Finite Group Databasebeta

← C22×C3×#4020 #14479965

Subgroups — C22×C3×#4020 #14479965

Order 1920.

6000 conjugacy classes of subgroups; only the 1610 normal subgroups are shown.

normal subgroups only

This group has 6000 conjugacy classes of subgroups — too many to draw. Only its 1610 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×C3×D20C216yesmaximal, complemented
2C22×C3×C42×C5C211yesmaximal, characteristic, complemented
3C2×C3×#4020C2124yesmaximal, direct product factor
4C22×#4020C311yesmaximal, characteristic, direct product factor, Hall
5C24×C3×D5C2214yes—
6C23×C3×C4×C5C2213yes—
7C22×C3×D20—248no—
8C22×C3×D20C22172yescomplemented
9C2×C3×C42×C5C22112yescomplemented
10C3×#4020C22164yesdirect product factor
11C22×C3×#127—51nomaximal, Hall
12C23×D20C2×C316yescomplemented
13C22×C42×C5C2×C311yescharacteristic, complemented
14C2×#4020C2×C3124yesdirect product factor
15C24×C3×C5C2311yescharacteristic
16C23×C3×D5—248no—
17C23×C3×D5C23124yes—
18C22×C3×C4×C5D4124yescomplemented
19C22×C3×C4×C5C23118yes—
20C2×C3×D20—2288no—
21C2×C3×D20C23196yescomplemented
22C3×C42×C5C23116yescomplemented
23C23×C3×D4—56no—
24C2×C3×#127—524no—
25C22×C3×C42D511yescharacteristic, complemented
26C24×D5C22×C314yes—
27C23×C4×C5C22×C313yes—
28C22×D20—248no—
29C22×D20C22×C3172yescomplemented
30C2×C42×C5C22×C3112yescomplemented
31#4020C22×C3164yesdirect product factor
32C22×#127—51noSylow
33C23×C3×C5C2×D4112yes—
34C23×C3×C5C2413yes—
35C22×C3×D5—2144no—
36C22×C3×D5—464no—
37C22×C3×D5C24116yes—
38C2×C3×C4×C5C2×D4172yescomplemented
39C2×C3×C4×C5C24112yes—
40C3×D20—2192no—
41C25×C3—54no—
42C22×C3×D4—572no—
43C22×C3×D4—1048no—
44C23×C3×C4C2×D513yes—
45C3×#127—564no—
46C2×C3×C42C2×D5112yescomplemented
47C24×C5C23×C311yescharacteristic
48C23×D5—248no—
49C23×D5C23×C3124yes—
50C22×C4×C5C3×D4124yescomplemented
51C22×C4×C5C23×C3118yes—
52C2×D20—2288no—
53C2×D20C23×C3196yescomplemented
54C42×C5C23×C3116yescomplemented
55C23×D4—56no—
56C2×#127—524no—
57C22×C42C3×D511yescharacteristic, complemented
58C22×C3×C5#127116yescomplemented
59C22×C3×C5C22×D4118yes—
60C22×C3×C5C2511yescharacteristic
61C2×C3×D5—248no—
62C2×C3×D5—496no—
63C3×C4×C5C22×D4124yescomplemented
64C24×C3—524no—
65C24×C3—1048no—
66C24×C3C22×D511yescharacteristic
67C2×C3×D4—596no—
68C2×C3×D4—10288no—
69C22×C3×C4D20124yescomplemented
70C22×C3×C4C22×D5118yes—
71C3×C42C22×D5116yescomplemented
72C23×C5C2×C3×D4112yes—
73C23×C5C24×C313yes—
74C22×D5—2144no—
75C22×D5—464no—
76C22×D5C24×C3116yes—
77C2×C4×C5C2×C3×D4172yescomplemented
78C2×C4×C5C24×C3112yes—
79D20—2192no—
80C25—54no—
81C22×D4—572no—
82C22×D4—1048no—
83C23×C4C2×C3×D513yes—
84#127—564no—
85C2×C42C2×C3×D5112yescomplemented
86C2×C3×C5C2×#127112yescomplemented
87C2×C3×C5C23×D413yes—
88C3×D5—416no—
89C23×C3—516no—
90C23×C3—10144no—
91C23×C3—2064no—
92C23×C3C2×D20112yes—
93C23×C3C23×D513yes—
94C3×D4—10192no—
95C2×C3×C4C2×D20172yescomplemented
96C2×C3×C4C23×D5112yes—
97C22×C5C3×#127116yescomplemented
98C22×C5C22×C3×D4118yes—
99C22×C5C25×C311yescharacteristic
100C2×D5—248no—
101C2×D5—496no—
102C4×C5C22×C3×D4124yescomplemented
103C24—524no—
104C24—1048no—
105C24C22×C3×D511yescharacteristic
106C2×D4—596no—
107C2×D4—10288no—
108C22×C4C3×D20124yescomplemented
109C22×C4C22×C3×D5118yes—
110C42C22×C3×D5116yescomplemented
111C3×C5C22×#12711yescharacteristic, complemented, Hall
112C22×C3—1048no—
113C22×C3—2096no—
114C22×C3#4020116yesdirect product factor
115C22×C3C22×D20118yes—
116C22×C3C24×D511yescharacteristic
117C3×C4C22×D20124yescomplemented
118C2×C5C2×C3×#127112yescomplemented
119C2×C5C23×C3×D413yes—
120D5—416no—
121C23—516no—
122C23—10144no—
123C23—2064no—
124C23C2×C3×D20112yes—
125C23C23×C3×D513yes—
126D4—10192no—
127C2×C4C2×C3×D20172yescomplemented
128C2×C4C23×C3×D5112yes—
129C2×C3—2016no—
130C2×C3C2×#4020112yesdirect product factor
131C2×C3C23×D2013yes—
132C5C22×C3×#12711yescharacteristic, complemented, Sylow
133C22—1048no—
134C22—2096no—
135C22C3×#4020116yesdirect product factor
136C22C22×C3×D20118yes—
137C22C24×C3×D511yescharacteristic
138C4C22×C3×D20124yescomplemented
139C3C22×#402011yescharacteristic, direct product factor, Sylow
140C2—2016no—
141C2C2×C3×#4020112yesdirect product factor
142C2C23×C3×D2013yes—
subgroupG/H
centerC24×C3C22×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC22×C3×C42×C5C2
socleC24×C3×C5C23
hypercenterC22×C3×C42D5
hypocenterC5C22×C3×#127
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C22×C3×C42

Complements

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

NH ≅ G/Ntype
1. C23×C3×D20C2semidirect
2. C22×C3×C42×C5C2semidirect
3. C2×C3×#4020C2direct (N × H)
4. C22×#4020C3direct (N × H)
8. C22×C3×D20C22semidirect
9. C2×C3×C42×C5C22semidirect
10. C3×#4020C22direct (N × H)
12. C23×D20C2×C3semidirect
13. C22×C42×C5C2×C3semidirect
14. C2×#4020C2×C3direct (N × H)
18. C22×C3×C4×C5D4semidirect
21. C2×C3×D20C23semidirect
22. C3×C42×C5C23semidirect
25. C22×C3×C42D5semidirect
29. C22×D20C22×C3semidirect
30. C2×C42×C5C22×C3semidirect
31. #4020C22×C3direct (N × H)
38. C2×C3×C4×C5C2×D4semidirect
46. C2×C3×C42C2×D5semidirect
50. C22×C4×C5C3×D4semidirect
53. C2×D20C23×C3semidirect
54. C42×C5C23×C3semidirect
57. C22×C42C3×D5semidirect
58. C22×C3×C5#127semidirect
63. C3×C4×C5C22×D4semidirect
69. C22×C3×C4D20semidirect
71. C3×C42C22×D5semidirect
77. C2×C4×C5C2×C3×D4semidirect
85. C2×C42C2×C3×D5semidirect
86. C2×C3×C5C2×#127semidirect
95. C2×C3×C4C2×D20semidirect
97. C22×C5C3×#127semidirect
102. C4×C5C22×C3×D4semidirect
108. C22×C4C3×D20semidirect
110. C42C22×C3×D5semidirect
111. C3×C5C22×#127semidirect
114. C22×C3#4020direct (N × H)
117. C3×C4C22×D20semidirect
118. C2×C5C2×C3×#127semidirect
127. C2×C4C2×C3×D20semidirect
130. C2×C3C2×#4020direct (N × H)
132. C5C22×C3×#127semidirect
135. C22C3×#4020direct (N × H)
138. C4C22×C3×D20semidirect
139. C3C22×#4020direct (N × H)
141. C2C2×C3×#4020direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×D202
C22×C3×C42×C52
C2×C3×#40202
C22×#40203
C22×C3×#1275