Finite Group Databasebeta

← #14293518

Subgroups — #14293518

Order 1920.

380 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 127 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
1#11750795C212yesmaximal
2#11750794C211yesmaximal, characteristic
3#11750782C212yesmaximal, complemented
4#11750781C211yesmaximal, characteristic, complemented
5C3×C5×C82C211yesmaximal, characteristic, complemented
6#10598852—31nomaximal, Hall
7C2×#6706—22no—
8#91763C2211yescharacteristic
9#91758C2212yes—
10#91758C2211yescharacteristic
11C3×C4×C5×C8C2211yescharacteristic
12C3×C4×C5×C8C2212yes—
13#91105—24no—
14#91101—22no—
15#91100—24no—
16#68059—51nomaximal, Hall
17#64983—32no—
18#64982—31no—
19#64970—32no—
20#64969—31no—
21C5×C82D311yescharacteristic, complemented
22C2×D60—21no—
23C2×D60—22no—
24C2×Dic30—21no—
25C2×Dic30—22no—
26C2×C3×C5×C8D414yes—
27C2×C3×C5×C8D412yes—
28C3×C42×C5C2311yescharacteristic
29C4⋊Dic15—22no—
30C4⋊Dic15—22no—
31C4⋊Dic15—22no—
32#6706—44no—
33#4694—52no—
34#4693—51no—
35#4681—52no—
36#4680—51no—
37C3×C82D511yescharacteristic, complemented
38C2×#677—62no—
39#4020—31no—
40#4015—32no—
41#4015—31no—
42C4×C5×C8C2×D311yescharacteristic
43C4×C5×C8C2×D312yes—
44#3953—64no—
45#3949—62no—
46#3948—64no—
47#1708—151noSylow
48C22×D15—41no—
49C2×C3×C4×C5C2×D411yescharacteristic
50C2×C3×C4×C5C2×D412yes—
51C2×Dic15—41no—
52C2×Dic15—42no—
53D60—42no—
54D60—44no—
55Dic30—42no—
56Dic30—44no—
57C3×C5×C8—24no—
58C3×C5×C8SD1614yes—
59C2×#204—102no—
60#874—51no—
61#869—52no—
62#869—51no—
63C3×C4×C8C2×D511yescharacteristic
64C3×C4×C8C2×D512yes—
65#821—104no—
66#817—102no—
67#816—104no—
68C2×D20—62no—
69C2×D20—61no—
70C2×Dic10—62no—
71C2×Dic10—61no—
72C2×C5×C8D1214yes—
73C2×C5×C8D1212yes—
74C42×C5C22×D311yescharacteristic
75C4⋊Dic5—62no—
76C4⋊Dic5—62no—
77C4⋊Dic5—62no—
78#677—124no—
79#498—151no—
80#492—151no—
81#487—152no—
82#486—152no—
83C82D1511yescharacteristic, complemented
84C22×C3×C5#12711yescharacteristic
85C2×D15—81no—
86C2×D15—82no—
87C3×C4×C5C2×SD1612yes—
88C3×C4×C5#13514yes—
89Dic15—81no—
90Dic15—82no—
91C2×D12—102no—
92C2×D12—101no—
93C2×Dic6—102no—
94C2×Dic6—101no—
95C2×C3×C8D2014yes—
96C2×C3×C8D2012yes—
97C3×C42C22×D511yescharacteristic
98C4⋊Dic3—102no—
99C4⋊Dic3—102no—
100C4⋊Dic3—102no—
101#204—204no—
102C22×D5—121no—
103C2×C4×C5C2×D1211yescharacteristic
104C2×C4×C5C2×D1212yes—
105C2×Dic5—121no—
106C2×Dic5—122no—
107D20—122no—
108D20—124no—
109Dic10—122no—
110Dic10—124no—
111C5×C8—24no—
112C5×C8#20414yes—
113C2×SD16—302no—
114C4⋊Q8—152no—
115C4⋊Q8—151no—
116#127—151no—
117#106—302no—
118#103—304no—
119#102—304no—
120C4×C8C2×D1512yes—
121C4×C8C2×D1511yescharacteristic
122C2×C3×C5#49211yescharacteristic
123C2×C3×C5#49512yes—
124D15—161no—
125C22×D3—201no—
126C2×C3×C4C2×D2011yescharacteristic
127C2×C3×C4C2×D2012yes—
128C2×Dic3—201no—
129C2×Dic3—202no—
130D12—202no—
131D12—204no—
132Dic6—202no—
133Dic6—204no—
134C3×C8—24no—
135C3×C8#67714yes—
136C22×C5#87411yescharacteristic
137C2×D5—241no—
138C2×D5—242no—
139C4×C5C2×#20412yes—
140C4×C5#90414yes—
141Dic5—241no—
142Dic5—242no—
143C2×Q8—302no—
144C2×Q8—301no—
145C2×D4—302no—
146C2×D4—301no—
147SD16—604no—
148C2×C8D6014yes—
149C2×C8D6012yes—
150C4⋊C4—302no—
151C4⋊C4—302no—
152C4⋊C4—302no—
153C42C22×D1511yescharacteristic
154C3×C5#170811yescharacteristic, complemented, Hall
155C22×C3#402011yescharacteristic
156C2×D3—401no—
157C2×D3—402no—
158C3×C4C2×#67712yes—
159C3×C4#405014yes—
160Dic3—401no—
161Dic3—402no—
162C2×C5#469311yescharacteristic
163C2×C5#469612yes—
164D5—481no—
165C23—601no—
166Q8—602no—
167Q8—604no—
168D4—602no—
169D4—604no—
170C2×C4—601no—
171C2×C4—602no—
172C2×C4C2×D6011yescharacteristic
173C2×C4C2×D6012yes—
174C8—24no—
175C8#670614yes—
176C2×C3#6498211yescharacteristic
177C2×C3#6498512yes—
178D3—801no—
179C5#6805911yescharacteristic, complemented, Sylow
180C22—1201no—
181C22—1202no—
182C22#9176311yescharacteristic
183C4—1201no—
184C4—1202no—
185C4C2×#670612yes—
186C4#9179314yes—
187C3#1059885211yescharacteristic, complemented, Sylow
188C2—2401no—
189C2#1175079411yescharacteristic
190C2#1175079712yes—
subgroupG/H
centerC22#91763
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×C82C2
socleC22×C3×C5#127
prime radical#91763C22
hypercenterC82D15
hypocenterC3×C5#1708
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C82

Complements

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

NH ≅ G/Ntype
3. #11750782C2semidirect
4. #11750781C2semidirect
5. C3×C5×C82C2semidirect
21. C5×C82D3semidirect
37. C3×C82D5semidirect
83. C82D15semidirect
154. C3×C5#1708semidirect
179. C5#68059semidirect
187. C3#10598852semidirect

Maximal subgroups

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

subgroupindex
#117507952
#117507942
#117507822
#117507812
C3×C5×C822
#105988523
#680595