Finite Group Databasebeta

← C2×C42×C5×D5 #13106625

Subgroups — C2×C42×C5×D5 #13106625

Order 1600.

1104 conjugacy classes of subgroups; only the 606 normal subgroups are shown.

normal subgroups only

This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 606 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×C4×C5×D5C213yesmaximal
2C2×C42×C52C211yesmaximal, characteristic, complemented
3C2×C4×C5×Dic5C213yesmaximal, complemented
4C42×C5×D5C218yesmaximal, direct product factor
5C23×C5×D5C2211yescharacteristic
6C22×C4×C52C2213yes—
7C22×C5×Dic5C2213yes—
8C2×C4×C5×D5C4124yesdirect product factor
9C2×C4×C5×D5C22112yes—
10C42×C52C2214yescomplemented
11C4×C5×Dic5C22112yescomplemented
12C22×C42×C5—51nomaximal
13C2×C42×D5C511yesmaximal, characteristic, direct product factor
14C23×C52C2311yescharacteristic
15C22×C5×D5C2×C4112yes—
16C22×C5×D5C2312yes—
17C2×C4×C52C2×C4112yescomplemented
18C2×C4×C52C2316yes—
19C2×C5×Dic5C2×C4112yescomplemented
20C2×C5×Dic5C2316yes—
21C4×C5×D5C2×C4148yesdirect product factor
22C23×C4×C5—53no—
23C22×C4×D5C2×C513yes—
24C2×C42×C5—22no—
25C2×C42×C5—53no—
26C2×C42×C5—58no—
27C2×C42×C5D511yescharacteristic, direct product factor
28C2×C42×C5C2×C511yescharacteristic, complemented
29C2×C4×Dic5C2×C513yescomplemented
30C42×D5C2×C518yesdirect product factor
31C22×C52C22×C416yes—
32C22×C52C2411yescharacteristic
33C2×C5×D5C42116yesdirect product factor
34C2×C5×D5C22×C4112yes—
35C4×C52C22×C4112yescomplemented
36C5×Dic5C22×C4112yescomplemented
37C24×C5—51no—
38C23×D5C22×C511yescharacteristic
39C22×C4×C5—26no—
40C22×C4×C5—53no—
41C22×C4×C5—524no—
42C22×C4×C5—512no—
43C22×C4×C5C2×D513yes—
44C22×C4×C5C22×C513yes—
45C22×Dic5C22×C513yes—
46C2×C4×D5C4×C5124yesdirect product factor
47C2×C4×D5C22×C5112yes—
48C42×C5—28no—
49C42×C5—512no—
50C42×C5C2×D514yesdirect product factor
51C42×C5C22×C514yescomplemented
52C4×Dic5C22×C5112yescomplemented
53C22×C42—51noSylow
54C2×C52C2×C4214yescomplemented
55C2×C52C23×C413yes—
56C5×D5C2×C4218yesdirect product factor
57C23×C5—22no—
58C23×C5—512no—
59C23×C5—52no—
60C23×C5C22×D511yescharacteristic
61C23×C5C23×C511yescharacteristic
62C22×D5C2×C4×C5112yes—
63C22×D5C23×C512yes—
64C2×C4×C5—224no—
65C2×C4×C5—212no—
66C2×C4×C5—512no—
67C2×C4×C5—56no—
68C2×C4×C5—548no—
69C2×C4×C5C4×D5112yesdirect product factor
70C2×C4×C5C2×C4×C5112yescomplemented
71C2×C4×C5C22×D516yes—
72C2×C4×C5C23×C516yes—
73C2×Dic5C2×C4×C5112yescomplemented
74C2×Dic5C23×C516yes—
75C4×D5C2×C4×C5148yesdirect product factor
76C23×C4—53no—
77C2×C42—53no—
78C2×C42—58no—
79C2×C42C5×D511yescharacteristic, direct product factor
80C52C22×C4211yescharacteristic, complemented, Sylow
81C22×C5—212no—
82C22×C5—22no—
83C22×C5—512no—
84C22×C5—516no—
85C22×C5C2×C4×D516yes—
86C22×C5C22×C4×C516yes—
87C22×C5C23×D511yescharacteristic
88C22×C5C24×C511yescharacteristic
89C2×D5C42×C5116yesdirect product factor
90C2×D5C22×C4×C5112yes—
91C4×C5—224no—
92C4×C5—512no—
93C4×C5C2×C4×D5112yesdirect product factor
94C4×C5C22×C4×C5112yescomplemented
95Dic5C22×C4×C5112yescomplemented
96C24—51no—
97C22×C4—53no—
98C22×C4—524no—
99C22×C4—512no—
100C22×C4C2×C5×D513yes—
101C42—512no—
102C42C2×C5×D514yesdirect product factor
103C2×C5—26no—
104C2×C5—28no—
105C2×C5—58no—
106C2×C5C42×D514yesdirect product factor
107C2×C5C2×C42×C514yescomplemented
108C2×C5C22×C4×D513yes—
109C2×C5C23×C4×C513yes—
110D5C2×C42×C518yesdirect product factor
111C23—512no—
112C23—52no—
113C23C22×C5×D511yescharacteristic
114C2×C4—512no—
115C2×C4—56no—
116C2×C4—548no—
117C2×C4C4×C5×D5112yesdirect product factor
118C2×C4C22×C5×D516yes—
119C5—22no—
120C5C2×C42×D511yescharacteristic, direct product factor
121C5C22×C42×C511yescharacteristic, complemented
122C22—512no—
123C22—516no—
124C22C2×C4×C5×D516yes—
125C22C23×C5×D511yescharacteristic
126C4—512no—
127C4C2×C4×C5×D5112yesdirect product factor
128C2—58no—
129C2C42×C5×D514yesdirect product factor
130C2C22×C4×C5×D513yes—
subgroupG/H
center, hypercenterC2×C42×C5D5
commutator, hypocenterC5C22×C42×C5
FrattiniC22C23×C5×D5
FittingC2×C42×C52C2
socleC23×C52C23
prime radicalC23×C5×D5C22
cosocleC22×C5C24×C5
LCSG ▷ C5
UCSC1 ◁ C2×C42×C5

Complements

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

NH ≅ G/Ntype
2. C2×C42×C52C2semidirect
3. C2×C4×C5×Dic5C2semidirect
4. C42×C5×D5C2direct (N × H)
8. C2×C4×C5×D5C4direct (N × H)
10. C42×C52C22semidirect
11. C4×C5×Dic5C22semidirect
13. C2×C42×D5C5direct (N × H)
17. C2×C4×C52C2×C4semidirect
19. C2×C5×Dic5C2×C4semidirect
21. C4×C5×D5C2×C4direct (N × H)
27. C2×C42×C5D5direct (N × H)
28. C2×C42×C5C2×C5semidirect
29. C2×C4×Dic5C2×C5semidirect
30. C42×D5C2×C5direct (N × H)
33. C2×C5×D5C42direct (N × H)
35. C4×C52C22×C4semidirect
36. C5×Dic5C22×C4semidirect
46. C2×C4×D5C4×C5direct (N × H)
50. C42×C5C2×D5direct (N × H)
51. C42×C5C22×C5semidirect
52. C4×Dic5C22×C5semidirect
54. C2×C52C2×C42semidirect
56. C5×D5C2×C42direct (N × H)
69. C2×C4×C5C4×D5direct (N × H)
70. C2×C4×C5C2×C4×C5semidirect
73. C2×Dic5C2×C4×C5semidirect
75. C4×D5C2×C4×C5direct (N × H)
79. C2×C42C5×D5direct (N × H)
80. C52C22×C42semidirect
89. C2×D5C42×C5direct (N × H)
93. C4×C5C2×C4×D5direct (N × H)
94. C4×C5C22×C4×C5semidirect
95. Dic5C22×C4×C5semidirect
102. C42C2×C5×D5direct (N × H)
106. C2×C5C42×D5direct (N × H)
107. C2×C5C2×C42×C5semidirect
110. D5C2×C42×C5direct (N × H)
117. C2×C4C4×C5×D5direct (N × H)
120. C5C2×C42×D5direct (N × H)
121. C5C22×C42×C5semidirect
127. C4C2×C4×C5×D5direct (N × H)
129. C2C42×C5×D5direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C5×D52
C2×C42×C522
C2×C4×C5×Dic52
C42×C5×D52
C22×C42×C55
C2×C42×D55