Finite Group Databasebeta

← C2×#11751559 #14512512

Subgroups — C2×#11751559 #14512512

Order 1920.

282 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 28 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⋊(#120⋊C3)C211yesmaximal, characteristic
2#11751559C212yesmaximal, direct product factor
3C2×#64934—31nomaximal, Hall
4C2×C5×C22⋊A4C411yescharacteristic, complemented
5C2×A4⋊AGL(1,𝔽5)—41nomaximal
6C5⋊(#120⋊C3)C411yescharacteristic, complemented
7C5⋊(#120⋊C3)C2211yescharacteristic
8C2×#4625—51nomaximal, Hall
9C2×#4099D311yescharacteristic
10C2×#4013—31no—
11C2×#4011—31no—
12#64934—32no—
13#64934—32no—
14C5×C22⋊A4C2×C411yescharacteristic, complemented
15C2×D5×A4—41no—
16A4⋊AGL(1,𝔽5)—42no—
17C2×#120⋊C3—51no—
18#4625—52no—
19C25×C5Dic311yescharacteristic, complemented
20C22×C22⋊D5—31no—
21C2×C22⋊AGL(1,𝔽5)—61no—
22C2×#704—61no—
23#4099—31no—
24#4099—31no—
25#4099Dic311yescharacteristic, complemented
26#4099C2×D311yescharacteristic
27C2×C22⋊Dic5—31no—
28#4013—32no—
29#4013—61no—
30#4011—32no—
31#4011—61no—
32C2×AΣL(1,𝔽16)—151noSylow
33C2×C5×A4—41no—
34C2×C5×A4—161no—
35C2×ΓL(1,𝔽16)—161no—
36D5×A4—41no—
37D5×A4—41no—
38C2×C22⋊A4AGL(1,𝔽5)11yescharacteristic, complemented
39C2×SL(2,ℤ/4)—201no—
40#120⋊C3—51no—
41#120⋊C3—51no—
42C24×C5—31no—
43C24×C5—31no—
44C24×C5—121no—
45C24×C5—121no—
46C24×C5C2×Dic311yescharacteristic, complemented
47C23×D5S411yescharacteristic
48C22×AGL(1,𝔽5)—121no—
49C2×C22⋊D5—31no—
50C2×C22⋊D5—31no—
51C2×C22⋊D5—31no—
52C2×C22⋊D5—31no—
53C2×C22⋊D5—121no—
54C2×C22⋊D5—121no—
55C22×Dic5—31no—
56C22⋊AGL(1,𝔽5)—62no—
57C22⋊AGL(1,𝔽5)—121no—
58#704—62no—
59#704—121no—
60C2×#170—121no—
61C22⋊Dic5—31no—
62C22⋊Dic5—31no—
63C22⋊Dic5—61no—
64C2×#120—51no—
65C2×#100—151no—
66C2×#99—151no—
67AΣL(1,𝔽16)—152no—
68AΣL(1,𝔽16)—152no—
69C2×C3×D5—161no—
70C5×A4—41no—
71C5×A4—161no—
72ΓL(1,𝔽16)—162no—
73C22⋊A4C2×AGL(1,𝔽5)11yescharacteristic, complemented
74C22×A4—201no—
75SL(2,ℤ/4)—202no—
76C23×C5—31no—
77C23×C5—31no—
78C23×C5—41no—
79C23×C5—61no—
80C23×C5—61no—
81C23×C5—121no—
82C23×C5—121no—
83C23×C5—121no—
84C23×C5—121no—
85C23×C5—122no—
86C23×C5—121no—
87C23×C5—121no—
88C23×C5—121no—
89C23×C5—122no—
90C23×C5SL(2,ℤ/4)11yescharacteristic
91C22×D5—61no—
92C22×D5—61no—
93C22×D5SL(2,ℤ/4)11yescharacteristic
94C22×D5C2×S411yescharacteristic
95C2×AGL(1,𝔽5)—122no—
96C2×AGL(1,𝔽5)—241no—
97C2×AGL(1,𝔽5)—241no—
98C22⋊D5—121no—
99C22⋊D5—121no—
100C22⋊D5—121no—
101C22⋊D5—121no—
102C2×Dic5—31no—
103C2×Dic5—31no—
104C2×Dic5—61no—
105C2×Dic5—61no—
106#170—122no—
107C25ΓL(1,𝔽16)11yescharacteristic, complemented
108C22×D4—151no—
109C2×M16—301no—
110#120—51no—
111#120—51no—
112#120—151no—
113#120—151no—
114C2×C22⋊C4—151no—
115C2×C22⋊C4—301no—
116#100—152no—
117#100—301no—
118#99—152no—
119#99—301no—
120C2×C3×C5—161no—
121C3×D5—161no—
122C3×D5—161no—
123C2×A4—41no—
124C2×A4—161no—
125C2×A4—201no—
126C2×A4—201no—
127C2×Dic3—801no—
128C22×C5—31no—
129C22×C5—31no—
130C22×C5—41no—
131C22×C5—61no—
132C22×C5—61no—
133C22×C5—121no—
134C22×C5—121no—
135C22×C5—122no—
136C22×C5—121no—
137C22×C5—121no—
138C22×C5—121no—
139C22×C5—121no—
140C22×C5—122no—
141C22×C5—121no—
142C22×C5C2×SL(2,ℤ/4)11yescharacteristic
143C2×D5—41no—
144C2×D5—61no—
145C2×D5—61no—
146C2×D5—121no—
147AGL(1,𝔽5)—242no—
148Dic5—61no—
149Dic5—61no—
150C24—31no—
151C24—31no—
152C24—51no—
153C24—121no—
154C24—121no—
155C24C2×ΓL(1,𝔽16)11yescharacteristic, complemented
156C2×D4—151no—
157C2×D4—151no—
158C2×D4—151no—
159C2×D4—151no—
160C2×D4—601no—
161C2×D4—601no—
162C22×C4—151no—
163C22×C4—601no—
164M16—302no—
165M16—601no—
166C2×C8—601no—
167C22⋊C4—151no—
168C22⋊C4—151no—
169C22⋊C4—301no—
170C22⋊C4—302no—
171C22⋊C4—601no—
172C3×C5—161noHall
173C22×C3—801no—
174A4—41no—
175A4—161no—
176Dic3—802no—
177C2×C5—31no—
178C2×C5—31no—
179C2×C5—121no—
180C2×C5—121no—
181C2×C5#462511yescharacteristic, complemented
182D5—41no—
183D5—41no—
184C23—31no—
185C23—31no—
186C23—41no—
187C23—51no—
188C23—51no—
189C23—61no—
190C23—61no—
191C23—121no—
192C23—121no—
193C23—121no—
194C23—121no—
195C23—122no—
196C23—121no—
197C23—121no—
198C23—121no—
199C23—122no—
200C23—301no—
201C23—301no—
202C23A4⋊AGL(1,𝔽5)11yescharacteristic
203D4—601no—
204D4—601no—
205D4—601no—
206D4—601no—
207C2×C4—151no—
208C2×C4—151no—
209C2×C4—301no—
210C2×C4—301no—
211C2×C4—602no—
212C2×C4—1201no—
213C2×C4—1201no—
214C8—602no—
215C2×C3—161no—
216C2×C3—801no—
217C2×C3—801no—
218C5C2×#462511yescharacteristic, complemented, Sylow
219C22—31no—
220C22—31no—
221C22—41no—
222C22—61no—
223C22—61no—
224C22—121no—
225C22—121no—
226C22—122no—
227C22—121no—
228C22—121no—
229C22—121no—
230C22—121no—
231C22—122no—
232C22—121no—
233C22—201no—
234C22—301no—
235C22—301no—
236C22—601no—
237C22C2×A4⋊AGL(1,𝔽5)11yescharacteristic
238C4—301no—
239C4—301no—
240C4—1202no—
241C3—161noSylow
242C2—31no—
243C2—31no—
244C2—121no—
245C2—121no—
246C2—201no—
247C2—201no—
248C2#1175155911yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2#11751559
commutator, hypocenterC5×C22⋊A4C2×C4
FrattiniC22C2×A4⋊AGL(1,𝔽5)
FittingC25×C5Dic3
socleC23×C5SL(2,ℤ/4)
prime radicalC2×C5⋊(#120⋊C3)C2
cosocleC5⋊(#120⋊C3)C22
LCSG ▷ C5×C22⋊A4
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #11751559C2direct (N × H)
4. C2×C5×C22⋊A4C4semidirect
6. C5⋊(#120⋊C3)C4semidirect
14. C5×C22⋊A4C2×C4semidirect
19. C25×C5Dic3semidirect
25. #4099Dic3semidirect
38. C2×C22⋊A4AGL(1,𝔽5)semidirect
46. C24×C5C2×Dic3semidirect
73. C22⋊A4C2×AGL(1,𝔽5)semidirect
107. C25ΓL(1,𝔽16)semidirect
155. C24C2×ΓL(1,𝔽16)semidirect
181. C2×C5#4625semidirect
218. C5C2×#4625semidirect
248. C2#11751559direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5⋊(#120⋊C3)2
#117515592
C2×#649343
C2×A4⋊AGL(1,𝔽5)4
C2×#46255