Finite Group Databasebeta

← #10617553⋊C3 #14512584

Subgroups — #10617553⋊C3 #14512584

Order 1920.

372 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 44 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
1C2×C5⋊#994C211yesmaximal, characteristic
2#66260⋊C3C212yesmaximal, complemented
3#10617553C311yesmaximal, characteristic, complemented, Hall
4C2×C5×#41⋊C3C411yescharacteristic
5C5⋊#994—22no—
6C2×C5⋊(#41⋊C3)C411yescharacteristic
7C2×C5⋊(#41⋊C3)C2211yescharacteristic
8#4133⋊C3—22no—
9C3×#4005—41nomaximal
10#2888⋊C3—51nomaximal, Hall
11C2×#4149C2×C311yescharacteristic
12#66260C2×C312yes—
13D5⋊#100—32no—
14#65761—31no—
15#65761—31no—
16C2×C3×Dic10—41no—
17C5×#41⋊C3—21no—
18C2×C5×SL(2,𝔽3)C2×C411yescharacteristic
19C3×#704—42no—
20C5⋊(#41⋊C3)—21no—
21C5⋊(#41⋊C3)D412yes—
22C2×#994—51no—
23#568⋊C3—52no—
24C2×C5×#41C3×C411yescharacteristic
25#4149—22no—
26#4149—62no—
27C2×#713C3×C411yescharacteristic
28C2×#713C22×C311yescharacteristic
29C2×D4×D5—31no—
30C2×D4×D5—31no—
31C2×#709—31no—
32C22×D20—31no—
33#4133—22no—
34#4133—62no—
35D5⋊M16—32no—
36D5⋊M16—32no—
37#4013—32no—
38#4013—32no—
39#4005—31no—
40#4005A411yescharacteristic
41#2888—51noSylow
42C2×C3×C4×C5—41no—
43C2×C3×Dic5—41no—
44C2×C3×Dic5—41no—
45C3×Dic10—82no—
46C5×SL(2,𝔽3)C22⋊C411yescharacteristic
47C3×#170—82no—
48#994—102no—
49C2×#41⋊C3—51no—
50C2×#41⋊C3—51no—
51C2×#41⋊C3AGL(1,𝔽5)11yescharacteristic
52#131⋊C3—102no—
53C3×#101—201no—
54C23×D5—32no—
55C5×#41—21no—
56C5×#41—61no—
57C2×C5×Q8C2×C3×C411yescharacteristic
58C2×C5×D4—31no—
59C22×C4×C5—31no—
60C2×C22⋊D5—31no—
61C2×C22⋊D5—31no—
62#713—21no—
63#713—32no—
64#713—61no—
65#713C3×D412yes—
66D4×D5—62no—
67D4×D5—62no—
68D4×D5—62no—
69D4×D5—62no—
70#709—62no—
71#709—62no—
72C2×D20—31no—
73C2×D20—31no—
74C2×D20—31no—
75C2×D20—62no—
76C2×D20—62no—
77C2×C4×D5—31no—
78C2×C4×D5—31no—
79C2×Dic10C2×A411yescharacteristic
80#704—32no—
81#704C2×A412yes—
82#700—62no—
83#700—62no—
84D5⋊C8—62no—
85D5⋊C8—62no—
86C2×H(5,𝔽2)—51no—
87#568—52no—
88#413—151no—
89#413—151no—
90C2×#100—152no—
91C22×C3×C5—41no—
92C3×C4×C5—81no—
93C3×Dic5—42no—
94C3×Dic5—81no—
95C2×C3×Q8—201no—
96#41⋊C3—21no—
97#41⋊C3—52no—
98#41⋊C3—101no—
99C2×SL(2,𝔽3)C2×AGL(1,𝔽5)11yescharacteristic
100C3×M16—202no—
101C23×C5—31no—
102C22×D5—31no—
103C22×D5—31no—
104C22×D5—64no—
105C22×D5—242no—
106C5×Q8—31no—
107C5×Q8C3×C22⋊C411yescharacteristic
108C5×D4—61no—
109C5×D4—61no—
110C2×C4×C5—31no—
111C2×C4×C5—61no—
112C2×C4×C5—61no—
113C2×C4×C5C4×A411yescharacteristic
114C22⋊D5—62no—
115C22⋊D5—62no—
116C2×Dic5C4×A411yescharacteristic
117C2×Dic5C22×A411yescharacteristic
118D20—32no—
119D20—32no—
120D20—62no—
121D20—61no—
122D20—61no—
123C4×D5—32no—
124C4×D5—32no—
125C4×D5—61no—
126C4×D5—61no—
127Dic10—22no—
128#170—22no—
129#170—62no—
130H(5,𝔽2)—102no—
131H(5,𝔽2)—302no—
132C2×#41—51no—
133C2×#41—51no—
134C2×#41—151no—
135C2×#41C3×AGL(1,𝔽5)11yescharacteristic
136C22×D4—151no—
137C22×D4—151no—
138C22×D4—151no—
139#131—102no—
140#131—302no—
141C2×M16—152no—
142C2×M16—152no—
143#101—51no—
144#101—151no—
145#100—152no—
146#100—152no—
147C2×C3×C5—41no—
148C2×C3×C5—81no—
149C3×Q8—402no—
150C2×C3×C4—41no—
151C2×C3×C4—201no—
152C2×C3×C4—201no—
153SL(2,𝔽3)C22⋊AGL(1,𝔽5)11yescharacteristic
154C3×C8—402no—
155C22×C5—61no—
156C22×C5—121no—
157C22×C5C2×C4×A411yescharacteristic
158C2×D5—32no—
159C2×D5—61no—
160C2×D5—121no—
161C2×D5—121no—
162C2×D5—244no—
163C4×C5—21no—
164C4×C5—31no—
165C4×C5—31no—
166Dic5—21no—
167Dic5D4×A412yes—
168C24—152no—
169#41—21no—
170#41—52no—
171#41—61no—
172#41—101no—
173#41—152no—
174#41—302no—
175#41—302no—
176#41—301no—
177C2×Q8—51no—
178C2×Q8C2×C3×AGL(1,𝔽5)11yescharacteristic
179C2×D4—31no—
180C2×D4—151no—
181C2×D4—151no—
182C2×D4—151no—
183C2×D4—151no—
184C2×D4—151no—
185C2×D4—302no—
186C2×D4—302no—
187C2×D4—302no—
188C2×D4—302no—
189C2×D4—302no—
190C2×D4—302no—
191C22×C4—31no—
192C22×C4—151no—
193C22×C4—151no—
194M16—52no—
195M16—152no—
196M16—302no—
197M16—302no—
198C2×C8—302no—
199C2×C8—302no—
200C3×C5—41noHall
201C22×C3—41no—
202C3×C4—81no—
203C3×C4—202no—
204C3×C4—401no—
205C2×C5—21no—
206C2×C5—121no—
207C2×C5A4×C22⋊C411yescharacteristic
208D5—62no—
209D5—121no—
210C23—31no—
211C23—151no—
212C23—151no—
213C23—304no—
214C23—1202no—
215Q8—31no—
216Q8—102no—
217Q8C3×C22⋊AGL(1,𝔽5)11yescharacteristic
218D4—61no—
219D4—61no—
220D4—152no—
221D4—152no—
222D4—302no—
223D4—301no—
224D4—301no—
225D4—302no—
226D4—302no—
227C2×C4—31no—
228C2×C4—51no—
229C2×C4—51no—
230C2×C4—61no—
231C2×C4—61no—
232C2×C4—152no—
233C2×C4—152no—
234C2×C4—301no—
235C2×C4—301no—
236C2×C4A4×AGL(1,𝔽5)11yescharacteristic
237C8—102no—
238C8—302no—
239C2×C3—41no—
240C2×C3—81no—
241C5#2888⋊C311yescharacteristic, complemented, Sylow
242C22—61no—
243C22—121no—
244C22—152no—
245C22—301no—
246C22—601no—
247C22—601no—
248C22—1204no—
249C22C2×A4×AGL(1,𝔽5)11yescharacteristic
250C4—21no—
251C4—31no—
252C4—31no—
253C4—52no—
254C4—101no—
255C3—41noSylow
256C2—21no—
257C2—121no—
258C2—302no—
259C2—601no—
260C2A4×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC2A4×C22⋊AGL(1,𝔽5)
commutatorC2×C5×Q8C2×C3×C4
FrattiniC22C2×A4×AGL(1,𝔽5)
FittingC2×C5×#41C3×C4
socleC2×C5A4×C22⋊C4
prime radicalC2×C5⋊#994C2
cosocleC2×#713C22×C3
hypercenterC2×C4A4×AGL(1,𝔽5)
hypocenterC5×Q8C3×C22⋊C4
LCSG ▷ C2×C5×Q8 ▷ C5×Q8
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #66260⋊C3C2semidirect
3. #10617553C3semidirect
241. C5#2888⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C5⋊#9942
#66260⋊C32
#106175533
C3×#40054
#2888⋊C35