Finite Group Databasebeta

← #14513736

Subgroups — #14513736

Order 1920.

408 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C4×C5×#41⋊C3C211yesmaximal, characteristic
2#11752143C212yesmaximal
3#11752110C211yesmaximal, characteristic, complemented
4#11752108C212yesmaximal, complemented
5#11752105C211yesmaximal, characteristic, complemented
6#10614238—31nomaximal, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8C4×Dic30—41nomaximal
9C4×C5×SL(2,𝔽3)C2211yescharacteristic
10C4×C5×SL(2,𝔽3)C2211yescharacteristic
11#91184C2212yes—
12#91184C2212yes—
13#85334—51nomaximal, Hall
14C4×C5×#41D311yescharacteristic
15#65804—31no—
16#65522—32no—
17#65311—32no—
18#65310—31no—
19#65309—31no—
20#65298—32no—
21#65297—31no—
22#65296—31no—
23#65287—32no—
24C2×C4⋊#168—31no—
25C2×Dic30—41no—
26C5×#41⋊C3Q812yescomplemented
27C2×C5×SL(2,𝔽3)C2311yescharacteristic
28C3×C42×C5—41no—
29C4⋊Dic15—41no—
30#6712—42no—
31C4×Dic15—42no—
32C4×#41⋊C3D511yescharacteristic
33#5424—52no—
34#5391—51no—
35#5389—52no—
36#5386—51no—
37C2×C5×#41C2×D311yescharacteristic
38C4×C5×Q8C2×D311yescharacteristic
39C4×C5×Q8C2×D311yescharacteristic
40C4×C5×D4—31no—
41C4×C5×D4—31no—
42C5×#117—31no—
43C2×C42×C5—31no—
44#4072—32no—
45#4070—61no—
46#4070—61no—
47C22×#168—32no—
48#4016—32no—
49#4015—31no—
50#4015—31no—
51C4×Dic10—61no—
52C4×Dic10—61no—
53#3967—32no—
54#3967—32no—
55#3964—32no—
56#3964—32no—
57#3940—32no—
58#3940—32no—
59#3939—32no—
60#3939—32no—
61C4⋊#168—31no—
62C4⋊#168—31no—
63C4⋊#168—32no—
64#3076—151noSylow
65C2×C3×C4×C5—41no—
66C2×C3×C4×C5—41no—
67C2×C3×C4×C5—41no—
68C2×Dic15—42no—
69C2×Dic15—42no—
70Dic30—44no—
71C5×SL(2,𝔽3)C2×Q811yescharacteristic
72C2×#41⋊C3C2×D511yescharacteristic
73C4×Dic6—201no—
74C4×SL(2,𝔽3)C2×D511yescharacteristic
75C4×SL(2,𝔽3)C2×D511yescharacteristic
76#859—52no—
77#859—52no—
78C5×#41—32no—
79C5×#41Dic612yescomplemented
80C2×C5×Q8C22×D311yescharacteristic
81C2×C5×D4—31no—
82C22×C4×C5—31no—
83C22×C4×C5—31no—
84C22×C4×C5—31no—
85C2×Dic10—61no—
86C2×Dic10—61no—
87C5×C4⋊C4—31no—
88C5×C4⋊C4—31no—
89C5×C22⋊C4—61no—
90C42×C5—31no—
91C42×C5—31no—
92C42×C5—31no—
93C42×C5S411yescharacteristic
94C22⋊Dic5—62no—
95C4⋊Dic5—32no—
96C4⋊Dic5—32no—
97C4⋊Dic5—61no—
98C4⋊Dic5—61no—
99#683—62no—
100#683—62no—
101C4×Dic5—62no—
102C2×#168—32no—
103C2×#168—32no—
104C2×#168—64no—
105#533—151no—
106C4×#41D1511yescharacteristic
107#479—152no—
108#478—152no—
109#477—151no—
110#476—151no—
111#475—151no—
112#474—151no—
113#427—152no—
114C2×C4⋊C8—151no—
115#416—152no—
116C22×C3×C5—41no—
117C3×C4×C5—42no—
118C3×C4×C5—42no—
119C3×C4×C5—81no—
120Dic15—44no—
121Dic15—82no—
122C2×Dic6—201no—
123#41⋊C3Dic1012yescomplemented
124C2×SL(2,𝔽3)C22×D511yescharacteristic
125C3×C42—41no—
126C4⋊Dic3—201no—
127Dic3⋊C4—202no—
128C4×Dic3—202no—
129C23×C5—31no—
130C5×Q8—31no—
131C5×Q8C2×Dic611yescharacteristic
132C5×D4—32no—
133C5×D4—61no—
134C2×C4×C5—31no—
135C2×C4×C5—32no—
136C2×C4×C5—32no—
137C2×C4×C5—31no—
138C2×C4×C5—31no—
139C2×C4×C5—62no—
140C2×C4×C5—121no—
141C2×C4×C5C2×S411yescharacteristic
142C2×C4×C5C2×S411yescharacteristic
143C2×C4×C5C2×S411yescharacteristic
144C2×Dic5—62no—
145C2×Dic5—62no—
146Dic10—122no—
147Dic10—122no—
148#168—62no—
149#168—62no—
150C2×#41C2×D1511yescharacteristic
151C22×C8—152no—
152C4⋊Q8—151no—
153C4⋊Q8—151no—
154#125—152no—
155C22⋊Q8—301no—
156C22⋊Q8—301no—
157C4×Q8—301no—
158C4×Q8—301no—
159C4×Q8C2×D1511yescharacteristic
160C4×Q8C2×D1511yescharacteristic
161C4×D4—31no—
162C4×D4—31no—
163#117—31no—
164#117—152no—
165C2×C42—31no—
166#107—152no—
167#107—152no—
168#106—152no—
169#106—152no—
170C4⋊C8—151no—
171C4⋊C8—151no—
172C4⋊C8—152no—
173#103—152no—
174#103—152no—
175#102—152no—
176#102—152no—
177C2×C3×C5—41no—
178C2×C3×C5—41no—
179C2×C3×C5—41no—
180C2×C3×C4—41no—
181C2×C3×C4—41no—
182C2×C3×C4—41no—
183C2×Dic3—202no—
184C2×Dic3—202no—
185Dic6—204no—
186SL(2,𝔽3)C2×Dic1011yescharacteristic
187C22×C5—32no—
188C22×C5—61no—
189C22×C5—61no—
190C22×C5C22×S411yescharacteristic
191C4×C5—21no—
192C4×C5—31no—
193C4×C5—31no—
194C4×C5—61no—
195C4×C5—61no—
196C4×C5A4⋊Q812yes—
197C4×C5#98512yes—
198Dic5—122no—
199Dic5—122no—
200#41—32no—
201#41Dic3012yescomplemented
202C2×Q8—301no—
203C2×Q8—301no—
204C2×Q8C22×D1511yescharacteristic
205C2×D4—31no—
206C22×C4—31no—
207C22×C4—31no—
208C22×C4—31no—
209C2×C8—152no—
210C2×C8—152no—
211C2×C8—304no—
212C4⋊C4—31no—
213C4⋊C4—31no—
214C4⋊C4—152no—
215C4⋊C4—152no—
216C4⋊C4—302no—
217C4⋊C4—301no—
218C4⋊C4—302no—
219C4⋊C4—301no—
220C22⋊C4—61no—
221C22⋊C4—302no—
222C42—31no—
223C42—31no—
224C42—31no—
225C42—302no—
226C42C5⋊S411yescharacteristic
227C3×C5—41noHall
228C22×C3—41no—
229C3×C4—42no—
230C3×C4—42no—
231C3×C4—81no—
232Dic3—204no—
233Dic3—402no—
234C2×C5—62no—
235C2×C5C2×A4⋊Q811yescharacteristic
236C2×C5C2×#98511yescharacteristic
237C2×C5#592311yescharacteristic
238C23—31no—
239Q8—31no—
240Q8—602no—
241Q8—602no—
242Q8C2×Dic3011yescharacteristic
243D4—32no—
244D4—61no—
245C2×C4—31no—
246C2×C4—32no—
247C2×C4—32no—
248C2×C4—31no—
249C2×C4—31no—
250C2×C4—62no—
251C2×C4—121no—
252C2×C4—302no—
253C2×C4—302no—
254C2×C4C2×C5⋊S411yescharacteristic
255C2×C4C2×C5⋊S411yescharacteristic
256C2×C4C2×C5⋊S411yescharacteristic
257C8—302no—
258C8—302no—
259C2×C3—41no—
260C2×C3—41no—
261C2×C3—41no—
262C5#8533411yescharacteristic, complemented, Sylow
263C22—32no—
264C22—61no—
265C22—61no—
266C22C22×C5⋊S411yescharacteristic
267C4—21no—
268C4—31no—
269C4—31no—
270C4—61no—
271C4—61no—
272C4—602no—
273C4—602no—
274C4#9194812yes—
275C4#9195512yes—
276C3—41noSylow
277C2—62no—
278C2C2×#9194811yescharacteristic
279C2C2×#9195511yescharacteristic
280C2#1175690711yescharacteristic
subgroupG/H
centerC2×C4C2×C5⋊S4
commutator, cosocleC2×C5×SL(2,𝔽3)C23
FrattiniC22C22×C5⋊S4
FittingC4×C5×#41D3
socleC22×C5C22×S4
prime radicalC2×C5×#41⋊C3C22
hypercenterC42C5⋊S4
hypocenterC5×SL(2,𝔽3)C2×Q8
LCSG ▷ C2×C5×SL(2,𝔽3) ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
3. #11752110C2semidirect
4. #11752108C2semidirect
5. #11752105C2semidirect
26. C5×#41⋊C3Q8semidirect
79. C5×#41Dic6semidirect
123. #41⋊C3Dic10semidirect
201. #41Dic30semidirect
262. C5#85334semidirect

Maximal subgroups

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

subgroupindex
C4×C5×#41⋊C32
#117521432
#117521102
#117521082
#117521052
#106142383
C4×Dic304
#853345