Finite Group Databasebeta

← C7×D4×D15 #13132884

Subgroups — C7×D4×D15 #13132884

Order 1680.

216 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 74 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×C7×D15C212yesmaximal, complemented
2C3×C5×C7×D4C211yesmaximal, characteristic, complemented
3C7×#1220C212yesmaximal, complemented
4C7×D60C211yesmaximal, characteristic, complemented
5C4×C7×D15C211yesmaximal, characteristic, complemented
6C7×D4×D5—31nomaximal, Hall
7C22×C3×C5×C7C2212yescomplemented
8C2×C7×D15—24no—
9C2×C7×D15C2211yescharacteristic
10C2×C7×D15C2212yescomplemented
11C3×C4×C5×C7C2211yescharacteristic, complemented
12C7×Dic15C2211yescharacteristic, complemented
13D3×C7×D4—51nomaximal, Hall
14C22×C7×D5—32no—
15C5×C7×D4D311yescharacteristic, complemented
16C7×C22⋊D5—32no—
17C7×D20—31no—
18C4×C7×D5—31no—
19D4×D15C711yesmaximal, characteristic, direct product factor, Hall
20C2×C3×C5×C7—22no—
21C2×C3×C5×C7C2311yescharacteristic
22C7×D15—22no—
23C7×D15D412yesdirect product factor
24C22×D3×C7—52no—
25C3×C7×D4D511yescharacteristic, complemented
26C7×#67—52no—
27C7×D12—51no—
28C4×D3×C7—51no—
29C22×C5×C7C2×D312yescomplemented
30C2×C7×D5—31no—
31C2×C7×D5—32no—
32C2×C7×D5—64no—
33C4×C5×C7C2×D311yescharacteristic, complemented
34C7×Dic5—31no—
35C22×D15C2×C712yescomplemented
36C3×C5×D4C2×C711yescharacteristic, complemented
37#1220C2×C712yescomplemented
38D60C2×C711yescharacteristic, complemented
39C4×D15C2×C711yescharacteristic, complemented
40C2×C7×D4—151noHall
41C3×C5×C7C2×D411yescharacteristic, complemented, Hall
42C22×C3×C7C2×D512yescomplemented
43C2×D3×C7—51no—
44C2×D3×C7—52no—
45C2×D3×C7—104no—
46C3×C4×C7C2×D511yescharacteristic, complemented
47C7×Dic3—51no—
48D4×D5—31noHall
49C2×C5×C7—22no—
50C2×C5×C7C22×D311yescharacteristic
51C7×D5—32no—
52C7×D5—62no—
53C22×C3×C5C22×C712yescomplemented
54C2×D15—24no—
55C2×D15C22×C711yescharacteristic
56C2×D15C22×C712yescomplemented
57C3×C4×C5C22×C711yescharacteristic, complemented
58Dic15C22×C711yescharacteristic, complemented
59C23×C7—152no—
60C7×D4—152no—
61C7×D4—151no—
62C7×D4D1511yescharacteristic, direct product factor
63C2×C4×C7—151no—
64D3×D4—51noHall
65C2×C3×C7—22no—
66C2×C3×C7C22×D511yescharacteristic
67D3×C7—52no—
68D3×C7—102no—
69C22×D5—32no—
70C5×D4D3×C711yescharacteristic, complemented
71C22⋊D5—32no—
72D20—31no—
73C4×D5—31no—
74C5×C7D3×D411yescharacteristic, complemented, Hall
75C2×C3×C5—22no—
76C2×C3×C5C23×C711yescharacteristic
77D15—22no—
78D15C7×D412yesdirect product factor
79C22×C7—151no—
80C22×C7—152no—
81C22×C7—304no—
82C22×C7C2×D1512yescomplemented
83C4×C7—151no—
84C4×C7C2×D1511yescharacteristic, complemented
85C22×D3—52no—
86C3×D4C7×D511yescharacteristic, complemented
87#67—52no—
88D12—51no—
89C4×D3—51no—
90C3×C7D4×D511yescharacteristic, complemented, Hall
91C22×C5C2×D3×C712yescomplemented
92C2×D5—31no—
93C2×D5—32no—
94C2×D5—64no—
95C4×C5C2×D3×C711yescharacteristic, complemented
96Dic5—31no—
97C2×D4—151noSylow
98C3×C5C2×C7×D411yescharacteristic, complemented, Hall
99C2×C7—22no—
100C2×C7—152no—
101C2×C7—302no—
102C2×C7C22×D1511yescharacteristic
103C22×C3C2×C7×D512yescomplemented
104C2×D3—51no—
105C2×D3—52no—
106C2×D3—104no—
107C3×C4C2×C7×D511yescharacteristic, complemented
108Dic3—51no—
109C2×C5—22no—
110C2×C5C22×D3×C711yescharacteristic
111D5—32no—
112D5—62no—
113C23—152no—
114D4—152no—
115D4—151no—
116D4C7×D1511yescharacteristic, direct product factor
117C2×C4—151no—
118C7D4×D1511yescharacteristic, direct product factor, Sylow
119C2×C3—22no—
120C2×C3C22×C7×D511yescharacteristic
121D3—52no—
122D3—102no—
123C5D3×C7×D411yescharacteristic, complemented, Sylow
124C22—151no—
125C22—152no—
126C22—304no—
127C22C2×C7×D1512yescomplemented
128C4—151no—
129C4C2×C7×D1511yescharacteristic, complemented
130C3C7×D4×D511yescharacteristic, complemented, Sylow
131C2—22no—
132C2—152no—
133C2—302no—
134C2C22×C7×D1511yescharacteristic
subgroupG/H
centerC2×C7C22×D15
commutator, cosocleC2×C3×C5C23×C7
FrattiniC2C22×C7×D15
FittingC3×C5×C7×D4C2
socleC2×C3×C5×C7C23
hypercenterC7×D4D15
hypocenterC3×C5C2×C7×D4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C7 ◁ C7×D4

Complements

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

NH ≅ G/Ntype
1. C22×C7×D15C2semidirect
2. C3×C5×C7×D4C2semidirect
3. C7×#1220C2semidirect
4. C7×D60C2semidirect
5. C4×C7×D15C2semidirect
7. C22×C3×C5×C7C22semidirect
10. C2×C7×D15C22semidirect
11. C3×C4×C5×C7C22semidirect
12. C7×Dic15C22semidirect
15. C5×C7×D4D3semidirect
19. D4×D15C7direct (N × H)
23. C7×D15D4direct (N × H)
25. C3×C7×D4D5semidirect
29. C22×C5×C7C2×D3semidirect
33. C4×C5×C7C2×D3semidirect
35. C22×D15C2×C7semidirect
36. C3×C5×D4C2×C7semidirect
37. #1220C2×C7semidirect
38. D60C2×C7semidirect
39. C4×D15C2×C7semidirect
41. C3×C5×C7C2×D4semidirect
42. C22×C3×C7C2×D5semidirect
46. C3×C4×C7C2×D5semidirect
53. C22×C3×C5C22×C7semidirect
56. C2×D15C22×C7semidirect
57. C3×C4×C5C22×C7semidirect
58. Dic15C22×C7semidirect
62. C7×D4D15direct (N × H)
70. C5×D4D3×C7semidirect
74. C5×C7D3×D4semidirect
78. D15C7×D4direct (N × H)
82. C22×C7C2×D15semidirect
84. C4×C7C2×D15semidirect
86. C3×D4C7×D5semidirect
90. C3×C7D4×D5semidirect
91. C22×C5C2×D3×C7semidirect
95. C4×C5C2×D3×C7semidirect
98. C3×C5C2×C7×D4semidirect
103. C22×C3C2×C7×D5semidirect
107. C3×C4C2×C7×D5semidirect
116. D4C7×D15direct (N × H)
118. C7D4×D15direct (N × H)
123. C5D3×C7×D4semidirect
127. C22C2×C7×D15semidirect
129. C4C2×C7×D15semidirect
130. C3C7×D4×D5semidirect

Maximal subgroups

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

subgroupindex
C22×C7×D152
C3×C5×C7×D42
C7×#12202
C7×D602
C4×C7×D152
C7×D4×D53
D3×C7×D45
D4×D157