Finite Group Databasebeta

← #10617525⋊C3 #14512574

Subgroups — #10617525⋊C3 #14512574

Order 1920.

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

normal subgroups only

This group has 368 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×#4147⋊C3C211yesmaximal, characteristic
2#66260⋊C3C212yesmaximal, complemented
3#10617525C311yesmaximal, characteristic, complemented, Hall
4C22×C5×SL(2,𝔽3)C411yescharacteristic
5#4147⋊C3—22no—
6C2×D5×SL(2,𝔽3)C411yescharacteristic
7C2×C5⋊(#41⋊C3)C2211yescharacteristic
8#4133⋊C3—22no—
9C3×#4013—41nomaximal
10#2889⋊C3—51nomaximal, Hall
11C2×#4147C2×C311yescharacteristic
12#66260C2×C312yescomplemented
13D5⋊#101—32no—
14#65761—31no—
15#65761—31no—
16C2×C3×C22⋊D5—41no—
17C2×C5×SL(2,𝔽3)—21no—
18C2×C5×SL(2,𝔽3)C2×C411yescharacteristic
19C3×#704—42no—
20D5×SL(2,𝔽3)—21no—
21C5⋊(#41⋊C3)D412yes—
22C2×2−1+4⋊C3—51no—
23#568⋊C3—52no—
24C22×C5×Q8C3×C411yescharacteristic
25#4147—22no—
26#4147—62no—
27C2×#713—31no—
28C2×#713C22×C311yescharacteristic
29C2×Q8×D5—31no—
30C2×Q8×D5C3×C411yescharacteristic
31C2×#709—31no—
32C2×#709—31no—
33#4133—22no—
34#4133—62no—
35D5⋊M16—32no—
36D5⋊M16—32no—
37#4013—31no—
38#4013A411yescharacteristic
39#4005—32no—
40#4005—32no—
41#2889—51noSylow
42C23×C3×C5—41no—
43C22×C3×D5—41no—
44C3×C22⋊D5—82no—
45C2×C3×Dic5—41no—
46C5×SL(2,𝔽3)C22⋊C411yescharacteristic
47C3×#170—82no—
482−1+4⋊C3—102no—
49C2×#41⋊C3—51no—
50C22×SL(2,𝔽3)—51no—
51C22×SL(2,𝔽3)AGL(1,𝔽5)11yescharacteristic
52#131⋊C3—102no—
53C3×#100—201no—
54C2×C5×Q8—21no—
55C2×C5×Q8—31no—
56C2×C5×Q8—61no—
57C2×C5×Q8C2×C3×C411yescharacteristic
58C22×C4×C5—31no—
59C2×C22⋊D5—31no—
60C2×C22⋊D5C2×A411yescharacteristic
61#713—32no—
62#713—62no—
63#713—62no—
64#713C3×D412yes—
65Q8×D5—21no—
66Q8×D5—62no—
67Q8×D5—62no—
68Q8×D5—61no—
69#709—62no—
70#709—62no—
71#709—62no—
72#709—62no—
73C2×D20—31no—
74C2×D20—31no—
75C2×C4×D5—31no—
76C2×C4×D5—32no—
77C2×C4×D5—31no—
78C2×Dic10—31no—
79C2×Dic10—31no—
80#704—32no—
81#704C2×A412yes—
82#700—62no—
83#700—62no—
84D5⋊C8—62no—
85D5⋊C8—62no—
86C2×2−1+4—51no—
87#568—52no—
88#413—151no—
89#413—151no—
90C2×#101—152no—
91C22×C3×C5—41no—
92C22×C3×C5—81no—
93C22×C3×C5—161no—
94C2×C3×D5—81no—
95C2×C3×D5—161no—
96C3×Dic5—42no—
97C2×C3×D4—201no—
98#41⋊C3—52no—
99C2×SL(2,𝔽3)—21no—
100C2×SL(2,𝔽3)—101no—
101C2×SL(2,𝔽3)C2×AGL(1,𝔽5)11yescharacteristic
102C3×M16—202no—
103C23×C5C4×A411yescharacteristic
104C22×D5—31no—
105C22×D5C4×A411yescharacteristic
106C5×Q8—31no—
107C5×Q8—61no—
108C5×Q8—61no—
109C5×Q8C3×C22⋊C411yescharacteristic
110C2×C4×C5—31no—
111C2×C4×C5—31no—
112C2×C4×C5—61no—
113C2×C4×C5—61no—
114C22⋊D5—22no—
115C22⋊D5—62no—
116C2×Dic5—31no—
117C2×Dic5C22×A411yescharacteristic
118D20—32no—
119D20—32no—
120D20—62no—
121C4×D5—32no—
122C4×D5—32no—
123C4×D5—61no—
124C4×D5—61no—
125C4×D5—64no—
126Dic10—62no—
127Dic10—61no—
128Dic10—61no—
129#170—22no—
130#170—62no—
1312−1+4—102no—
1322−1+4—302no—
133C2×#41—51no—
134C2×#41—151no—
135C2×#41—151no—
136C2×#41—151no—
137C22×Q8—51no—
138C22×Q8—151no—
139C22×Q8C3×AGL(1,𝔽5)11yescharacteristic
140#131—102no—
141#131—302no—
142C2×M16—152no—
143C2×M16—152no—
144#101—152no—
145#101—152no—
146#100—51no—
147#100—151no—
148C2×C3×C5—41no—
149C2×C3×C5—81no—
150C2×C3×C5—161no—
151C3×D5—161no—
152C23×C3—41no—
153C23×C3—201no—
154C3×D4—402no—
155C2×C3×C4—201no—
156SL(2,𝔽3)C22⋊AGL(1,𝔽5)11yescharacteristic
157C3×C8—402no—
158C22×C5—21no—
159C22×C5—41no—
160C22×C5C2×C4×A411yescharacteristic
161C2×D5—21no—
162C2×D5—32no—
163C2×D5—41no—
164C2×D5—121no—
165C4×C5—31no—
166C4×C5—31no—
167C4×C5—61no—
168Dic5—61no—
169Dic5D4×A412yes—
170#41—52no—
171#41—152no—
172#41—302no—
173#41—302no—
174#41—302no—
175#41—302no—
176#41—302no—
177#41—302no—
178C2×Q8—21no—
179C2×Q8—31no—
180C2×Q8—61no—
181C2×Q8—101no—
182C2×Q8—151no—
183C2×Q8—151no—
184C2×Q8—302no—
185C2×Q8—302no—
186C2×Q8—301no—
187C2×Q8C2×C3×AGL(1,𝔽5)11yescharacteristic
188C2×D4—51no—
189C2×D4—151no—
190C2×D4—151no—
191C2×D4—151no—
192C22×C4—31no—
193C22×C4—151no—
194C22×C4—151no—
195C22×C4—152no—
196M16—52no—
197M16—152no—
198M16—302no—
199M16—302no—
200C2×C8—302no—
201C2×C8—302no—
202C3×C5—41noHall
203C22×C3—41no—
204C22×C3—81no—
205C22×C3—161no—
206C22×C3—401no—
207C22×C3—801no—
208C3×C4—202no—
209C2×C5—21no—
210C2×C5—41no—
211C2×C5A4×C22⋊C411yescharacteristic
212D5—41no—
213D5—62no—
214C23—51no—
215C23—151no—
216C23A4×AGL(1,𝔽5)11yescharacteristic
217Q8—31no—
218Q8—61no—
219Q8—61no—
220Q8—301no—
221Q8—301no—
222Q8—302no—
223Q8C3×C22⋊AGL(1,𝔽5)11yescharacteristic
224D4—102no—
225D4—152no—
226D4—152no—
227D4—302no—
228D4—302no—
229C2×C4—31no—
230C2×C4—31no—
231C2×C4—51no—
232C2×C4—61no—
233C2×C4—61no—
234C2×C4—152no—
235C2×C4—152no—
236C2×C4—151no—
237C2×C4—301no—
238C2×C4—301no—
239C2×C4—304no—
240C8—102no—
241C8—302no—
242C2×C3—41no—
243C2×C3—81no—
244C2×C3—161no—
245C2×C3—801no—
246C5#2889⋊C311yescharacteristic, complemented, Sylow
247C22—21no—
248C22—41no—
249C22—101no—
250C22—152no—
251C22—201no—
252C22—601no—
253C22C2×A4×AGL(1,𝔽5)11yescharacteristic
254C4—31no—
255C4—31no—
256C4—52no—
257C4—61no—
258C4—301no—
259C3—41noSylow
260C2—21no—
261C2—41no—
262C2—201no—
263C2—302no—
264C2A4×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC2A4×C22⋊AGL(1,𝔽5)
commutatorC2×C5×Q8C2×C3×C4
FrattiniC22C2×A4×AGL(1,𝔽5)
FittingC22×C5×Q8C3×C4
socleC2×C5A4×C22⋊C4
prime radicalC2×#4147⋊C3C2
cosocleC2×#713C22×C3
hypercenterC23A4×AGL(1,𝔽5)
hypocenterC5×Q8C3×C22⋊C4
LCSG ▷ C2×C5×Q8 ▷ C5×Q8
UCSC1 ◁ C2 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. #66260⋊C3C2semidirect
3. #10617525C3semidirect
12. #66260C2×C3semidirect
246. C5#2889⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×#4147⋊C32
#66260⋊C32
#106175253
C3×#40134
#2889⋊C35