Finite Group Databasebeta

← #14513429

Subgroups — #14513429

Order 1920.

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

normal subgroups only

This group has 386 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#11751598C212yesmaximal, complemented
5#11751592C212yesmaximal, complemented
6#10610554—31nomaximal, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8#91381—41nomaximal
9Dic5×SL(2,𝔽3)C2212yes—
10#91184C2212yes—
11C5×#859C2211yescharacteristic
12C5×#859C2211yescharacteristic
13#85363—51nomaximal, Hall
14#66161D311yescharacteristic
15#65853—31no—
16C5×#416—31no—
17#65521—31no—
18C2×#3950—31no—
19#65391—31no—
20#65284—31no—
21#65085—32no—
22#65083—32no—
23#65055—32no—
24#65048—32no—
25C5×#41⋊C3Q812yescomplemented
26C2×C5×SL(2,𝔽3)C2311yescharacteristic
27C4⋊Dic15—41no—
28C4×C5×Dic3—41no—
29C3×C4⋊Dic5—41no—
30#6669—42no—
31#6668—42no—
32#520⋊C3—51no—
33#5426—51no—
34#5424D511yescharacteristic
35#5391—52no—
36#5389—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#3950—32no—
58#3950—32no—
59#3946—32no—
60#3946—32no—
61#3940—32no—
62#3939—32no—
63#3083—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
70C2×#41⋊C3C2×D511yescharacteristic
71#890—201no—
72C4×SL(2,𝔽3)—52no—
73#859—52no—
74#859C2×D511yescharacteristic
75#859C2×D511yescharacteristic
76C5×#41—32no—
77C5×#41Dic612yes—
78C2×C5×Q8C22×D311yescharacteristic
79C2×C5×D4—31no—
80C22×C4×C5—31no—
81C22×Dic5—61no—
82C22×Dic5—61no—
83C2×Dic10—62no—
84C2×C5×C8—31no—
85C2×C5×C8—31no—
86C2×C5×C8—62no—
87C5×C4⋊C4—31no—
88C5×C4⋊C4—31no—
89C5×C22⋊C4—61no—
90C42×C5—61no—
91C22⋊Dic5—32no—
92C4⋊Dic5—31no—
93C4⋊Dic5—32no—
94C4⋊Dic5—32no—
95C4⋊Dic5—62no—
96C4⋊Dic5—61no—
97C4⋊Dic5S411yescharacteristic
98#683—62no—
99#683—62no—
100C4×Dic5—32no—
101#681—62no—
102C2×#168—32no—
103#544—151no—
104#520—51no—
105#479—152no—
106#478—152no—
107#477—152no—
108#474—152no—
109#428—151no—
110C2×#107—151no—
111#424—151no—
112#417—151no—
113#416—31no—
114C22×C3×C5—41no—
115C3×C4×C5—42no—
116Dic15—82no—
117C3×Dic5—82no—
118C5×Dic3—81no—
119C5×Dic3—81no—
120#41⋊C3Dic1012yescomplemented
121C2×SL(2,𝔽3)C22×D511yescharacteristic
122C3×C4⋊C4—201no—
123C4⋊Dic3—202no—
124C4⋊Dic3—201no—
125Dic3⋊C4—202no—
126C4×Dic3—41no—
127C23×C5—31no—
128C5×Q8—31no—
129C5×Q8C2×Dic611yescharacteristic
130C5×D4—32no—
131C5×D4—61no—
132C2×C4×C5—31no—
133C2×C4×C5—32no—
134C2×C4×C5—32no—
135C2×C4×C5—61no—
136C2×C4×C5—61no—
137C2×C4×C5C2×S411yescharacteristic
138C2×Dic5—32no—
139C2×Dic5—62no—
140C2×Dic5—241no—
141C2×Dic5—241no—
142C2×Dic5C2×S412yes—
143Dic10—242no—
144C5×C8—61no—
145C5×C8—61no—
146#168—62no—
147C2×#41D3×D511yescharacteristic
148C2×M16—151no—
149C22×C8—31no—
150C4⋊Q8—152no—
151C4⋊Q8—301no—
152#125—152no—
153#125—301no—
154C22⋊Q8—302no—
155C4×Q8—52no—
156C4×D4—152no—
157#117—31no—
158#117—151no—
159C2×C4⋊C4—151no—
160C2×C4⋊C4—151no—
161#107—152no—
162#107—152no—
163#107—152no—
164#106—152no—
165C4⋊C8—152no—
166C4⋊C8—152no—
167#103—31no—
168#103—31no—
169#103—152no—
170#102—31no—
171#102—31no—
172#102—152no—
173C2×C3×C5—41no—
174C2×C3×C5—41no—
175C2×C3×C5—41no—
176C2×C3×C4—41no—
177C2×C3×C4—202no—
178C2×Dic3—41no—
179C2×Dic3—41no—
180C2×Dic3—202no—
181SL(2,𝔽3)C2×Dic1011yescharacteristic
182C22×C5—32no—
183C22×C5—61no—
184C22×C5—61no—
185C22×C5C22×S411yescharacteristic
186C4×C5—31no—
187C4×C5—31no—
188C4×C5—121no—
189C4×C5—121no—
190C4×C5A4⋊Q812yes—
191Dic5—22no—
192Dic5—62no—
193Dic5—122no—
194#41—32no—
195#41#120412yes—
196C2×Q8—302no—
197C2×Q8C2×D3×D511yescharacteristic
198C2×D4—31no—
199C22×C4—31no—
200C22×C4—301no—
201C22×C4—301no—
202M16—302no—
203C2×C8—31no—
204C2×C8—31no—
205C2×C8—62no—
206C2×C8—152no—
207C4⋊C4—31no—
208C4⋊C4—31no—
209C4⋊C4—51no—
210C4⋊C4—152no—
211C4⋊C4—152no—
212C4⋊C4—151no—
213C4⋊C4—302no—
214C4⋊C4—302no—
215C4⋊C4—302no—
216C4⋊C4—301no—
217C22⋊C4—61no—
218C22⋊C4—152no—
219C42—61no—
220C42—152no—
221C3×C5—41noHall
222C22×C3—41no—
223C3×C4—42no—
224C3×C4—402no—
225Dic3—81no—
226Dic3—81no—
227Dic3—402no—
228C2×C5—62no—
229C2×C5C2×A4⋊Q811yescharacteristic
230C2×C5#592511yescharacteristic
231C2×C5#592711yescharacteristic
232C23—31no—
233Q8—31no—
234Q8—1202no—
235Q8C2×#120411yescharacteristic
236D4—32no—
237D4—61no—
238C2×C4—31no—
239C2×C4—32no—
240C2×C4—32no—
241C2×C4—52no—
242C2×C4—61no—
243C2×C4—61no—
244C2×C4—152no—
245C2×C4—302no—
246C2×C4—1201no—
247C2×C4—1201no—
248C2×C4D5×S411yescharacteristic
249C8—61no—
250C8—61no—
251C8—302no—
252C2×C3—41no—
253C2×C3—41no—
254C2×C3—41no—
255C5#8536311yescharacteristic, complemented, Sylow
256C22—32no—
257C22—61no—
258C22—61no—
259C22C2×D5×S411yescharacteristic
260C4—31no—
261C4—31no—
262C4—102no—
263C4—121no—
264C4—121no—
265C4—302no—
266C4—602no—
267C4#9189912yes—
268C3—41noSylow
269C2—62no—
270C2#1175677511yescharacteristic
271C2#1175677811yescharacteristic
272C2C2×#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. #11751598C2semidirect
5. #11751592C2semidirect
25. C5×#41⋊C3Q8semidirect
120. #41⋊C3Dic10semidirect
255. C5#85363semidirect

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
#117515982
#117515922
#106105543
#913814
#853635