Finite Group Databasebeta

← #14513478

Subgroups — #14513478

Order 1920.

398 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 59 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#66161⋊C3C211yesmaximal, characteristic
2#11752145C211yesmaximal, characteristic
3C5×#5424C211yesmaximal, characteristic
4#11751608C212yesmaximal, complemented
5#11751595C212yesmaximal, complemented
6#10610555—31nomaximal, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8#91469—41nomaximal
9Dic5×SL(2,𝔽3)C2212yes—
10#91184C2212yes—
11C5×#859C2211yescharacteristic
12C5×#859C2211yescharacteristic
13#85361—51nomaximal, Hall
14#66161D311yescharacteristic
15#65853—31no—
16C5×#416—31no—
17#65521—31no—
18C2×#3949—31no—
19#65391—31no—
20#65284—31no—
21#65088—32no—
22#65080—32no—
23#65052—32no—
24#65050—32no—
25C5×#41⋊C3Q812yescomplemented
26C2×C5×SL(2,𝔽3)C2311yescharacteristic
27C2×#1204—42no—
28C4⋊Dic15—41no—
29C4×C5×Dic3—41no—
30C3×C4⋊Dic5—41no—
31Dic3⋊Dic5—42no—
32#520⋊C3—51no—
33#5426—51no—
34#5424D511yescharacteristic
35#5389—52no—
36#5386—52no—
37C2×C5×#41C2×D311yescharacteristic
38C22×C5×C8—31no—
39C5×#117—31no—
40Q8×Dic5C2×D312yes—
41D4×Dic5—32no—
42#4072—31no—
43C2×C4⋊Dic5—31no—
44C2×C4⋊Dic5—31no—
45C2×#681—31no—
46#4036—32no—
47#4034—32no—
48#4024—62no—
49#4016—61no—
50#4015—61no—
51C5×#103—31no—
52C5×#103—31no—
53C5×#102—31no—
54C5×#102—31no—
55#3967—32no—
56#3964—32no—
57#3949—32no—
58#3949—32no—
59#3946—32no—
60#3946—32no—
61#3940—32no—
62#3939—32no—
63#3084—151noSylow
64C2×C3×C4×C5—41no—
65C2×Dic15—42no—
66C2×C5×Dic3—41no—
67C2×C5×Dic3—41no—
68C2×C3×Dic5—42no—
69C5×SL(2,𝔽3)C2×Q811yescharacteristic
70#1204—84no—
71C2×#41⋊C3C2×D511yescharacteristic
72#888—201no—
73C4×SL(2,𝔽3)—52no—
74#859—52no—
75#859C2×D511yescharacteristic
76#859C2×D511yescharacteristic
77C5×#41—32no—
78C5×#41Dic612yescomplemented
79C2×C5×Q8C22×D311yescharacteristic
80C2×C5×D4—31no—
81C22×C4×C5—31no—
82C22×Dic5—61no—
83C22×Dic5—61no—
84C2×Dic10—62no—
85C2×C5×C8—31no—
86C2×C5×C8—31no—
87C2×C5×C8—62no—
88C5×C4⋊C4—31no—
89C5×C4⋊C4—31no—
90C5×C22⋊C4—61no—
91C42×C5—61no—
92C22⋊Dic5—32no—
93C4⋊Dic5—31no—
94C4⋊Dic5—32no—
95C4⋊Dic5—32no—
96C4⋊Dic5—61no—
97C4⋊Dic5—62no—
98C4⋊Dic5S411yescharacteristic
99#683—62no—
100#683—62no—
101C4×Dic5—32no—
102#681—62no—
103C2×#168—32no—
104#544—151no—
105#520—51no—
106#479—152no—
107#478—152no—
108#476—152no—
109#475—152no—
110#428—151no—
111C2×#106—151no—
112#424—151no—
113#417—151no—
114#416—31no—
115C22×C3×C5—41no—
116C3×C4×C5—42no—
117Dic15—82no—
118C3×Dic5—82no—
119C5×Dic3—42no—
120C5×Dic3—42no—
121C2×Dic6—202no—
122#41⋊C3Dic1012yescomplemented
123C2×SL(2,𝔽3)C22×D511yescharacteristic
124C3×C4⋊C4—201no—
125C4⋊Dic3—201no—
126Dic3⋊C4—202no—
127C4×Dic3—41no—
128C23×C5—31no—
129C5×Q8—31no—
130C5×Q8C2×Dic611yescharacteristic
131C5×D4—32no—
132C5×D4—61no—
133C2×C4×C5—31no—
134C2×C4×C5—32no—
135C2×C4×C5—32no—
136C2×C4×C5—61no—
137C2×C4×C5—61no—
138C2×C4×C5C2×S411yescharacteristic
139C2×Dic5—32no—
140C2×Dic5—62no—
141C2×Dic5—241no—
142C2×Dic5—241no—
143C2×Dic5C2×S412yes—
144Dic10—242no—
145C5×C8—61no—
146C5×C8—61no—
147#168—62no—
148C2×#41D3×D511yescharacteristic
149C2×M16—151no—
150C22×C8—31no—
151C4⋊Q8—152no—
152C4⋊Q8—301no—
153#125—152no—
154#125—301no—
155C22⋊Q8—302no—
156C4×Q8—52no—
157C4×D4—152no—
158#117—31no—
159#117—151no—
160C2×C4⋊C4—151no—
161C2×C4⋊C4—151no—
162#107—152no—
163#106—152no—
164#106—152no—
165#106—152no—
166C4⋊C8—152no—
167C4⋊C8—152no—
168#103—31no—
169#103—31no—
170#103—152no—
171#102—31no—
172#102—31no—
173#102—152no—
174C2×C3×C5—41no—
175C2×C3×C5—41no—
176C2×C3×C5—41no—
177C2×C3×C4—41no—
178C2×C3×C4—202no—
179C2×Dic3—41no—
180C2×Dic3—41no—
181C2×Dic3—202no—
182Dic6—404no—
183SL(2,𝔽3)C2×Dic1011yescharacteristic
184C22×C5—32no—
185C22×C5—61no—
186C22×C5—61no—
187C22×C5C22×S411yescharacteristic
188C4×C5—31no—
189C4×C5—31no—
190C4×C5—121no—
191C4×C5—121no—
192C4×C5A4⋊Q812yes—
193Dic5—22no—
194Dic5—62no—
195Dic5—122no—
196#41—32no—
197#41#120412yescomplemented
198C2×Q8—302no—
199C2×Q8C2×D3×D511yescharacteristic
200C2×D4—31no—
201C22×C4—31no—
202C22×C4—301no—
203C22×C4—301no—
204M16—302no—
205C2×C8—31no—
206C2×C8—31no—
207C2×C8—62no—
208C2×C8—152no—
209C4⋊C4—31no—
210C4⋊C4—31no—
211C4⋊C4—51no—
212C4⋊C4—152no—
213C4⋊C4—152no—
214C4⋊C4—151no—
215C4⋊C4—302no—
216C4⋊C4—302no—
217C4⋊C4—302no—
218C4⋊C4—301no—
219C22⋊C4—61no—
220C22⋊C4—152no—
221C42—61no—
222C42—152no—
223C3×C5—41noHall
224C22×C3—41no—
225C3×C4—42no—
226C3×C4—402no—
227Dic3—42no—
228Dic3—42no—
229Dic3—402no—
230C2×C5—62no—
231C2×C5C2×A4⋊Q811yescharacteristic
232C2×C5#592411yescharacteristic
233C2×C5#592611yescharacteristic
234C23—31no—
235Q8—31no—
236Q8—1202no—
237Q8C2×#120411yescharacteristic
238D4—32no—
239D4—61no—
240C2×C4—31no—
241C2×C4—32no—
242C2×C4—32no—
243C2×C4—52no—
244C2×C4—61no—
245C2×C4—61no—
246C2×C4—152no—
247C2×C4—302no—
248C2×C4—1201no—
249C2×C4—1201no—
250C2×C4D5×S411yescharacteristic
251C8—61no—
252C8—61no—
253C8—302no—
254C2×C3—41no—
255C2×C3—41no—
256C2×C3—41no—
257C5#8536111yescharacteristic, complemented, Sylow
258C22—32no—
259C22—61no—
260C22—61no—
261C22C2×D5×S411yescharacteristic
262C4—31no—
263C4—31no—
264C4—102no—
265C4—121no—
266C4—121no—
267C4—302no—
268C4—602no—
269C4#9189912yes—
270C3—41noSylow
271C2—62no—
272C2#1175677311yescharacteristic
273C2#1175678511yescharacteristic
274C2C2×#9189911yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×S4
commutator, cosocleC2×C5×SL(2,𝔽3)C23
FittingC2×C5×#41C2×D3
socleC22×C5C22×S4
prime radicalC2×C5×#41⋊C3C22
hypercenterC2×C4D5×S4
hypocenterC5×SL(2,𝔽3)C2×Q8
LCSG ▷ C2×C5×SL(2,𝔽3) ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. #11751608C2semidirect
5. #11751595C2semidirect
25. C5×#41⋊C3Q8semidirect
78. C5×#41Dic6semidirect
122. #41⋊C3Dic10semidirect
197. #41#1204semidirect
257. C5#85361semidirect

Maximal subgroups

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

subgroupindex
#66161⋊C32
#117521452
C5×#54242
#117516082
#117515952
#106105553
#914694
#853615