Finite Group Databasebeta

← C22×D3×D35 #13132971

Subgroups — C22×D3×D35 #13132971

Order 1680.

536 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 146 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×D105C211yesmaximal, characteristic, complemented
2C22×C5×D3×C7C211yesmaximal, characteristic, complemented
3C22×C3×D35C211yesmaximal, characteristic, complemented
4C2×D3×D35C2112yesmaximal, direct product factor
5C23×D35—31nomaximal, Hall
6C22×C3×C5×C7C2211yescharacteristic, complemented
7C2×D105C2216yescomplemented
8C2×C5×D3×C7C2216yescomplemented
9C2×C3×D35C2216yescomplemented
10D3×D35C22116yesdirect product factor
11C22×D3×D7—51nomaximal, Hall
12C23×C5×C7—31no—
13C22×D35—31no—
14C22×D35—312no—
15C22×D35D311yescharacteristic, direct product factor
16C22×D3×D5—71nomaximal, Hall
17C2×C3×C5×C7C2313yescomplemented
18D105C2314yescomplemented
19C5×D3×C7C2314yescomplemented
20C3×D35C2314yescomplemented
21C22×D21—51no—
22C22×D3×C7D511yescharacteristic, complemented
23C22×C3×D7—51no—
24C2×D3×D7—512no—
25C22×C5×C7—36no—
26C22×C5×C7C2×D311yescharacteristic, complemented
27C2×D35—36no—
28C2×D35—316no—
29C2×D35C2×D316yesdirect product factor
30C22×D15—71no—
31C22×C5×D3D711yescharacteristic, complemented
32C22×C3×D5—71no—
33C2×D3×D5—712no—
34C23×D7—151noHall
35C3×C5×C7C2411yescharacteristic, complemented, Hall
36C22×C3×C7C2×D511yescharacteristic, complemented
37C2×D21—56no—
38C2×D3×C7C2×D516yescomplemented
39C2×C3×D7—56no—
40D3×D7—516no—
41C23×D5—211noHall
42C2×C5×C7—34no—
43C2×C5×C7C22×D313yescomplemented
44D35—34no—
45D35C22×D314yesdirect product factor
46C22×C3×C5C2×D711yescharacteristic, complemented
47C2×D15—76no—
48C2×C5×D3C2×D716yescomplemented
49C2×C3×D5—76no—
50D3×D5—716no—
51C23×C7—31no—
52C22×D7—51no—
53C22×D7—1512no—
54C22×D7—151no—
55C23×D3—351noHall
56C2×C3×C7C22×D513yescomplemented
57D21—54no—
58C3×D7—54no—
59D3×C7C22×D514yescomplemented
60C23×C5—31no—
61C22×D5—71no—
62C22×D5—2112no—
63C22×D5—211no—
64C5×C7C23×D311yescharacteristic, complemented, Hall
65C2×C3×C5C22×D713yescomplemented
66D15—74no—
67C3×D5—74no—
68C5×D3C22×D714yescomplemented
69C22×C7—36no—
70C22×C7D3×D511yescharacteristic, complemented
71C2×D7—56no—
72C2×D7—1516no—
73C2×D7—156no—
74C23×C3—351no—
75C22×D3—351no—
76C22×D3—3512no—
77C22×D3D3511yescharacteristic, direct product factor
78C3×C7C23×D511yescharacteristic, complemented, Hall
79C22×C5—36no—
80C22×C5D3×D711yescharacteristic, complemented
81C2×D5—76no—
82C2×D5—2116no—
83C2×D5—216no—
84C24—1051noSylow
85C3×C5C23×D711yescharacteristic, complemented, Hall
86C2×C7—34no—
87C2×C7C2×D3×D513yescomplemented
88D7—54no—
89D7—154no—
90C22×C3—356no—
91C22×C3C2×D3511yescharacteristic, complemented
92C2×D3—356no—
93C2×D3—3516no—
94C2×D3C2×D3516yesdirect product factor
95C2×C5—34no—
96C2×C5C2×D3×D713yescomplemented
97D5—74no—
98D5—214no—
99C23—31no—
100C23—351no—
101C23—10512no—
102C23—1051no—
103C7C22×D3×D511yescharacteristic, complemented, Sylow
104C2×C3—354no—
105C2×C3C22×D3513yescomplemented
106D3—354no—
107D3C22×D3514yesdirect product factor
108C5C22×D3×D711yescharacteristic, complemented, Sylow
109C22—36no—
110C22—356no—
111C22—10516no—
112C22—1056no—
113C22D3×D3511yescharacteristic, direct product factor
114C3C23×D3511yescharacteristic, complemented, Sylow
115C2—34no—
116C2—354no—
117C2—1054no—
118C2C2×D3×D3513yesdirect product factor
subgroupG/H
center, hypercenterC22D3×D35
commutator, cosocle, hypocenterC3×C5×C7C24
FrattiniC1G
Fitting, socleC22×C3×C5×C7C22
LCSG ▷ C3×C5×C7
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×D105C2semidirect
2. C22×C5×D3×C7C2semidirect
3. C22×C3×D35C2semidirect
4. C2×D3×D35C2direct (N × H)
6. C22×C3×C5×C7C22semidirect
7. C2×D105C22semidirect
8. C2×C5×D3×C7C22semidirect
9. C2×C3×D35C22semidirect
10. D3×D35C22direct (N × H)
15. C22×D35D3direct (N × H)
17. C2×C3×C5×C7C23semidirect
18. D105C23semidirect
19. C5×D3×C7C23semidirect
20. C3×D35C23semidirect
22. C22×D3×C7D5semidirect
26. C22×C5×C7C2×D3semidirect
29. C2×D35C2×D3direct (N × H)
31. C22×C5×D3D7semidirect
35. C3×C5×C7C24semidirect
36. C22×C3×C7C2×D5semidirect
38. C2×D3×C7C2×D5semidirect
43. C2×C5×C7C22×D3semidirect
45. D35C22×D3direct (N × H)
46. C22×C3×C5C2×D7semidirect
48. C2×C5×D3C2×D7semidirect
56. C2×C3×C7C22×D5semidirect
59. D3×C7C22×D5semidirect
64. C5×C7C23×D3semidirect
65. C2×C3×C5C22×D7semidirect
68. C5×D3C22×D7semidirect
70. C22×C7D3×D5semidirect
77. C22×D3D35direct (N × H)
78. C3×C7C23×D5semidirect
80. C22×C5D3×D7semidirect
85. C3×C5C23×D7semidirect
87. C2×C7C2×D3×D5semidirect
91. C22×C3C2×D35semidirect
94. C2×D3C2×D35direct (N × H)
96. C2×C5C2×D3×D7semidirect
103. C7C22×D3×D5semidirect
105. C2×C3C22×D35semidirect
107. D3C22×D35direct (N × H)
108. C5C22×D3×D7semidirect
113. C22D3×D35direct (N × H)
114. C3C23×D35semidirect
118. C2C2×D3×D35direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D1052
C22×C5×D3×C72
C22×C3×D352
C2×D3×D352
C23×D353
C22×D3×D75
C22×D3×D57