Finite Group Databasebeta

← #14512380

Subgroups — #14512380

Order 1920.

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

normal subgroups only

This group has 286 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×#4133⋊C3C211yesmaximal, characteristic
2C2×#91885C211yesmaximal, characteristic
3#11751587C211yesmaximal, characteristic
4#10603992—31nomaximal, Hall
5C2×C5⋊(#41⋊C3)C2211yescharacteristic
6#4133⋊C3C412yescomplemented
7#91885C412yescomplemented
8#91184C411yescharacteristic, complemented
9C5×#859C411yescharacteristic, complemented
10#91169—41nomaximal
11#73123—51nomaximal, Hall
12C2×#4133D311yescharacteristic
13C2×#4010—31no—
14C2×#3992—31no—
15#65701—31no—
16#65093—31no—
17#64896—31no—
18#64875—31no—
19C2×C5×SL(2,𝔽3)C2×C411yescharacteristic
20C2×C3⋊#170—41no—
21C2×C3×#170—41no—
22C5⋊(#41⋊C3)C2×C411yescharacteristic
23C5⋊(#41⋊C3)C2×C411yescharacteristic
24Dic3×Dic5—41no—
25C2×#131⋊C3—51no—
26#5424—51no—
27C2×GU(2,𝔽3)—51no—
28C2×#713C2×D311yescharacteristic
29#4133—32no—
30#4133Dic312yescomplemented
31C2×C4×AGL(1,𝔽5)—31no—
32C2×#700—31no—
33C2×#700—31no—
34C2×D5⋊C8—31no—
35C2×C8×D5—31no—
36#4038—31no—
37#4010—32no—
38#4010—32no—
39#4002—61no—
40C4×#170—61no—
41#3992—62no—
42C5×#103—31no—
43#3967—31no—
44#3953—31no—
45#3941—31no—
46#1765—151noSylow
47C2×Dic15—41no—
48C2×C5×Dic3—41no—
49C2×C3×Dic5—41no—
50C5×SL(2,𝔽3)C4211yescharacteristic
51C3⋊#170—42no—
52C3×#170—42no—
53C2×#41⋊C3—51no—
54#131⋊C3—52no—
55GU(2,𝔽3)—52no—
56#859—51no—
57#859AGL(1,𝔽5)11yescharacteristic, complemented
58#815—201no—
59C22×AGL(1,𝔽5)—61no—
60C2×C5×Q8C4×D311yescharacteristic
61#713—31no—
62#713—31no—
63#713C4×D311yescharacteristic
64#713C2×Dic311yescharacteristic
65C2×D20—31no—
66C2×C4×D5—31no—
67C2×#170—31no—
68C2×#170—61no—
69C2×#170S411yescharacteristic
70C4×AGL(1,𝔽5)—32no—
71C4×AGL(1,𝔽5)—61no—
72#700—32no—
73#700—32no—
74#700—61no—
75#700—61no—
76D5⋊C8—32no—
77D5⋊C8—32no—
78C2×C5×C8—31no—
79C5×C4⋊C4—31no—
80#685—61no—
81C4⋊Dic5—31no—
82C4×Dic5—61no—
83C2×#168—31no—
84C8×D5—61no—
85C8×D5—61no—
86C2×#131—51no—
87C2×#104—151no—
88#416—151no—
89#405—151no—
90C2×#97—151no—
91#341—151no—
92#339—151no—
93C22×C3×C5—41no—
94Dic15—81no—
95C3×Dic5—41no—
96C3×Dic5—41no—
97C5×Dic3—81no—
98#41⋊C3—51no—
99#41⋊C3—51no—
100C2×SL(2,𝔽3)C2×AGL(1,𝔽5)11yescharacteristic
101C2×C3×C8—201no—
102C4×Dic3—201no—
103C2×C3⋊C8—201no—
104C22×D5—31no—
105C2×AGL(1,𝔽5)—62no—
106C2×AGL(1,𝔽5)—121no—
107C2×AGL(1,𝔽5)—121no—
108C5×Q8—31no—
109C5×Q8C4×Dic311yescharacteristic
110C2×C4×C5—31no—
111C2×C4×C5—61no—
112C2×Dic5—61no—
113C2×Dic5C2×S411yescharacteristic
114D20—31no—
115D20—31no—
116D20—61no—
117C4×D5—31no—
118C4×D5—31no—
119C4×D5—31no—
120C4×D5—31no—
121#170—32no—
122#170—62no—
123#170SL(2,ℤ/4)12yes—
124C5×C8—61no—
125#168—61no—
126C2×#41—51no—
127#131—52no—
128#131—152no—
129C2×M16—151no—
130C2×M16—151no—
131C22×C8—151no—
132C22×C8—151no—
133#117—151no—
134C2×C42—151no—
135#104—152no—
136#104—152no—
137#103—31no—
138#103—151no—
139#102—151no—
140#102—151no—
141#97—301no—
142#97—302no—
143C4×C8—301no—
144C2×C3×C5—41no—
145C2×C3×C5—41no—
146C2×C3×C5—41no—
147C2×C3×C4—201no—
148C2×Dic3—41no—
149C2×Dic3—201no—
150SL(2,𝔽3)C4×AGL(1,𝔽5)11yescharacteristic
151C3×C8—202no—
152C3⋊C8—202no—
153C22×C5C4×S411yescharacteristic
154C2×D5—31no—
155C2×D5—31no—
156C2×D5—61no—
157C2×D5—61no—
158AGL(1,𝔽5)—122no—
159C4×C5—31no—
160C4×C5—31no—
161C4×C5—121no—
162Dic5—121no—
163Dic5C4×S411yescharacteristic
164Dic5C2×SL(2,ℤ/4)11yescharacteristic
165#41—51no—
166#41—51no—
167#41—151no—
168#41—151no—
169C2×Q8D3×AGL(1,𝔽5)11yescharacteristic
170C2×D4—151no—
171C22×C4—151no—
172C22×C4—301no—
173M16—152no—
174M16—152no—
175M16—301no—
176M16—301no—
177C2×C8—31no—
178C2×C8—51no—
179C2×C8—152no—
180C2×C8—152no—
181C2×C8—151no—
182C2×C8—151no—
183C2×C8—301no—
184C2×C8—301no—
185C2×C8—301no—
186C4⋊C4—31no—
187C4⋊C4—151no—
188C22⋊C4—301no—
189C42—152no—
190C42—301no—
191C42—301no—
192C3×C5—41noHall
193C22×C3—41no—
194C3×C4—201no—
195C3×C4—201no—
196Dic3—81no—
197Dic3—401no—
198C2×C5#540511yescharacteristic
199C2×C5#540511yescharacteristic
200C2×C5C4×SL(2,ℤ/4)11yescharacteristic
201D5—61no—
202D5—61no—
203C23—151no—
204Q8—31no—
205Q8Dic3×AGL(1,𝔽5)11yescharacteristic
206D4—151no—
207D4—151no—
208D4—301no—
209C2×C4—31no—
210C2×C4—51no—
211C2×C4—61no—
212C2×C4—151no—
213C2×C4—151no—
214C2×C4—151no—
215C2×C4—151no—
216C2×C4—302no—
217C2×C4—301no—
218C2×C4—601no—
219C2×C4—601no—
220C8—52no—
221C8—61no—
222C8—152no—
223C8—301no—
224C8—302no—
225C2×C3—41no—
226C2×C3—41no—
227C2×C3—41no—
228C5#7312311yescharacteristic, complemented, Sylow
229C22—151no—
230C22—151no—
231C22—301no—
232C22—301no—
233C22AGL(1,𝔽5)×S411yescharacteristic
234C4—31no—
235C4—31no—
236C4—51no—
237C4—51no—
238C4—121no—
239C4—602no—
240C4—601no—
241C3—41noSylow
242C2—301no—
243C2—301no—
244C2#1175670111yescharacteristic
245C2#1175670211yescharacteristic
246C2AGL(1,𝔽5)×SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22AGL(1,𝔽5)×S4
commutator, hypocenterC5×SL(2,𝔽3)C42
FittingC2×C5×Q8C4×D3
socleC22×C5C4×S4
prime radical, cosocleC2×C5⋊(#41⋊C3)C22
LCSG ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
6. #4133⋊C3C4semidirect
7. #91885C4semidirect
8. #91184C4semidirect
9. C5×#859C4semidirect
30. #4133Dic3semidirect
57. #859AGL(1,𝔽5)semidirect
228. C5#73123semidirect

Maximal subgroups

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

subgroupindex
C2×#4133⋊C32
C2×#918852
#117515872
#106039923
#911694
#731235