Finite Group Databasebeta

← C23×D120 #14509644

Subgroups — C23×D120 #14509644

Order 1920.

3952 conjugacy classes of subgroups; only the 983 normal subgroups are shown.

normal subgroups only

This group has 3952 conjugacy classes of subgroups — too many to draw. Only its 983 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×D60C212yesmaximal, complemented
2C23×C3×C5×C8C211yesmaximal, characteristic, complemented
3C22×D120C2128yesmaximal, direct product factor
4C23×D40—31nomaximal, Hall
5C24×D15—22no—
6C23×C3×C4×C5C2211yescharacteristic
7C22×D60—214no—
8C22×D60C22128yescomplemented
9C22×C3×C5×C8C22114yescomplemented
10C2×D120C221112yesdirect product factor
11C23×D24—51nomaximal, Hall
12C23×D20—32no—
13C23×C5×C8D311yescharacteristic, complemented
14C22×D40—328no—
15C24×C3×C5D411yescharacteristic
16C23×D15—228no—
17C23×D15—416no—
18C22×C3×C4×C5D417yes—
19C22×C3×C4×C5C2317yes—
20C2×D60—284no—
21C2×D60C23156yescomplemented
22C2×C3×C5×C8C23128yescomplemented
23D120C23164yesdirect product factor
24C23×D12—52no—
25C23×C3×C8D511yescharacteristic, complemented
26C22×D24—528no—
27C24×D5—62no—
28C23×C4×C5C2×D311yescharacteristic
29C22×D20—328no—
30C22×D20—614no—
31C22×C5×C8C2×D3114yescomplemented
32C2×D40—3112no—
33C23×D8—151noSylow
34C23×C3×C5D818yescomplemented
35C23×C3×C5C2×D417yes—
36C22×D15—256no—
37C22×D15—4112no—
38C2×C3×C4×C5C2×D4121yes—
39C2×C3×C4×C5C2417yes—
40D60—256no—
41D60C24116yescomplemented
42C3×C5×C8C2418yescomplemented
43C24×D3—102no—
44C23×C3×C4C2×D511yescharacteristic
45C22×D12—528no—
46C22×D12—1014no—
47C22×C3×C8C2×D5114yescomplemented
48C2×D24—5112no—
49C24×C5D1211yescharacteristic
50C23×D5—628no—
51C23×D5—1216no—
52C22×C4×C5D1217yes—
53C22×C4×C5C22×D317yes—
54C2×D20—356no—
55C2×D20—684no—
56C2×C5×C8C22×D3128yescomplemented
57D40—364no—
58C23×D4—152no—
59C22×D8—1528no—
60C23×C8D1511yescharacteristic, complemented
61C22×C3×C5C2×D8128yescomplemented
62C22×C3×C5C22×D417yes—
63C2×D15—216no—
64C2×D15—4112no—
65C3×C4×C5C22×D417yes—
66C3×C4×C5C2511yescharacteristic
67C24×C3D2011yescharacteristic
68C23×D3—1028no—
69C23×D3—2016no—
70C22×C3×C4D2017yes—
71C22×C3×C4C22×D517yes—
72C2×D12—556no—
73C2×D12—1084no—
74C2×C3×C8C22×D5128yescomplemented
75D24—564no—
76C23×C5D2418yescomplemented
77C23×C5C2×D1217yes—
78C22×D5—656no—
79C22×D5—12112no—
80C2×C4×C5C2×D12121yes—
81C2×C4×C5C23×D317yes—
82D20—316no—
83D20—656no—
84C5×C8C23×D318yescomplemented
85C25—302no—
86C22×D4—1528no—
87C22×D4—3014no—
88C23×C4C2×D1511yescharacteristic
89C2×D8—15112no—
90C22×C8C2×D15114yescomplemented
91C2×C3×C5C22×D8114yescomplemented
92C2×C3×C5C23×D411yescharacteristic
93D15—416no—
94C23×C3D4018yescomplemented
95C23×C3C2×D2017yes—
96C22×D3—1056no—
97C22×D3—20112no—
98C2×C3×C4C2×D20121yes—
99C2×C3×C4C23×D517yes—
100D12—516no—
101D12—1056no—
102C3×C8C23×D518yescomplemented
103C22×C5C2×D24128yescomplemented
104C22×C5C22×D1217yes—
105C2×D5—616no—
106C2×D5—12112no—
107C4×C5C22×D1217yes—
108C4×C5C24×D311yescharacteristic
109C24—3028no—
110C24—6016no—
111C24D6011yescharacteristic
112C2×D4—1556no—
113C2×D4—3084no—
114C22×C4D6017yes—
115C22×C4C22×D1517yes—
116D8—1564no—
117C2×C8C22×D15128yescomplemented
118C3×C5C23×D811yescharacteristic, complemented, Hall
119C22×C3C2×D40128yescomplemented
120C22×C3C22×D2017yes—
121C2×D3—1016no—
122C2×D3—20112no—
123C3×C4C22×D2017yes—
124C3×C4C24×D511yescharacteristic
125C2×C5C22×D24114yescomplemented
126C2×C5C23×D1211yescharacteristic
127D5—1216no—
128C23—3056no—
129C23—60112no—
130C23D12018yesdirect product factor
131C23C2×D6017yes—
132D4—1516no—
133D4—3056no—
134C2×C4C2×D60121yes—
135C2×C4C23×D1517yes—
136C8C23×D1518yescomplemented
137C2×C3C22×D40114yescomplemented
138C2×C3C23×D2011yescharacteristic
139D3—2016no—
140C5C23×D2411yescharacteristic, complemented, Sylow
141C22—3016no—
142C22—60112no—
143C22C2×D120128yesdirect product factor
144C22C22×D6017yes—
145C4C22×D6017yes—
146C4C24×D1511yescharacteristic
147C3C23×D4011yescharacteristic, complemented, Sylow
148C2—6016no—
149C2C22×D120114yesdirect product factor
150C2C23×D6011yescharacteristic
subgroupG/H
centerC24D60
commutator, cosocleC3×C4×C5C25
FrattiniC4C24×D15
FittingC23×C3×C5×C8C2
socleC24×C3×C5D4
hypercenterC23×C8D15
hypocenterC3×C5C23×D8
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
1. C23×D60C2semidirect
2. C23×C3×C5×C8C2semidirect
3. C22×D120C2direct (N × H)
8. C22×D60C22semidirect
9. C22×C3×C5×C8C22semidirect
10. C2×D120C22direct (N × H)
13. C23×C5×C8D3semidirect
21. C2×D60C23semidirect
22. C2×C3×C5×C8C23semidirect
23. D120C23direct (N × H)
25. C23×C3×C8D5semidirect
31. C22×C5×C8C2×D3semidirect
34. C23×C3×C5D8semidirect
41. D60C24semidirect
42. C3×C5×C8C24semidirect
47. C22×C3×C8C2×D5semidirect
56. C2×C5×C8C22×D3semidirect
60. C23×C8D15semidirect
61. C22×C3×C5C2×D8semidirect
74. C2×C3×C8C22×D5semidirect
76. C23×C5D24semidirect
84. C5×C8C23×D3semidirect
90. C22×C8C2×D15semidirect
91. C2×C3×C5C22×D8semidirect
94. C23×C3D40semidirect
102. C3×C8C23×D5semidirect
103. C22×C5C2×D24semidirect
117. C2×C8C22×D15semidirect
118. C3×C5C23×D8semidirect
119. C22×C3C2×D40semidirect
125. C2×C5C22×D24semidirect
130. C23D120direct (N × H)
136. C8C23×D15semidirect
137. C2×C3C22×D40semidirect
140. C5C23×D24semidirect
143. C22C2×D120direct (N × H)
147. C3C23×D40semidirect
149. C2C22×D120direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D602
C23×C3×C5×C82
C22×D1202
C23×D403
C23×D245