Finite Group Databasebeta

← #14279445

Subgroups — #14279445

Order 1920.

240 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 34 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#11747039C211yesmaximal, characteristic
2#11746724C211yesmaximal, characteristic, complemented
3C3×#64853C211yesmaximal, characteristic, complemented
4#10598747—31nomaximal, Hall
5C5×#874C411yescharacteristic, complemented
6C3×#4020C2211yescharacteristic
7C2×#6652—21no—
8C2×#6652—21no—
9#91228—21no—
10C3×#3999—21no—
11C4×C3⋊#168C411yescharacteristic, complemented
12#67541—51nomaximal, Hall
13#65362—31no—
14#64853—31no—
15#64853D311yescharacteristic, complemented
16C2×C5×D12—21no—
17C2×C5×D12—41no—
18C2×C3×D20—41no—
19C2×C3×D20D411yescharacteristic
20C2×C3×D20D411yescharacteristic
21#6763—41no—
22C3×C22⋊AGL(1,𝔽5)—41no—
23C3×C42×C5C2×C411yescharacteristic
24C2×C3⋊#168—21no—
25#6652—42no—
26#6652—42no—
27#5073—51no—
28C3×#353—51no—
29#4545—51no—
30C5×#127—31no—
31C2×#686—61no—
32C2×#686—61no—
33#4020C2×D311yescharacteristic
34#3999—21no—
35#3999—61no—
36C4×#168—31no—
37#1408—151noSylow
38C22×C5×D3—41no—
39C22×C3×D5—21no—
40C22×C3×D5—21no—
41C2×ΓL(1,𝔽16)—81no—
42C2×C3×AGL(1,𝔽5)—81no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5C22⋊C411yescharacteristic
45C5×D12—41no—
46C5×D12—41no—
47C5×D12—82no—
48C3×D20—41no—
49C3×D20—41no—
50C3×D20—82no—
51C3⋊#168—22no—
52C3×#127—51no—
53C2×#213—101no—
54C2×#213—101no—
55#874AGL(1,𝔽5)11yescharacteristic, complemented
56C3×#99—101no—
57#834—101no—
58C4×C3⋊C8—51no—
59C2×C5×D4—61no—
60C2×C5×D4—121no—
61C2×D20—41no—
62C2×D20D1211yescharacteristic
63C2×D20#6711yescharacteristic
64C22⋊AGL(1,𝔽5)—41no—
65C22⋊AGL(1,𝔽5)—121no—
66C42×C5C4×D311yescharacteristic
67#686—122no—
68#686—122no—
69C2×#168—61no—
70#493—151no—
71#353—51no—
72#353—151no—
73C22×C3×C5#9911yescharacteristic
74C2×C5×D3—82no—
75C2×C5×D3—81no—
76C2×C3×D5—41no—
77C2×C3×D5—41no—
78C2×C3×D5—81no—
79C2×C3×D5—81no—
80ΓL(1,𝔽16)—161no—
81C3×AGL(1,𝔽5)—161no—
82C3×C4×C5—22no—
83C3×C4×C5—21no—
84C2×C3×D4—51no—
85C2×C3×D4—51no—
86C2×C3×D4—201no—
87C2×D12—21no—
88C2×D12—41no—
89C3×C22⋊C4—201no—
90C3×C42C2×AGL(1,𝔽5)11yescharacteristic
91#217—201no—
92#213—202no—
93#213—202no—
94C2×C3⋊C8—101no—
95C23×C5—121no—
96C22×D5—21no—
97C22×D5—21no—
98C2×AGL(1,𝔽5)—81no—
99C2×AGL(1,𝔽5)—241no—
100C5×D4—121no—
101C5×D4—121no—
102C5×D4—242no—
103C2×C4×C5—21no—
104C2×C4×C5(C2×D3)⋊C411yescharacteristic
105D20—41no—
106D20—41no—
107D20—82no—
108#168—62no—
109C2×D8—301no—
110C2×D8—301no—
111#127—31no—
112#127—51no—
113#99—101no—
114#99—301no—
115C4×C8—151no—
116C2×C3×C5—21no—
117C2×C3×C5#35311yescharacteristic
118C3×D5—81no—
119C3×D5—81no—
120C5×D3—161no—
121C23×C3—101no—
122C23×C3—101no—
123C22×D3—41no—
124C3×D4—201no—
125C3×D4—201no—
126C3×D4—402no—
127C2×C3×C4—21no—
128C2×C3×C4—401no—
129C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
130C2×Dic3—401no—
131D12—41no—
132D12—41no—
133D12—82no—
134C3⋊C8—102no—
135C22×C5—242no—
136C22×C5—241no—
137C22×C5#80611yescharacteristic
138C2×D5—41no—
139C2×D5—41no—
140C2×D5—81no—
141C2×D5—81no—
142AGL(1,𝔽5)—161no—
143AGL(1,𝔽5)—481no—
144C4×C5—22no—
145C4×C5—21no—
146C2×D4—51no—
147C2×D4—51no—
148C2×D4—61no—
149C2×D4—121no—
150C2×D4—201no—
151D8—602no—
152D8—602no—
153C2×C8—301no—
154C22⋊C4—201no—
155C22⋊C4—601no—
156C42D3×AGL(1,𝔽5)11yescharacteristic
157C3×C5#140811yescharacteristic, complemented, Hall
158C22×C3—201no—
159C22×C3—201no—
160C22×C3—401no—
161C22×C3—401no—
162C22×C3#401111yescharacteristic
163C2×D3—82no—
164C2×D3—81no—
165C3×C4—22no—
166C3×C4—21no—
167C3×C4—801no—
168Dic3—801no—
169C2×C5—21no—
170C2×C5—481no—
171C2×C5#447411yescharacteristic
172D5—81no—
173D5—81no—
174C23—101no—
175C23—101no—
176C23—121no—
177D4—121no—
178D4—121no—
179D4—201no—
180D4—201no—
181D4—242no—
182D4—402no—
183C2×C4—21no—
184C2×C4—401no—
185C2×C4—1201no—
186C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
187C8—302no—
188C2×C3—21no—
189C2×C3—401no—
190C2×C3—401no—
191C2×C3#6492211yescharacteristic
192D3—161no—
193C5#6754111yescharacteristic, complemented, Sylow
194C22—201no—
195C22—201no—
196C22—242no—
197C22—241no—
198C22—401no—
199C22—401no—
200C22#9117211yescharacteristic
201C4—22no—
202C4—21no—
203C4—801no—
204C4—2401no—
205C3#1059874711yescharacteristic, complemented, Sylow
206C2—21no—
207C2—401no—
208C2—401no—
209C2—481no—
210C2#1174655411yescharacteristic
subgroupG/H
centerC2#11746554
commutator, FittingC3×C42×C5C2×C4
Frattini, hypercenterC42D3×AGL(1,𝔽5)
socleC2×C3×C5#353
prime radical#11747039C2
cosocleC3×#4020C22
hypocenterC3×C5#1408
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #11746724C2semidirect
3. C3×#64853C2semidirect
5. C5×#874C4semidirect
11. C4×C3⋊#168C4semidirect
15. #64853D3semidirect
55. #874AGL(1,𝔽5)semidirect
157. C3×C5#1408semidirect
193. C5#67541semidirect
205. C3#10598747semidirect

Maximal subgroups

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

subgroupindex
#117470392
#117467242
C3×#648532
#105987473
#675415