Finite Group Databasebeta

← C3×C7×C25×D21 #36347773

Subgroups — C3×C7×C25×D21 #36347773

Order 22050.

162 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C32×C72×C25C211yesmaximal, characteristic, complemented, Hall
2C7×C25×D21C311yesmaximal, characteristic, direct product factor
3C3×C7×D7×C25—31nomaximal
4C3×C5×C7×D21C511yesmaximal, characteristic
5C3×C72×C25—21no—
6C3×C72×C25D311yescharacteristic, complemented
7C3×C72×C25C2×C311yescharacteristic, complemented
8C3×C25×D21C711yesmaximal, characteristic, direct product factor
9C3×D3×C7×C25—71nomaximal
10C7×D7×C25—31noHall
11C32×C5×C72C2×C511yescharacteristic
12C32×C7×C25—23no—
13C32×C7×C25D711yescharacteristic, complemented
14C32×C7×C25C2×C711yescharacteristic, complemented
15C5×C7×D21C3×C511yescharacteristic
16C3×C5×C7×D7—31no—
17C72×C25C3×D311yescharacteristic, complemented, Hall
18C2×C3×C7×C25—211no—
19C25×D21C3×C711yescharacteristic, direct product factor
20D3×C7×C25—71no—
21C3×D7×C25—31no—
22C3×C7×D21C2511yescharacteristic, direct product factor, Hall
23C3×C5×C72—21no—
24C3×C5×C72C5×D311yescharacteristic
25C3×C5×C72C2×C3×C511yescharacteristic
26C3×C5×D21C5×C711yescharacteristic
27C3×C5×D3×C7—71no—
28C3×C7×C25—26no—
29C3×C7×C25—21no—
30C3×C7×C25—21no—
31C3×C7×C25—23no—
32C3×C7×C25—23no—
33C3×C7×C25D3×C711yescharacteristic, complemented
34C3×C7×C25C3×D711yescharacteristic, complemented
35C3×C7×C25D2111yescharacteristic, direct product factor
36C3×C7×C25C2×C3×C711yescharacteristic, complemented
37C5×C7×D7—31no—
38C3×D3×C25—71noHall
39C32×C72C2×C2511yescharacteristic, complemented, Hall
40C2×C7×C25—211no—
41D7×C25—31no—
42C32×C5×C7—23no—
43C32×C5×C7C5×D711yescharacteristic
44C32×C5×C7C2×C5×C711yescharacteristic
45C7×D21C3×C2511yescharacteristic, direct product factor
46C3×C7×D7—31no—
47C5×C72C3×C5×D311yescharacteristic
48C32×C25C7×D711yescharacteristic, complemented, Hall
49C2×C3×C5×C7—211no—
50C5×D21C3×C5×C711yescharacteristic
51C5×D3×C7—71no—
52C3×C5×D7—31no—
53C7×C25—23no—
54C7×C25C3×D3×C711yescharacteristic, complemented
55C7×C25C3×D2111yescharacteristic, direct product factor
56C2×C3×C25—211no—
57D3×C25—71no—
58C3×C72—21no—
59C3×C72D3×C2511yescharacteristic, complemented
60C3×C72C2×C3×C2511yescharacteristic, complemented
61C3×D21C7×C2511yescharacteristic, direct product factor
62C3×D3×C7—71no—
63C3×C5×C7—26no—
64C3×C5×C7—21no—
65C3×C5×C7—21no—
66C3×C5×C7—23no—
67C3×C5×C7—23no—
68C3×C5×C7C3×C5×D711yescharacteristic
69C3×C5×C7C5×D3×C711yescharacteristic
70C3×C5×C7C5×D2111yescharacteristic
71C3×C5×C7C2×C3×C5×C711yescharacteristic
72C7×D7—31noHall
73C3×C5×D3—71no—
74C3×C25—21no—
75C3×C25C3×C7×D711yescharacteristic, complemented
76C3×C25C7×D2111yescharacteristic, direct product factor
77C2×C5×C7—211no—
78C5×D7—31no—
79C32×C7—23no—
80C32×C7D7×C2511yescharacteristic, complemented
81C32×C7C2×C7×C2511yescharacteristic, complemented
82C2×C25—211noHall
83C72C3×D3×C2511yescharacteristic, complemented, Sylow
84C32×C5C5×C7×D711yescharacteristic
85C2×C3×C7—211no—
86D21C3×C7×C2511yescharacteristic, direct product factor
87C3×D7—31no—
88D3×C7—71no—
89C5×C7—23no—
90C5×C7C3×C5×D3×C711yescharacteristic
91C5×C7C3×C5×D2111yescharacteristic
92C2×C3×C5—211no—
93C5×D3—71no—
94C25C3×C7×D2111yescharacteristic, direct product factor, Sylow
95C3×C7—26no—
96C3×C7—21no—
97C3×C7—21no—
98C3×C7—23no—
99C3×C7—23no—
100C3×C7C3×D7×C2511yescharacteristic, complemented
101C3×C7D3×C7×C2511yescharacteristic, complemented
102C3×C7C25×D2111yescharacteristic, direct product factor
103C3×C7C2×C3×C7×C2511yescharacteristic, complemented
104C3×D3—71noHall
105C3×C5—21no—
106C3×C5C3×C5×C7×D711yescharacteristic
107C3×C5C5×C7×D2111yescharacteristic
108C2×C7—211no—
109D7—31no—
110C2×C5—211no—
111C32C7×D7×C2511yescharacteristic, complemented, Sylow
112C7—23no—
113C7C3×D3×C7×C2511yescharacteristic, complemented
114C7C3×C25×D2111yescharacteristic, direct product factor
115C2×C3—211no—
116D3—71no—
117C5C3×C5×C7×D2111yescharacteristic
118C3—21no—
119C3C3×C7×D7×C2511yescharacteristic, complemented
120C3C7×C25×D2111yescharacteristic, direct product factor
121C2—211noSylow
subgroupG/H
center, hypercenterC3×C7×C25D21
commutator, hypocenterC3×C7C2×C3×C7×C25
FrattiniC5C3×C5×C7×D21
FittingC32×C72×C25C2
socleC32×C5×C72C2×C5
prime radicalC3×C5×C7×D21C5
cosocleC3×C5×C7C2×C3×C5×C7
LCSG ▷ C3×C7
UCSC1 ◁ C3×C7×C25

Complements

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

NH ≅ G/Ntype
1. C32×C72×C25C2semidirect
2. C7×C25×D21C3direct (N × H)
6. C3×C72×C25D3semidirect
7. C3×C72×C25C2×C3semidirect
8. C3×C25×D21C7direct (N × H)
13. C32×C7×C25D7semidirect
14. C32×C7×C25C2×C7semidirect
17. C72×C25C3×D3semidirect
19. C25×D21C3×C7direct (N × H)
22. C3×C7×D21C25direct (N × H)
33. C3×C7×C25D3×C7semidirect
34. C3×C7×C25C3×D7semidirect
35. C3×C7×C25D21direct (N × H)
36. C3×C7×C25C2×C3×C7semidirect
39. C32×C72C2×C25semidirect
45. C7×D21C3×C25direct (N × H)
48. C32×C25C7×D7semidirect
54. C7×C25C3×D3×C7semidirect
55. C7×C25C3×D21direct (N × H)
59. C3×C72D3×C25semidirect
60. C3×C72C2×C3×C25semidirect
61. C3×D21C7×C25direct (N × H)
75. C3×C25C3×C7×D7semidirect
76. C3×C25C7×D21direct (N × H)
80. C32×C7D7×C25semidirect
81. C32×C7C2×C7×C25semidirect
83. C72C3×D3×C25semidirect
86. D21C3×C7×C25direct (N × H)
94. C25C3×C7×D21direct (N × H)
100. C3×C7C3×D7×C25semidirect
101. C3×C7D3×C7×C25semidirect
102. C3×C7C25×D21direct (N × H)
103. C3×C7C2×C3×C7×C25semidirect
111. C32C7×D7×C25semidirect
113. C7C3×D3×C7×C25semidirect
114. C7C3×C25×D21direct (N × H)
119. C3C3×C7×D7×C25semidirect
120. C3C7×C25×D21direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C72×C252
C7×C25×D213
C3×C7×D7×C253
C3×C5×C7×D215
C3×C25×D217
C3×D3×C7×C257