Finite Group Databasebeta

← C22×D15⋊D7 #13132972

Subgroups — C22×D15⋊D7 #13132972

Order 1680.

536 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 135 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×D15C211yesmaximal, characteristic, complemented
2C22×C5×D21C211yesmaximal, characteristic, complemented
3C22×C3×D35C211yesmaximal, characteristic, complemented
4C2×D15⋊D7C2112yesmaximal, direct product factor
5C22×D5×D7—31nomaximal, Hall
6C22×C3×C5×C7C2211yescharacteristic, complemented
7C2×C7×D15C2216yescomplemented
8C2×C5×D21C2216yescomplemented
9C2×C3×D35C2216yescomplemented
10D15⋊D7C22116yesdirect product factor
11C22×D3×D7—51nomaximal, Hall
12C22×D35D311yescharacteristic, complemented
13C22×C7×D5—31no—
14C22×C5×D7—31no—
15C2×D5×D7—312no—
16C22×D3×D5—71nomaximal, Hall
17C2×C3×C5×C7C2313yescomplemented
18C7×D15C2314yescomplemented
19C5×D21C2314yescomplemented
20C3×D35C2314yescomplemented
21C22×D21D511yescharacteristic, complemented
22C22×D3×C7—51no—
23C22×C3×D7—51no—
24C2×D3×D7—512no—
25C22×C5×C7C2×D311yescharacteristic, complemented
26C2×D35C2×D316yescomplemented
27C2×C7×D5—36no—
28C2×C5×D7—36no—
29D5×D7—316no—
30C22×D15D711yescharacteristic, complemented
31C22×C5×D3—71no—
32C22×C3×D5—71no—
33C2×D3×D5—712no—
34C23×D7—151noHall
35C3×C5×C7C2411yescharacteristic, complemented, Hall
36C22×C3×C7C2×D511yescharacteristic, complemented
37C2×D21C2×D516yescomplemented
38C2×D3×C7—56no—
39C2×C3×D7—56no—
40D3×D7—516no—
41C23×D5—211noHall
42C2×C5×C7C22×D313yescomplemented
43D35C22×D314yescomplemented
44C5×D7—34no—
45C7×D5—34no—
46C22×C3×C5C2×D711yescharacteristic, complemented
47C2×D15C2×D716yescomplemented
48C2×C5×D3—76no—
49C2×C3×D5—76no—
50D3×D5—716no—
51C23×C7—151no—
52C22×D7—31no—
53C22×D7—51no—
54C22×D7—1512no—
55C23×D3—351noHall
56C2×C3×C7C22×D513yescomplemented
57D21C22×D514yescomplemented
58C3×D7—54no—
59D3×C7—54no—
60C23×C5—211no—
61C22×D5—31no—
62C22×D5—71no—
63C22×D5—2112no—
64C5×C7C23×D311yescharacteristic, complemented, Hall
65C2×C3×C5C22×D713yescomplemented
66D15C22×D714yescomplemented
67C3×D5—74no—
68C5×D3—74no—
69C22×C7—156no—
70C22×C7D3×D511yescharacteristic, complemented
71C2×D7—36no—
72C2×D7—56no—
73C2×D7—1516no—
74C23×C3—351no—
75C22×D3—51no—
76C22×D3—71no—
77C22×D3—3512no—
78C3×C7C23×D511yescharacteristic, complemented, Hall
79C22×C5—216no—
80C22×C5D3×D711yescharacteristic, complemented
81C2×D5—36no—
82C2×D5—76no—
83C2×D5—2116no—
84C24—1051noSylow
85C3×C5C23×D711yescharacteristic, complemented, Hall
86C2×C7—154no—
87C2×C7C2×D3×D513yescomplemented
88D7—34no—
89D7—54no—
90C22×C3—356no—
91C22×C3D5×D711yescharacteristic, complemented
92C2×D3—56no—
93C2×D3—76no—
94C2×D3—3516no—
95C2×C5—214no—
96C2×C5C2×D3×D713yescomplemented
97D5—34no—
98D5—74no—
99C23—151no—
100C23—211no—
101C23—351no—
102C23—10512no—
103C7C22×D3×D511yescharacteristic, complemented, Sylow
104C2×C3—354no—
105C2×C3C2×D5×D713yescomplemented
106D3—54no—
107D3—74no—
108C5C22×D3×D711yescharacteristic, complemented, Sylow
109C22—156no—
110C22—216no—
111C22—356no—
112C22—10516no—
113C22D15⋊D711yescharacteristic, direct product factor
114C3C22×D5×D711yescharacteristic, complemented, Sylow
115C2—154no—
116C2—214no—
117C2—354no—
118C2C2×D15⋊D713yesdirect product factor
subgroupG/H
center, hypercenterC22D15⋊D7
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×C7×D15C2semidirect
2. C22×C5×D21C2semidirect
3. C22×C3×D35C2semidirect
4. C2×D15⋊D7C2direct (N × H)
6. C22×C3×C5×C7C22semidirect
7. C2×C7×D15C22semidirect
8. C2×C5×D21C22semidirect
9. C2×C3×D35C22semidirect
10. D15⋊D7C22direct (N × H)
12. C22×D35D3semidirect
17. C2×C3×C5×C7C23semidirect
18. C7×D15C23semidirect
19. C5×D21C23semidirect
20. C3×D35C23semidirect
21. C22×D21D5semidirect
25. C22×C5×C7C2×D3semidirect
26. C2×D35C2×D3semidirect
30. C22×D15D7semidirect
35. C3×C5×C7C24semidirect
36. C22×C3×C7C2×D5semidirect
37. C2×D21C2×D5semidirect
42. C2×C5×C7C22×D3semidirect
43. D35C22×D3semidirect
46. C22×C3×C5C2×D7semidirect
47. C2×D15C2×D7semidirect
56. C2×C3×C7C22×D5semidirect
57. D21C22×D5semidirect
64. C5×C7C23×D3semidirect
65. C2×C3×C5C22×D7semidirect
66. D15C22×D7semidirect
70. C22×C7D3×D5semidirect
78. C3×C7C23×D5semidirect
80. C22×C5D3×D7semidirect
85. C3×C5C23×D7semidirect
87. C2×C7C2×D3×D5semidirect
91. C22×C3D5×D7semidirect
96. C2×C5C2×D3×D7semidirect
103. C7C22×D3×D5semidirect
105. C2×C3C2×D5×D7semidirect
108. C5C22×D3×D7semidirect
113. C22D15⋊D7direct (N × H)
114. C3C22×D5×D7semidirect
118. C2C2×D15⋊D7direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×D152
C22×C5×D212
C22×C3×D352
C2×D15⋊D72
C22×D5×D73
C22×D3×D75
C22×D3×D57