Finite Group Databasebeta

← #14513965

Subgroups — #14513965

Order 1920.

370 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 29 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
1C5×#5948C211yesmaximal, characteristic
2#10602931—31nomaximal, Hall
3C5×C22⋊SL(2,𝔽3)C411yescharacteristic, complemented
4#91185—42nomaximal
5A4⋊#168—41nomaximal
6#85563—51nomaximal, Hall
7C22×C5×#41D311yescharacteristic
8C2×#3969—32no—
9C2×#3969—32no—
10C4×C22⋊Dic5—31no—
11#65496—31no—
12C5×#41⋊C3—42no—
13C5×#41⋊C3—81no—
14C4×C5×A4—41no—
15#5948D511yescharacteristic
16C2×C5×#41—32no—
17C2×C5×#41—32no—
18C2×C5×#41—61no—
19C2×C5×#41—61no—
20C22×C5×Q8Dic311yescharacteristic
21C22×C5×D4—31no—
22C23×C4×C5—31no—
23C2×C22⋊Dic5—61no—
24C2×C4×Dic5—32no—
25C2×#681—31no—
26C2×#681—31no—
27#3969—62no—
28#3969—62no—
29#3969—62no—
30#3969—62no—
31#3963—61no—
32C22⋊#168—61no—
33C22⋊#168—61no—
34#1789—151noSylow
35C2×C5×A4—41no—
36C5×SL(2,𝔽3)—42no—
37C5×SL(2,𝔽3)—81no—
38C3⋊#168—161no—
39C22⋊SL(2,𝔽3)Dic511yescharacteristic, complemented
40GU(2,𝔽3)—202no—
41A4⋊C8—201no—
42C24×C5—31no—
43C5×#41—21no—
44C5×#41—32no—
45C5×#41—32no—
46C5×#41—32no—
47C5×#41—61no—
48C5×#41—62no—
49C5×#41—61no—
50C5×#41—61no—
51C5×#41—62no—
52C5×#41S412yes—
53C2×C5×Q8—32no—
54C2×C5×Q8—61no—
55C2×C5×D4—32no—
56C2×C5×D4—61no—
57C2×C5×D4—62no—
58C2×C5×D4—62no—
59C22×C4×C5—31no—
60C22×C4×C5—31no—
61C22×C4×C5—31no—
62C22×C4×C5—31no—
63C22×C4×C5—31no—
64C22×C4×C5—62no—
65C22×C4×C5—62no—
66C22×C4×C5S411yescharacteristic
67C22×Dic5—62no—
68C22⋊Dic5—62no—
69C22⋊Dic5—62no—
70C4×Dic5—62no—
71C4×Dic5—62no—
72#681—62no—
73#681—62no—
74C2×#168—61no—
75C2×#168—61no—
76C22×#41D1511yescharacteristic
77C2×#104—152no—
78C2×#104—152no—
79#407—151no—
80C4×C22⋊C4—151no—
81C5×A4—41no—
82C3×C4×C5—161no—
83#41⋊C3—42no—
84#41⋊C3—81no—
85C4×A4—41no—
86C23×C5—31no—
87C23×C5—31no—
88C23×C5—62no—
89C23×C5—61no—
90C23×C5—61no—
91C23×C5—121no—
92C23×C5SL(2,ℤ/4)11yescharacteristic
93C5×Q8—21no—
94C5×Q8—32no—
95C5×Q8—61no—
96C5×Q8SL(2,ℤ/4)12yes—
97C5×D4—32no—
98C5×D4—32no—
99C5×D4—62no—
100C5×D4—61no—
101C5×D4—62no—
102C5×D4—61no—
103C2×C4×C5—32no—
104C2×C4×C5—31no—
105C2×C4×C5—31no—
106C2×C4×C5—32no—
107C2×C4×C5—31no—
108C2×C4×C5—31no—
109C2×C4×C5—62no—
110C2×C4×C5—62no—
111C2×C4×C5—62no—
112C2×C4×C5—61no—
113C2×C4×C5—61no—
114C2×Dic5—64no—
115C2×Dic5—122no—
116C2×Dic5—122no—
117#168—121no—
118#168—121no—
119C2×#41—32no—
120C2×#41—32no—
121C2×#41—61no—
122C2×#41—61no—
123C22×Q8Dic1511yescharacteristic
124C22×D4—31no—
125C23×C4—31no—
126C2×M16—151no—
127C2×M16—151no—
128C2×C22⋊C4—301no—
129C2×C42—152no—
130#104—302no—
131#104—302no—
132#104—302no—
133#104—302no—
134C22⋊C8—301no—
135C22⋊C8—301no—
136#95—301no—
137C2×C3×C5—161no—
138C2×A4—41no—
139SL(2,𝔽3)—42no—
140SL(2,𝔽3)—81no—
141C3⋊C8—801no—
142C22×C5—31no—
143C22×C5—31no—
144C22×C5—32no—
145C22×C5—61no—
146C22×C5—61no—
147C22×C5—61no—
148C22×C5—61no—
149C22×C5—61no—
150C22×C5—122no—
151C22×C5—122no—
152C22×C5GU(2,𝔽3)11yescharacteristic, complemented
153C4×C5—31no—
154C4×C5—32no—
155C4×C5—61no—
156C4×C5#102011yescharacteristic
157Dic5—124no—
158C24—31no—
159#41—21no—
160#41—32no—
161#41—32no—
162#41—32no—
163#41—61no—
164#41—62no—
165#41—61no—
166#41—61no—
167#41—62no—
168#41C5⋊S412yes—
169C2×Q8—32no—
170C2×Q8—61no—
171C2×D4—32no—
172C2×D4—61no—
173C2×D4—62no—
174C2×D4—62no—
175C22×C4—31no—
176C22×C4—31no—
177C22×C4—31no—
178C22×C4—31no—
179C22×C4—31no—
180C22×C4—62no—
181C22×C4—62no—
182C22×C4—302no—
183C22×C4C5⋊S411yescharacteristic
184M16—302no—
185M16—302no—
186C2×C8—301no—
187C2×C8—301no—
188C22⋊C4—302no—
189C22⋊C4—302no—
190C42—302no—
191C42—302no—
192C3×C5—161noHall
193A4—41no—
194C3×C4—161no—
195C2×C5—31no—
196C2×C5—31no—
197C2×C5—62no—
198C2×C5—121no—
199C2×C5#593611yescharacteristic
200C23—31no—
201C23—31no—
202C23—62no—
203C23—61no—
204C23—61no—
205C23—121no—
206C23A4⋊Dic511yescharacteristic
207Q8—21no—
208Q8—32no—
209Q8—61no—
210Q8A4⋊Dic512yes—
211D4—32no—
212D4—32no—
213D4—62no—
214D4—61no—
215D4—62no—
216D4—61no—
217C2×C4—32no—
218C2×C4—31no—
219C2×C4—32no—
220C2×C4—31no—
221C2×C4—31no—
222C2×C4—31no—
223C2×C4—62no—
224C2×C4—62no—
225C2×C4—62no—
226C2×C4—61no—
227C2×C4—61no—
228C2×C4—304no—
229C2×C4—602no—
230C2×C4—602no—
231C8—601no—
232C8—601no—
233C2×C3—161no—
234C5#8556311yescharacteristic, complemented, Sylow
235C22—31no—
236C22—31no—
237C22—32no—
238C22—61no—
239C22—61no—
240C22—61no—
241C22—61no—
242C22—61no—
243C22—122no—
244C22—122no—
245C22#9118511yescharacteristic, complemented
246C4—31no—
247C4—32no—
248C4—61no—
249C4—604no—
250C4C5⋊#102011yescharacteristic
251C3—161noSylow
252C2—31no—
253C2—31no—
254C2—62no—
255C2—121no—
256C2#1175692711yescharacteristic
subgroupG/H
center, Frattini, hypercenterC4C5⋊#1020
commutator, hypocenterC5×C22⋊SL(2,𝔽3)C4
FittingC22×C5×#41D3
socleC23×C5SL(2,ℤ/4)
prime radical, cosocleC5×#5948C2
LCSG ▷ C5×C22⋊SL(2,𝔽3)
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
3. C5×C22⋊SL(2,𝔽3)C4semidirect
39. C22⋊SL(2,𝔽3)Dic5semidirect
152. C22×C5GU(2,𝔽3)semidirect
234. C5#85563semidirect
245. C22#91185semidirect

Maximal subgroups

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

subgroupindex
C5×#59482
#106029313
#911854
A4⋊#1684
#855635