Finite Group Databasebeta

← #14511629

Subgroups — #14511629

Order 1920.

294 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 25 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×C5⋊#857C211yesmaximal, characteristic
2#65224⋊C3C211yesmaximal, characteristic, complemented
3C5×#4623C211yesmaximal, characteristic, complemented
4#10599564—31nomaximal, Hall
5#91901—41nomaximal
6C2×C5×C42⋊C3C2211yescharacteristic
7C5⋊#857C412yescomplemented
8#857⋊C4—51nomaximal, Hall
9#65857—31no—
10#65422—31no—
11#65284—31no—
12#65224D311yescharacteristic, complemented
13C2×#3937—31no—
14C5×#339—31no—
15#64774—31no—
16C2×C5⋊S4—41no—
17A4×Dic5—41no—
18C5×SL(2,ℤ/4)—41no—
19C5×C42⋊C3C2×C411yescharacteristic, complemented
20C2×#857—51no—
21#384⋊C3—51no—
22#4623D511yescharacteristic, complemented
23C2×#709—31no—
24C2×C5×M16—31no—
25C5×#117—31no—
26C2×C42×C5C2×D311yescharacteristic
27C2×C4⋊Dic5—31no—
28C2×C4⋊Dic5—31no—
29C2×#681—31no—
30#4038—61no—
31D5×C4⋊C4—61no—
32#4027—61no—
33#4027—61no—
34C4×D20—61no—
35C4×Dic10—61no—
36#3953—61no—
37#3948—61no—
38#3940—61no—
39#3939—61no—
40#3937—32no—
41#3937—32no—
42#1859—151noSylow
43C2×C5×A4—41no—
44C5⋊S4—42no—
45#1200—161no—
46C4×S4—201no—
47C2×C42⋊C3C2×D511yescharacteristic
48#857—52no—
49C22×C4×C5—31no—
50C2×C22⋊D5—61no—
51C22×Dic5—31no—
52C22×Dic5S411yescharacteristic
53#709—32no—
54#709—32no—
55#709—61no—
56#709—61no—
57C2×D20—31no—
58C2×C4×D5—61no—
59C2×C4×D5—61no—
60C2×C4×D5—61no—
61C2×Dic10—31no—
62C5×M16—61no—
63C5×M16—61no—
64C2×C5×C8—61no—
65C5×C4⋊C4—31no—
66C5×C4⋊C4—31no—
67C5×C22⋊C4—61no—
68C42×C5—31no—
69C42×C5—61no—
70C42×C5C4×D311yescharacteristic, complemented
71#685—61no—
72#685—61no—
73C4⋊Dic5—61no—
74C4⋊Dic5—61no—
75C4⋊Dic5—61no—
76C4⋊Dic5—61no—
77#683—61no—
78#683—61no—
79C4×Dic5—61no—
80C4×Dic5—61no—
81#681—32no—
82#681—61no—
83C2×#168—61no—
84#520—151no—
85#428—151no—
86C2×#104—151no—
87#417—151no—
88#384—51no—
89#343—151no—
90#339—31no—
91C2×D15—161no—
92C5×A4—41no—
93C3×Dic5—161no—
94C5×Dic3—161no—
95C2×S4—201no—
96C4×A4—201no—
97SL(2,ℤ/4)—41no—
98C42⋊C3C4×D511yescharacteristic, complemented
99C23×C5C2×S411yescharacteristic
100C22×D5—61no—
101C2×C4×C5—31no—
102C2×C4×C5—31no—
103C2×C4×C5—31no—
104C2×C4×C5—31no—
105C2×C4×C5—31no—
106C2×C4×C5—31no—
107C2×C4×C5—61no—
108C2×C4×C5—61no—
109C22⋊D5—62no—
110C22⋊D5—62no—
111C2×Dic5—61no—
112C2×Dic5—61no—
113C2×Dic5—61no—
114C2×Dic5—121no—
115D20—32no—
116D20—61no—
117C4×D5—62no—
118C4×D5—62no—
119C4×D5—241no—
120C4×D5—241no—
121Dic10—32no—
122Dic10—61no—
123C5×C8—121no—
124#168—62no—
125C2×#41—151no—
126C2×M16—31no—
127C2×M16—151no—
128C4×Q8—301no—
129C4×D4—301no—
130C4×D4—301no—
131C4×D4—301no—
132#117—31no—
133#117—301no—
134C2×C4⋊C4—151no—
135C2×C4⋊C4—151no—
136C2×C4⋊C4—301no—
137C2×C42D3×D511yescharacteristic
138#107—301no—
139#106—301no—
140#104—152no—
141#104—152no—
142#103—301no—
143#102—301no—
144C2×C3×C5—161no—
145D15—162no—
146C2×A4—41no—
147S4—202no—
148C4×D3—801no—
149C22×C5—31no—
150C22×C5—31no—
151C22×C5C4×S411yescharacteristic
152C2×D5—62no—
153C2×D5—121no—
154C2×D5—121no—
155C4×C5—31no—
156C4×C5—31no—
157C4×C5—31no—
158C4×C5—31no—
159C4×C5—121no—
160C4×C5—121no—
161Dic5—41no—
162Dic5—62no—
163Dic5—121no—
164#41—152no—
165#41—152no—
166#41—301no—
167#41—301no—
168C2×Q8—151no—
169C2×D4—151no—
170C2×D4—301no—
171C22×C4—31no—
172C22×C4—51no—
173C22×C4—151no—
174C22×C4—301no—
175C22×C4—301no—
176C22×C4—301no—
177M16—61no—
178M16—61no—
179M16—152no—
180M16—301no—
181C2×C8—61no—
182C2×C8—301no—
183C4⋊C4—31no—
184C4⋊C4—31no—
185C4⋊C4—301no—
186C4⋊C4—301no—
187C4⋊C4—301no—
188C4⋊C4—301no—
189C4⋊C4—301no—
190C4⋊C4—301no—
191C22⋊C4—61no—
192C22⋊C4—301no—
193C22⋊C4—301no—
194C42—31no—
195C42—61no—
196C42—301no—
197C42—301no—
198C42#120011yescharacteristic, complemented
199C3×C5—161noHall
200C2×D3—801no—
201A4—41no—
202C3×C4—801no—
203Dic3—161no—
204C2×C5—31no—
205C2×C5—31no—
206C2×C5#857⋊C211yescharacteristic
207D5—122no—
208C23—301no—
209C23D5×S411yescharacteristic
210Q8—152no—
211Q8—301no—
212D4—152no—
213D4—301no—
214D4—302no—
215D4—302no—
216C2×C4—31no—
217C2×C4—31no—
218C2×C4—31no—
219C2×C4—31no—
220C2×C4—31no—
221C2×C4—31no—
222C2×C4—61no—
223C2×C4—61no—
224C2×C4—302no—
225C2×C4—302no—
226C2×C4—301no—
227C2×C4—301no—
228C2×C4—301no—
229C2×C4—601no—
230C2×C4—1201no—
231C2×C4—1201no—
232C8—121no—
233C8—302no—
234C2×C3—161no—
235D3—802no—
236C5#857⋊C411yescharacteristic, complemented, Sylow
237C22—31no—
238C22—31no—
239C22—302no—
240C22—601no—
241C22—601no—
242C22#9190111yescharacteristic
243C4—31no—
244C4—31no—
245C4—31no—
246C4—31no—
247C4—121no—
248C4—121no—
249C4—201no—
250C4—302no—
251C4—601no—
252C3—161noSylow
253C2—31no—
254C2—31no—
255C2—602no—
256C2#857⋊D511yescharacteristic
subgroupG/H
center, hypercenterC2#857⋊D5
commutator, hypocenterC5×C42⋊C3C2×C4
FrattiniC23D5×S4
FittingC2×C42×C5C2×D3
socleC23×C5C2×S4
prime radicalC2×C5⋊#857C2
cosocleC2×C5×C42⋊C3C22
LCSG ▷ C5×C42⋊C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #65224⋊C3C2semidirect
3. C5×#4623C2semidirect
7. C5⋊#857C4semidirect
12. #65224D3semidirect
19. C5×C42⋊C3C2×C4semidirect
22. #4623D5semidirect
70. C42×C5C4×D3semidirect
98. C42⋊C3C4×D5semidirect
198. C42#1200semidirect
236. C5#857⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C5⋊#8572
#65224⋊C32
C5×#46232
#105995643
#919014
#857⋊C45