Finite Group Databasebeta

← C22×C4×D45 #13085345

Subgroups — C22×C4×D45 #13085345

Order 1440.

708 conjugacy classes of subgroups; only the 253 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 253 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×D45C211yesmaximal, characteristic
2C22×C4×C5×C9C211yesmaximal, characteristic, complemented
3C22×Dic45C211yesmaximal, characteristic, complemented
4C2×C4×D45C2112yesmaximal, direct product factor
5C22×C4×D15—31nomaximal
6C23×C5×C9C2211yescharacteristic
7C22×D45C418yesdirect product factor
8C22×D45C2216yes—
9C2×C4×C5×C9C2216yescomplemented
10C2×Dic45C2216yescomplemented
11C4×D45C22116yesdirect product factor
12C22×C4×D9—51nomaximal, Hall
13C23×D15—31no—
14C22×C3×C4×C5D311yescharacteristic
15C22×Dic15—31no—
16C2×C4×D15—312no—
17C22×C5×C9C2×C414yescomplemented
18C22×C5×C9C2313yes—
19C2×D45C2×C4124yesdirect product factor
20C2×D45C2314yes—
21C4×C5×C9C2314yescomplemented
22Dic45C2314yescomplemented
23C22×C4×D5—91noHall
24C23×D9—51no—
25C22×C4×C9D511yescharacteristic, complemented
26C22×Dic9—51no—
27C2×C4×D9—512no—
28C23×C3×C5C2×D311yescharacteristic
29C22×D15—38no—
30C22×D15—36no—
31C2×C3×C4×C5C2×D316yes—
32C2×Dic15—36no—
33C4×D15—316no—
34C22×C4×D3—151no—
35C2×C5×C9C22×C416yescomplemented
36C2×C5×C9C2411yescharacteristic
37D45C22×C418yesdirect product factor
38C23×D5—91no—
39C22×C4×C5D911yescharacteristic, complemented
40C22×Dic5—91no—
41C2×C4×D5—912no—
42C23×C9C2×D511yescharacteristic
43C22×D9—58no—
44C22×D9—56no—
45C2×C4×C9C2×D516yescomplemented
46C2×Dic9—56no—
47C4×D9—516no—
48C22×C3×C5C4×D314yes—
49C22×C3×C5C22×D313yes—
50C2×D15—324no—
51C2×D15—34no—
52C3×C4×C5C22×D314yes—
53Dic15—34no—
54C23×D3—151no—
55C22×C3×C4D1511yescharacteristic
56C22×Dic3—151no—
57C2×C4×D3—1512no—
58C5×C9C23×C411yescharacteristic, complemented, Hall
59C23×C5C2×D911yescharacteristic
60C22×D5—98no—
61C22×D5—96no—
62C2×C4×C5C2×D916yescomplemented
63C2×Dic5—96no—
64C4×D5—916no—
65C22×C9C4×D514yescomplemented
66C22×C9C22×D513yes—
67C2×D9—524no—
68C2×D9—54no—
69C4×C9C22×D514yescomplemented
70Dic9—54no—
71C23×C4—451noSylow
72C2×C3×C5C2×C4×D316yes—
73C2×C3×C5C23×D311yescharacteristic
74D15—38no—
75C23×C3C2×D1511yescharacteristic
76C22×D3—158no—
77C22×D3—156no—
78C2×C3×C4C2×D1516yes—
79C2×Dic3—156no—
80C4×D3—1516no—
81C22×C5C4×D914yescomplemented
82C22×C5C22×D913yes—
83C2×D5—924no—
84C2×D5—94no—
85C4×C5C22×D914yescomplemented
86Dic5—94no—
87C2×C9C2×C4×D516yescomplemented
88C2×C9C23×D511yescharacteristic
89D9—58no—
90C24—451no—
91C22×C4—451no—
92C22×C4—4512no—
93C22×C4D4511yescharacteristic, direct product factor
94C3×C5C22×C4×D311yescharacteristic
95C22×C3C4×D1514yes—
96C22×C3C22×D1513yes—
97C2×D3—1524no—
98C2×D3—154no—
99C3×C4C22×D1514yes—
100Dic3—154no—
101C2×C5C2×C4×D916yescomplemented
102C2×C5C23×D911yescharacteristic
103D5—98no—
104C9C22×C4×D511yescharacteristic, complemented, Sylow
105C23—458no—
106C23—456no—
107C23C2×D4511yescharacteristic
108C2×C4—456no—
109C2×C4—4516no—
110C2×C4C2×D4516yesdirect product factor
111C2×C3C2×C4×D1516yes—
112C2×C3C23×D1511yescharacteristic
113D3—158no—
114C5C22×C4×D911yescharacteristic, complemented, Sylow
115C22—454no—
116C22—4524no—
117C22C4×D4514yesdirect product factor
118C22C22×D4513yes—
119C4—454no—
120C4C22×D4514yesdirect product factor
121C3C22×C4×D1511yescharacteristic
122C2—458no—
123C2C2×C4×D4516yesdirect product factor
124C2C23×D4511yescharacteristic
subgroupG/H
center, hypercenterC22×C4D45
commutator, hypocenterC5×C9C23×C4
FrattiniC2×C3C23×D15
FittingC22×C4×C5×C9C2
socleC23×C3×C5C2×D3
prime radicalC23×D45C2
cosocleC2×C5×C9C24
LCSG ▷ C5×C9
UCSC1 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×C5×C9C2semidirect
3. C22×Dic45C2semidirect
4. C2×C4×D45C2direct (N × H)
7. C22×D45C4direct (N × H)
9. C2×C4×C5×C9C22semidirect
10. C2×Dic45C22semidirect
11. C4×D45C22direct (N × H)
17. C22×C5×C9C2×C4semidirect
19. C2×D45C2×C4direct (N × H)
21. C4×C5×C9C23semidirect
22. Dic45C23semidirect
25. C22×C4×C9D5semidirect
35. C2×C5×C9C22×C4semidirect
37. D45C22×C4direct (N × H)
39. C22×C4×C5D9semidirect
45. C2×C4×C9C2×D5semidirect
58. C5×C9C23×C4semidirect
62. C2×C4×C5C2×D9semidirect
65. C22×C9C4×D5semidirect
69. C4×C9C22×D5semidirect
81. C22×C5C4×D9semidirect
85. C4×C5C22×D9semidirect
87. C2×C9C2×C4×D5semidirect
93. C22×C4D45direct (N × H)
101. C2×C5C2×C4×D9semidirect
104. C9C22×C4×D5semidirect
110. C2×C4C2×D45direct (N × H)
114. C5C22×C4×D9semidirect
117. C22C4×D45direct (N × H)
120. C4C22×D45direct (N × H)
123. C2C2×C4×D45direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D452
C22×C4×C5×C92
C22×Dic452
C2×C4×D452
C22×C4×D153
C22×C4×D95