Finite Group Databasebeta

← C3×D4×D35 #13132854

Subgroups — C3×D4×D35 #13132854

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×C3×D35C212yesmaximal, complemented
2C3×C5×C7×D4C211yesmaximal, characteristic, complemented
3C3×C22⋊D35C212yesmaximal, complemented
4C3×D140C211yesmaximal, characteristic, complemented
5C3×C4×D35C211yesmaximal, characteristic, complemented
6D4×D35C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×C7C2212yescomplemented
8C2×C3×D35—24no—
9C2×C3×D35C2211yescharacteristic
10C2×C3×D35C2212yescomplemented
11C3×C4×C5×C7C2211yescharacteristic, complemented
12C3×Dic35C2211yescharacteristic, complemented
13C3×D4×D7—51nomaximal, Hall
14C22×D35C2×C312yescomplemented
15C5×C7×D4C2×C311yescharacteristic, complemented
16C22⋊D35C2×C312yescomplemented
17D140C2×C311yescharacteristic, complemented
18C4×D35C2×C311yescharacteristic, complemented
19C3×D4×D5—71nomaximal, Hall
20C2×C3×C5×C7—22no—
21C2×C3×C5×C7C2311yescharacteristic
22C3×D35—22no—
23C3×D35D412yesdirect product factor
24C22×C3×D7—52no—
25C3×C7×D4D511yescharacteristic, complemented
26C3×C22⋊D7—52no—
27C3×D28—51no—
28C3×C4×D7—51no—
29C22×C5×C7C22×C312yescomplemented
30C2×D35—24no—
31C2×D35C22×C311yescharacteristic
32C2×D35C22×C312yescomplemented
33C4×C5×C7C22×C311yescharacteristic, complemented
34Dic35C22×C311yescharacteristic, complemented
35C22×C3×D5—72no—
36C3×C5×D4D711yescharacteristic, complemented
37C3×C22⋊D5—72no—
38C3×D20—71no—
39C3×C4×D5—71no—
40D4×D7—51noHall
41C3×C5×C7C2×D411yescharacteristic, complemented, Hall
42C22×C3×C7C2×D512yescomplemented
43C2×C3×D7—51no—
44C2×C3×D7—52no—
45C2×C3×D7—104no—
46C3×C4×C7C2×D511yescharacteristic, complemented
47C3×Dic7—51no—
48D4×D5—71noHall
49C2×C5×C7—22no—
50C2×C5×C7C23×C311yescharacteristic
51D35—22no—
52D35C3×D412yesdirect product factor
53C22×C3×C5C2×D712yescomplemented
54C2×C3×D5—71no—
55C2×C3×D5—72no—
56C2×C3×D5—144no—
57C3×C4×C5C2×D711yescharacteristic, complemented
58C3×Dic5—71no—
59C22×D7—52no—
60C7×D4C3×D511yescharacteristic, complemented
61C22⋊D7—52no—
62D28—51no—
63C4×D7—51no—
64C2×C3×D4—351noHall
65C2×C3×C7—22no—
66C2×C3×C7C22×D511yescharacteristic
67C3×D7—52no—
68C3×D7—102no—
69C22×D5—72no—
70C5×D4C3×D711yescharacteristic, complemented
71C22⋊D5—72no—
72D20—71no—
73C4×D5—71no—
74C5×C7C2×C3×D411yescharacteristic, complemented, Hall
75C2×C3×C5—22no—
76C2×C3×C5C22×D711yescharacteristic
77C3×D5—72no—
78C3×D5—142no—
79C22×C7C2×C3×D512yescomplemented
80C2×D7—51no—
81C2×D7—52no—
82C2×D7—104no—
83C4×C7C2×C3×D511yescharacteristic, complemented
84Dic7—51no—
85C23×C3—352no—
86C3×D4—352no—
87C3×D4—351no—
88C3×D4D3511yescharacteristic, direct product factor
89C2×C3×C4—351no—
90C3×C7D4×D511yescharacteristic, complemented, Hall
91C22×C5C2×C3×D712yescomplemented
92C2×D5—71no—
93C2×D5—72no—
94C2×D5—144no—
95C4×C5C2×C3×D711yescharacteristic, complemented
96Dic5—71no—
97C2×D4—351noSylow
98C3×C5D4×D711yescharacteristic, complemented, Hall
99C2×C7—22no—
100C2×C7C22×C3×D511yescharacteristic
101D7—52no—
102D7—102no—
103C22×C3—351no—
104C22×C3—352no—
105C22×C3—704no—
106C22×C3C2×D3512yescomplemented
107C3×C4—351no—
108C3×C4C2×D3511yescharacteristic, complemented
109C2×C5—22no—
110C2×C5C22×C3×D711yescharacteristic
111D5—72no—
112D5—142no—
113C23—352no—
114D4—352no—
115D4—351no—
116D4C3×D3511yescharacteristic, direct product factor
117C2×C4—351no—
118C7C3×D4×D511yescharacteristic, complemented, Sylow
119C2×C3—22no—
120C2×C3—352no—
121C2×C3—702no—
122C2×C3C22×D3511yescharacteristic
123C5C3×D4×D711yescharacteristic, complemented, Sylow
124C22—351no—
125C22—352no—
126C22—704no—
127C22C2×C3×D3512yescomplemented
128C4—351no—
129C4C2×C3×D3511yescharacteristic, complemented
130C3D4×D3511yescharacteristic, direct product factor, Sylow
131C2—22no—
132C2—352no—
133C2—702no—
134C2C22×C3×D3511yescharacteristic
subgroupG/H
centerC2×C3C22×D35
commutator, cosocleC2×C5×C7C23×C3
FrattiniC2C22×C3×D35
FittingC3×C5×C7×D4C2
socleC2×C3×C5×C7C23
hypercenterC3×D4D35
hypocenterC5×C7C2×C3×D4
LCSG ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C2×C3 ◁ C3×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×D35C2semidirect
2. C3×C5×C7×D4C2semidirect
3. C3×C22⋊D35C2semidirect
4. C3×D140C2semidirect
5. C3×C4×D35C2semidirect
6. D4×D35C3direct (N × H)
7. C22×C3×C5×C7C22semidirect
10. C2×C3×D35C22semidirect
11. C3×C4×C5×C7C22semidirect
12. C3×Dic35C22semidirect
14. C22×D35C2×C3semidirect
15. C5×C7×D4C2×C3semidirect
16. C22⋊D35C2×C3semidirect
17. D140C2×C3semidirect
18. C4×D35C2×C3semidirect
23. C3×D35D4direct (N × H)
25. C3×C7×D4D5semidirect
29. C22×C5×C7C22×C3semidirect
32. C2×D35C22×C3semidirect
33. C4×C5×C7C22×C3semidirect
34. Dic35C22×C3semidirect
36. C3×C5×D4D7semidirect
41. C3×C5×C7C2×D4semidirect
42. C22×C3×C7C2×D5semidirect
46. C3×C4×C7C2×D5semidirect
52. D35C3×D4direct (N × H)
53. C22×C3×C5C2×D7semidirect
57. C3×C4×C5C2×D7semidirect
60. C7×D4C3×D5semidirect
70. C5×D4C3×D7semidirect
74. C5×C7C2×C3×D4semidirect
79. C22×C7C2×C3×D5semidirect
83. C4×C7C2×C3×D5semidirect
88. C3×D4D35direct (N × H)
90. C3×C7D4×D5semidirect
91. C22×C5C2×C3×D7semidirect
95. C4×C5C2×C3×D7semidirect
98. C3×C5D4×D7semidirect
106. C22×C3C2×D35semidirect
108. C3×C4C2×D35semidirect
116. D4C3×D35direct (N × H)
118. C7C3×D4×D5semidirect
123. C5C3×D4×D7semidirect
127. C22C2×C3×D35semidirect
129. C4C2×C3×D35semidirect
130. C3D4×D35direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D352
C3×C5×C7×D42
C3×C22⋊D352
C3×D1402
C3×C4×D352
D4×D353
C3×D4×D75
C3×D4×D57