Finite Group Databasebeta

← C22×#67155 #13089427

Subgroups — C22×#67155 #13089427

Order 1440.

1078 conjugacy classes of subgroups; only the 303 normal subgroups are shown.

normal subgroups only

This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 303 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×C5×C3⋊D3C211yesmaximal, characteristic
2C22×C3×Dic15C212yesmaximal, complemented
3C2×#67155C2112yesmaximal, direct product factor
4C22×D3×Dic5—32nomaximal
5C23×C32×C5C2211yescharacteristic
6C22×C5×C3⋊D3C418yescomplemented
7C22×C5×C3⋊D3C2216yes—
8C2×C3×Dic15C22112yescomplemented
9#67155C22116yesdirect product factor
10C22×#624—51nomaximal, Hall
11C23×C5×D3—32no—
12C23×C5×D3—61no—
13C22×Dic15D312yescomplemented
14C22×C3×Dic5—32no—
15C2×D3×Dic5—324no—
16C22×C32×C5C2×C414yescomplemented
17C22×C32×C5C2313yes—
18C2×C5×C3⋊D3C2×C4124yescomplemented
19C2×C5×C3⋊D3C2314yes—
20C3×Dic15C2318yescomplemented
21C23×Dic5—91noHall
22C23×C3⋊D3D511yescharacteristic
23C22×C3×Dic3—52no—
24C2×#624—512no—
25C23×C3×C5—21no—
26C23×C3×C5C2×D312yes—
27C22×C5×D3—316no—
28C22×C5×D3—312no—
29C22×C5×D3—68no—
30C22×C5×D3—66no—
31C2×Dic15C2×D3112yescomplemented
32C2×C3×Dic5—312no—
33D3×Dic5—332no—
34C22×C4×D3—152no—
35C2×C32×C5C22×C416yescomplemented
36C2×C32×C5C2411yescharacteristic
37C5×C3⋊D3C22×C418yescomplemented
38C24×C5—91no—
39C22×Dic5—32no—
40C22×Dic5—912no—
41C23×C32C2×D511yescharacteristic
42C22×C3⋊D3Dic518yescomplemented
43C22×C3⋊D3C2×D516yes—
44C2×C3×Dic3—512no—
45#624—516no—
46C22×C3×C5—24no—
47C22×C3×C5—23no—
48C22×C3×C5C4×D318yescomplemented
49C22×C3×C5C22×D316yes—
50C2×C5×D3—348no—
51C2×C5×D3—38no—
52C2×C5×D3—624no—
53C2×C5×D3—64no—
54Dic15C22×D318yescomplemented
55C3×Dic5—38no—
56C23×D3—32no—
57C23×D3—61no—
58C22×C3×C4—152no—
59C22×Dic3—52no—
60C2×C4×D3—1524no—
61C32×C5C23×C411yescharacteristic, complemented, Hall
62C23×C5—98no—
63C23×C5—96no—
64C23×C5D3211yescharacteristic
65C2×Dic5—312no—
66C2×Dic5—916no—
67C22×C32C2×Dic514yescomplemented
68C22×C32C22×D513yes—
69C2×C3⋊D3C2×Dic5124yescomplemented
70C2×C3⋊D3C22×D514yes—
71C3×Dic3—58no—
72C23×C4—451noSylow
73C2×C3×C5—21no—
74C2×C3×C5—26no—
75C2×C3×C5C2×C4×D3112yescomplemented
76C2×C3×C5C23×D312yes—
77C5×D3—316no—
78C5×D3—68no—
79C23×C3—21no—
80C23×C3D3×D512yes—
81C22×D3—316no—
82C22×D3—312no—
83C22×D3—68no—
84C22×D3—66no—
85C2×C3×C4—1512no—
86C2×Dic3—512no—
87C4×D3—1532no—
88C22×C5—94no—
89C22×C5—924no—
90C22×C5#62414yescomplemented
91C22×C5C2×D3213yes—
92Dic5—38no—
93C2×C32C22×Dic516yescomplemented
94C2×C32C23×D511yescharacteristic
95C3⋊D3C22×Dic518yescomplemented
96C24—91no—
97C22×C4—152no—
98C22×C4—4512no—
99C3×C5—21no—
100C3×C5C22×C4×D312yescomplemented
101C22×C3—24no—
102C22×C3—23no—
103C22×C3D3×Dic518yescomplemented
104C22×C3C2×D3×D516yes—
105C2×D3—348no—
106C2×D3—38no—
107C2×D3—624no—
108C2×D3—64no—
109C3×C4—158no—
110Dic3—58no—
111C2×C5—98no—
112C2×C5C2×#62416yescomplemented
113C2×C5C22×D3211yescharacteristic
114C32C23×Dic511yescharacteristic, complemented, Sylow
115C23—98no—
116C23—96no—
117C23(C3⋊D3)⋊D511yescharacteristic
118C2×C4—1512no—
119C2×C4—4516no—
120C2×C3—21no—
121C2×C3—26no—
122C2×C3C2×D3×Dic5112yescomplemented
123C2×C3C22×D3×D512yes—
124D3—316no—
125D3—68no—
126C5C22×#62411yescharacteristic, complemented, Sylow
127C22—94no—
128C22—924no—
129C22#6715514yesdirect product factor
130C22C2×(C3⋊D3)⋊D513yes—
131C4—158no—
132C3—21no—
133C3C22×D3×Dic512yescomplemented
134C2—98no—
135C2C2×#6715516yesdirect product factor
136C2C22×(C3⋊D3)⋊D511yescharacteristic
subgroupG/H
center, hypercenterC23(C3⋊D3)⋊D5
commutator, hypocenterC32×C5C23×C4
FrattiniC2C22×(C3⋊D3)⋊D5
Fitting, socleC23×C32×C5C22
prime radicalC23×C5×C3⋊D3C2
cosocleC2×C32×C5C24
LCSG ▷ C32×C5
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C22×C3×Dic15C2semidirect
3. C2×#67155C2direct (N × H)
6. C22×C5×C3⋊D3C4semidirect
8. C2×C3×Dic15C22semidirect
9. #67155C22direct (N × H)
13. C22×Dic15D3semidirect
16. C22×C32×C5C2×C4semidirect
18. C2×C5×C3⋊D3C2×C4semidirect
20. C3×Dic15C23semidirect
31. C2×Dic15C2×D3semidirect
35. C2×C32×C5C22×C4semidirect
37. C5×C3⋊D3C22×C4semidirect
42. C22×C3⋊D3Dic5semidirect
48. C22×C3×C5C4×D3semidirect
54. Dic15C22×D3semidirect
61. C32×C5C23×C4semidirect
67. C22×C32C2×Dic5semidirect
69. C2×C3⋊D3C2×Dic5semidirect
75. C2×C3×C5C2×C4×D3semidirect
90. C22×C5#624semidirect
93. C2×C32C22×Dic5semidirect
95. C3⋊D3C22×Dic5semidirect
100. C3×C5C22×C4×D3semidirect
103. C22×C3D3×Dic5semidirect
112. C2×C5C2×#624semidirect
114. C32C23×Dic5semidirect
122. C2×C3C2×D3×Dic5semidirect
126. C5C22×#624semidirect
129. C22#67155direct (N × H)
133. C3C22×D3×Dic5semidirect
135. C2C2×#67155direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×C3⋊D32
C22×C3×Dic152
C2×#671552
C22×D3×Dic53
C22×#6245