Finite Group Databasebeta

← #14278047

Subgroups — #14278047

Order 1920.

220 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 46 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#11747904C211yesmaximal, characteristic
2#11746768C211yesmaximal, characteristic, complemented
3C3×#64891C211yesmaximal, characteristic, complemented
4#10598601—31nomaximal, Hall
5D5⋊#208—21no—
6C2×D120C411yescharacteristic
7C2×C3×#676C2211yescharacteristic
8#91450—21no—
9C3×#3998—21no—
10C5×#817C411yescharacteristic
11#90969—21no—
12#67535—51nomaximal, Hall
13#65154—31no—
14#64897—31no—
15#64891D311yescharacteristic, complemented
16C2×D60—21no—
17C2×C3×C4×D5D411yescharacteristic
18C2×#1202—41no—
19#6762—41no—
20#6758—41no—
21D5⋊(C3⋊C8)—22no—
22C2×C3×C5×C8C2×C411yescharacteristic
23D120—41no—
24C5×C4⋊Dic3—21no—
25C2×C3×#168D411yescharacteristic
26C3×#676—41no—
27#6667—41no—
28C3×#674—41no—
29#5135—51no—
30C3×#349—51no—
31C3⋊#338—51no—
32D5⋊M16—61no—
33C2×D40—31no—
34C2×#676C2×D311yescharacteristic
35#4041—61no—
36#3998—21no—
37C5×#106—31no—
38#3941—61no—
39#1341—151noSylow
40C22×D15—41no—
41C22×C3×D5SD1611yescharacteristic
42C2×C3×C4×C5C22⋊C411yescharacteristic
43D60—41no—
44D60—41no—
45C2×C5×Dic3—41no—
46C2×C3×Dic5D811yescharacteristic
47C3×C4×D5—21no—
48C3×C4×D5—21no—
49#1202—82no—
50C3⋊#170—42no—
51C3×C5×C8—21no—
52C3×#168—21no—
53C2×C3×M16—51no—
54#930—101no—
55C2×#208—101no—
56C2×D24—51no—
57C3×M32—101no—
58#821—101no—
59#817AGL(1,𝔽5)11yescharacteristic
60C2×D20—61no—
61C2×D20—121no—
62C2×C4×D5D1211yescharacteristic
63#704—121no—
64#700—121no—
65D5⋊C8—62no—
66C2×C5×C8C4×D311yescharacteristic
67C5×C4⋊C4—61no—
68#685—121no—
69C2×#168#6711yescharacteristic
70D40—121no—
71#676—41no—
72#674—41no—
73#469—151no—
74#349—51no—
75#338—151no—
76C22×C3×C5#10211yescharacteristic
77C2×D15—81no—
78C2×D15—81no—
79C2×D15—81no—
80C2×C3×D5—21no—
81C2×C3×D5—41no—
82C3×C4×C5#9911yescharacteristic
83C3×C4×C5#10411yescharacteristic
84C3×Dic5—21no—
85C5×Dic3—81no—
86C22×C3×C4—51no—
87C2×#67—201no—
88C2×D12—101no—
89C3×M16—201no—
90C2×C3×C8—51no—
91C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
92(C2×D3)⋊C4—201no—
93C4⋊Dic3—21no—
94#208—201no—
95#208—201no—
96C2×C3⋊C8—102no—
97D24—201no—
98C3×C16—201no—
99C22×D5—121no—
100C22×D5#20411yescharacteristic
101C2×C4×C5—121no—
102C2×C4×C5(C2×D3)⋊C411yescharacteristic
103C2×Dic5D2411yescharacteristic
104D20—121no—
105D20—121no—
106D20—242no—
107C4×D5—21no—
108C4×D5—21no—
109#170—122no—
110C5×C8—21no—
111#168—21no—
112C2×D8—151no—
113C2×M16—51no—
114C2×M16—301no—
115#121—301no—
116M32—101no—
117#106—31no—
118#102—301no—
119C2×C3×C5—21no—
120C2×C3×C5#32711yescharacteristic
121D15—161no—
122C3×D5—41no—
123C23×C3—51no—
124C22×D3—201no—
125C2×C3×C4—51no—
126C2×C3×C4—101no—
127C2×C3×C4—101no—
128C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
129#67—402no—
130C2×Dic3—41no—
131D12—201no—
132D12—201no—
133C3×C8—21no—
134C3×C8—101no—
135C3⋊C8—202no—
136C22×C5#82111yescharacteristic
137C2×D5—21no—
138C2×D5—41no—
139C2×D5—241no—
140C2×D5—241no—
141C2×D5—241no—
142C4×C5—241no—
143C4×C5#80611yescharacteristic
144C4×C5#82511yescharacteristic
145Dic5—21no—
146C2×D4—301no—
147C2×D4—601no—
148C22×C4—51no—
149D8—601no—
150M16—201no—
151M16—601no—
152M16—601no—
153C2×C8—51no—
154C2×C8—302no—
155C2×C8D3×AGL(1,𝔽5)11yescharacteristic
156C4⋊C4—61no—
157C22⋊C4—601no—
158C16—201no—
159C3×C5#134111yescharacteristic, complemented, Hall
160C22×C3—101no—
161C22×C3—201no—
162C22×C3#400711yescharacteristic
163C2×D3—401no—
164C2×D3—401no—
165C2×D3—401no—
166C3×C4—101no—
167C3×C4#399911yescharacteristic
168C3×C4#401011yescharacteristic
169Dic3—81no—
170C2×C5—21no—
171C2×C5#447011yescharacteristic
172D5—41no—
173D5—481no—
174C23—51no—
175C23—601no—
176D4—601no—
177D4—601no—
178D4—1202no—
179C2×C4—51no—
180C2×C4—101no—
181C2×C4—101no—
182C2×C4—121no—
183C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
184C8—21no—
185C8—101no—
186C8—602no—
187C2×C3—21no—
188C2×C3—201no—
189C2×C3#6486811yescharacteristic
190D3—801no—
191C5#6753511yescharacteristic, complemented, Sylow
192C22—101no—
193C22—201no—
194C22—1201no—
195C22—1201no—
196C22—1201no—
197C22#9115211yescharacteristic
198C4—101no—
199C4—241no—
200C4#9115711yescharacteristic
201C4#9117311yescharacteristic
202C3#1059860111yescharacteristic, complemented, Sylow
203C2—21no—
204C2—201no—
205C2—2401no—
206C2#1174649911yescharacteristic
subgroupG/H
centerC2#11746499
commutator, FittingC2×C3×C5×C8C2×C4
Frattini, hypercenterC2×C8D3×AGL(1,𝔽5)
socleC2×C3×C5#327
prime radical#11747904C2
cosocleC2×C3×#676C22
hypocenterC3×C5#1341
LCSG ▷ C2×C3×C5×C8 ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #11746768C2semidirect
3. C3×#64891C2semidirect
15. #64891D3semidirect
159. C3×C5#1341semidirect
191. C5#67535semidirect
202. C3#10598601semidirect

Maximal subgroups

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

subgroupindex
#117479042
#117467682
C3×#648912
#105986013
#675355