C3×D711yescharacteristic, complemented
130C2×D5—22no—
131C2×D5—71no—
132C2×D5—142no—
133C2×D5C2×C3×D711yescharacteristic
134C2×D5C2×C3×D711yescharacteristic, complemented
135C4×C5—71no—
136Dic5—71no—
137C2×D4—351noSylow
138C3×C5C2×C22⋊D711yescharacteristic, complemented, Hall
139C2×C7—21no—
140C2×C7—52no—
141C2×C7—101no—
142C2×C7C22×C3×D511yescharacteristic
143D7—21no—
144D7—101no—
145C22×C3—51no—
146C22×C3—51no—
147C22×C3—71no—
148C22×C3—102no—
149C22×C3—351no—
150C22×C3—702no—
151C22×C3D5×D711yescharacteristic, complemented
152C3×C4—71no—
153C3×C4—351no—
154C2×C5—21no—
155C2×C5—141no—
156C2×C5C22×C3×D711yescharacteristic
157D5—21no—
158D5—141no—
159D5C3×C22⋊D712yesdirect product factor
160C23—51no—
161C23—351no—
162D4—71no—
163D4—351no—
164D4—351no—
165D4—351no—
166C2×C4—351no—
167C7C3×D4×D511yescharacteristic, complemented, Sylow
168C2×C3—21no—
169C2×C3—52no—
170C2×C3—101no—
171C2×C3—141no—
172C2×C3—701no—
173C2×C3C2×D5×D711yescharacteristic
174C5C2×C3×C22⋊D711yescharacteristic, complemented, Sylow
175C22—51no—
176C22—51no—
177C22—71no—
178C22—102no—
179C22—351no—
180C22—702no—
181C22C3×D5×D711yescharacteristic, complemented
182C4—71no—
183C4—351no—
184C3D5×C22⋊D711yescharacteristic, direct product factor, Sylow
185C2—21no—
186C2—52no—
187C2—101no—
188C2—141no—
189C2—701no—
190C2C2×C3×D5×D711yescharacteristic
subgroupG/H
centerC2×C3C2×D5×D7
commutator, cosocleC2×C5×C7C23×C3
FrattiniC2C2×C3×D5×D7
FittingC22×C3×C5×C7C22
socleC2×C3×C5×C7C23
hypercenterC22×C3D5×D7
hypocenterC5×C7C2×C3×D4
LCSG ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C2×C3 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C22×C3×C7×D5C2semidirect
2. C2×C3×D5×D7C2semidirect
3. C3×C22⋊D35C2semidirect
4. C3×C5×C22⋊D7C2semidirect
5. C3×#63307C2semidirect
6. C3×#63305C2semidirect
7. C3×D5×Dic7C2semidirect
8. D5×C22⋊D7C3direct (N × H)
9. C22×C3×C5×C7C22semidirect
10. C2×C3×D35C22semidirect
13. C2×C3×C7×D5C22semidirect
14. C2×C3×C5×D7C22semidirect
16. C3×Dic35C22semidirect
17. C3×C5×Dic7C22semidirect
19. C22×C7×D5C2×C3semidirect
20. C2×D5×D7C2×C3semidirect
21. C22⋊D35C2×C3semidirect
22. C5×C22⋊D7C2×C3semidirect
23. #63307C2×C3semidirect
24. #63305C2×C3semidirect
25. D5×Dic7C2×C3semidirect
31. C3×C7×D5D4semidirect
38. C3×C22⋊D7D5direct (N × H)
40. C22×C5×C7C22×C3semidirect
41. C2×D35C22×C3semidirect
44. C2×C7×D5C22×C3semidirect
45. C2×C5×D7C22×C3semidirect
47. Dic35C22×C3semidirect
48. C5×Dic7C22×C3semidirect
50. C22×C3×D5D7semidirect
57. C3×C5×C7C2×D4semidirect
61. C22×C3×C7C2×D5semidirect
64. C2×C3×D7C2×D5semidirect
66. C3×Dic7C2×D5semidirect
73. C7×D5C3×D4semidirect
75. C22×C3×C5C2×D7semidirect
80. C2×C3×D5C2×D7semidirect
88. C22⋊D7C3×D5direct (N × H)
98. C22×D5C3×D7semidirect
104. C5×C7C2×C3×D4semidirect
110. C3×D5C22⋊D7direct (N × H)
114. C22×C7C2×C3×D5semidirect
117. C2×D7C2×C3×D5semidirect
119. Dic7C2×C3×D5semidirect
127. C3×C7D4×D5semidirect
129. C22×C5C2×C3×D7semidirect
134. C2×D5C2×C3×D7semidirect
138. C3×C5C2×C22⋊D7semidirect
151. C22×C3D5×D7semidirect
159. D5C3×C22⋊D7direct (N × H)
167. C7C3×D4×D5semidirect
174. C5C2×C3×C22⋊D7semidirect
181. C22C3×D5×D7semidirect
184. C3D5×C22⋊D7direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C7×D52
C2×C3×D5×D72
C3×C22⋊D352
C3×C5×C22⋊D72
C3×#633072
C3×#633052
C3×D5×Dic72
D5×C22⋊D73
C2×C3×C22⋊D75
C3×D4×D57