Finite Group Databasebeta

← C22×C4×C5×Dic5 #13106936

Subgroups — C22×C4×C5×Dic5 #13106936

Order 1600.

1232 conjugacy classes of subgroups; only the 734 normal subgroups are shown.

normal subgroups only

This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 734 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
1C23×C4×C52C211yesmaximal, characteristic
2C23×C5×Dic5C212yesmaximal
3C2×C4×C5×Dic5C2112yesmaximal, direct product factor
4C24×C52C2211yescharacteristic
5C22×C4×C52C418yescomplemented
6C22×C4×C52C2216yes—
7C22×C5×Dic5C4116yesdirect product factor
8C22×C5×Dic5C22112yes—
9C4×C5×Dic5C22116yesdirect product factor
10C22×C42×C5—51nomaximal
11C22×C4×Dic5C511yesmaximal, characteristic, direct product factor
12C23×C52C2×C418yes—
13C23×C52C2×C414yes—
14C23×C52C2313yes—
15C2×C4×C52C2×C4124yescomplemented
16C2×C4×C52C2314yes—
17C2×C5×Dic5C2×C4148yesdirect product factor
18C2×C5×Dic5C2318yes—
19C23×C4×C5—22no—
20C23×C4×C5—52no—
21C23×C4×C5D511yescharacteristic
22C23×C4×C5C2×C511yescharacteristic
23C23×Dic5C2×C512yes—
24C2×C42×C5—512no—
25C2×C4×Dic5C2×C5112yesdirect product factor
26C22×C52C42116yescomplemented
27C22×C52C22×C4112yes—
28C22×C52C22×C416yes—
29C22×C52C2411yescharacteristic
30C4×C52C22×C418yescomplemented
31C5×Dic5C22×C4116yesdirect product factor
32C24×C5—22no—
33C24×C5C2×D511yescharacteristic
34C24×C5C22×C511yescharacteristic
35C22×C4×C5—216no—
36C22×C4×C5—212no—
37C22×C4×C5—516no—
38C22×C4×C5—512no—
39C22×C4×C5Dic518yesdirect product factor
40C22×C4×C5C4×C518yescomplemented
41C22×C4×C5C2×D516yes—
42C22×C4×C5C22×C516yes—
43C22×Dic5C4×C5116yesdirect product factor
44C22×Dic5C22×C5112yes—
45C42×C5—516no—
46C4×Dic5C22×C5116yesdirect product factor
47C22×C42—51noSylow
48C2×C52C2×C42112yescomplemented
49C2×C52C23×C412yes—
50C2×C52C23×C411yescharacteristic
51C23×C5—216no—
52C23×C5—28no—
53C23×C5—26no—
54C23×C5C4×D518yes—
55C23×C5C2×Dic514yes—
56C23×C5C2×C4×C518yes—
57C23×C5C2×C4×C514yes—
58C23×C5C22×D513yes—
59C23×C5C23×C513yes—
60C2×C4×C5—248no—
61C2×C4×C5—28no—
62C2×C4×C5—548no—
63C2×C4×C5—58no—
64C2×C4×C5C2×Dic5124yesdirect product factor
65C2×C4×C5C2×C4×C5124yescomplemented
66C2×C4×C5C22×D514yes—
67C2×C4×C5C23×C514yes—
68C2×Dic5C2×C4×C5148yesdirect product factor
69C2×Dic5C23×C518yes—
70C23×C4—52no—
71C23×C4C5×D511yescharacteristic
72C2×C42—512no—
73C52C22×C4211yescharacteristic, complemented, Sylow
74C22×C5—224no—
75C22×C5—212no—
76C22×C5—22no—
77C22×C5—232no—
78C22×C5C4×Dic5116yesdirect product factor
79C22×C5C42×C5116yescomplemented
80C22×C5C2×C4×D5112yes—
81C22×C5C22×Dic516yes—
82C22×C5C22×C4×C5112yes—
83C22×C5C22×C4×C516yes—
84C22×C5C23×D511yescharacteristic
85C22×C5C24×C511yescharacteristic
86C4×C5—216no—
87C4×C5—516no—
88C4×C5C22×Dic518yesdirect product factor
89C4×C5C22×C4×C518yescomplemented
90Dic5C22×C4×C5116yesdirect product factor
91C24C2×C5×D511yescharacteristic
92C22×C4—516no—
93C22×C4—512no—
94C22×C4C5×Dic518yesdirect product factor
95C22×C4C2×C5×D516yes—
96C42—516no—
97C2×C5—224no—
98C2×C5—24no—
99C2×C5—22no—
100C2×C5C2×C4×Dic5112yesdirect product factor
101C2×C5C2×C42×C5112yescomplemented
102C2×C5C22×C4×D512yes—
103C2×C5C23×Dic511yescharacteristic
104C2×C5C23×C4×C512yes—
105C2×C5C23×C4×C511yescharacteristic
106C23C4×C5×D518yes—
107C23C2×C5×Dic514yes—
108C23C22×C5×D513yes—
109C2×C4—548no—
110C2×C4—58no—
111C2×C4C2×C5×Dic5124yesdirect product factor
112C2×C4C22×C5×D514yes—
113C5—22no—
114C5C22×C4×Dic511yescharacteristic, direct product factor
115C5C22×C42×C511yescharacteristic, complemented
116C22C4×C5×Dic5116yesdirect product factor
117C22C2×C4×C5×D5112yes—
118C22C22×C5×Dic516yes—
119C22C23×C5×D511yescharacteristic
120C4—516no—
121C4C22×C5×Dic518yesdirect product factor
122C2C2×C4×C5×Dic5112yesdirect product factor
123C2C22×C4×C5×D512yes—
124C2C23×C5×Dic511yescharacteristic
subgroupG/H
center, hypercenterC23×C4×C5D5
commutator, hypocenterC5C22×C42×C5
FrattiniC22C23×C5×D5
FittingC23×C4×C52C2
socle, prime radicalC24×C52C22
cosocleC22×C5C24×C5
LCSG ▷ C5
UCSC1 ◁ C23×C4×C5

Complements

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

NH ≅ G/Ntype
3. C2×C4×C5×Dic5C2direct (N × H)
5. C22×C4×C52C4semidirect
7. C22×C5×Dic5C4direct (N × H)
9. C4×C5×Dic5C22direct (N × H)
11. C22×C4×Dic5C5direct (N × H)
15. C2×C4×C52C2×C4semidirect
17. C2×C5×Dic5C2×C4direct (N × H)
25. C2×C4×Dic5C2×C5direct (N × H)
26. C22×C52C42semidirect
30. C4×C52C22×C4semidirect
31. C5×Dic5C22×C4direct (N × H)
39. C22×C4×C5Dic5direct (N × H)
40. C22×C4×C5C4×C5semidirect
43. C22×Dic5C4×C5direct (N × H)
46. C4×Dic5C22×C5direct (N × H)
48. C2×C52C2×C42semidirect
64. C2×C4×C5C2×Dic5direct (N × H)
65. C2×C4×C5C2×C4×C5semidirect
68. C2×Dic5C2×C4×C5direct (N × H)
73. C52C22×C42semidirect
78. C22×C5C4×Dic5direct (N × H)
79. C22×C5C42×C5semidirect
88. C4×C5C22×Dic5direct (N × H)
89. C4×C5C22×C4×C5semidirect
90. Dic5C22×C4×C5direct (N × H)
94. C22×C4C5×Dic5direct (N × H)
100. C2×C5C2×C4×Dic5direct (N × H)
101. C2×C5C2×C42×C5semidirect
111. C2×C4C2×C5×Dic5direct (N × H)
114. C5C22×C4×Dic5direct (N × H)
115. C5C22×C42×C5semidirect
116. C22C4×C5×Dic5direct (N × H)
121. C4C22×C5×Dic5direct (N × H)
122. C2C2×C4×C5×Dic5direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×C522
C23×C5×Dic52
C2×C4×C5×Dic52
C22×C42×C55
C22×C4×Dic55