Finite Group Databasebeta

← (C2×AGL(1,𝔽5))⋊(#41⋊C3) #14512585

Subgroups — (C2×AGL(1,𝔽5))⋊(#41⋊C3) #14512585

Order 1920.

474 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 60 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×D5×#41⋊C3C211yesmaximal, characteristic
2C2×AGL(1,𝔽5)×SL(2,𝔽3)C212yesmaximal, complemented
3#10617558C311yesmaximal, characteristic, complemented, Hall
4C2×C5×#41⋊C3C411yescharacteristic, complemented
5D5×#41⋊C3—22no—
6C2×D5×SL(2,𝔽3)C2211yescharacteristic
7C2×C5⋊(#41⋊C3)C411yescharacteristic, complemented
8AGL(1,𝔽5)×SL(2,𝔽3)—22no—
9C3×(C2×AGL(1,𝔽5))⋊C4—41nomaximal
10#2341⋊C3—51nomaximal, Hall
11C2×D5×#41C2×C311yescharacteristic
12C2×Q8×AGL(1,𝔽5)C2×C312yes—
13#65780—32no—
14#65765—31no—
15C4×C22⋊AGL(1,𝔽5)—31no—
16C22×C3×AGL(1,𝔽5)—42no—
17C2×C3×C4×D5—41no—
18C5×#41⋊C3—21no—
19C2×C5×SL(2,𝔽3)C2×C411yescharacteristic
20D5×SL(2,𝔽3)D412yes—
21C5⋊(#41⋊C3)—21no—
22C22×#41⋊C3—51no—
23C2×C4×SL(2,𝔽3)—52no—
24C2×C5×#41C3×C411yescharacteristic, complemented
25D5×#41—22no—
26D5×#41—62no—
27C2×#713C3×C411yescharacteristic, complemented
28C2×Q8×D5C22×C311yescharacteristic
29C2×#711—31no—
30C2×D4×D5—31no—
31C2×#709—31no—
32C22×C4×D5—31no—
33C2×C22⋊AGL(1,𝔽5)—32no—
34C2×C22⋊AGL(1,𝔽5)—32no—
35Q8×AGL(1,𝔽5)—22no—
36Q8×AGL(1,𝔽5)—62no—
37C2×C4⋊AGL(1,𝔽5)—32no—
38C2×C4×AGL(1,𝔽5)—32no—
39(C2×AGL(1,𝔽5))⋊C4—31no—
40(C2×AGL(1,𝔽5))⋊C4A411yescharacteristic
41#2341—51noSylow
42C22×C3×D5—41no—
43C2×C3×AGL(1,𝔽5)—44no—
44C2×C3×AGL(1,𝔽5)—82no—
45C2×C3×AGL(1,𝔽5)—82no—
46C2×C3×C4×C5—41no—
47C2×C3×Dic5—41no—
48C3×C4×D5—82no—
49C5×SL(2,𝔽3)C22⋊C411yescharacteristic, complemented
50C2×#41⋊C3—51no—
51C2×#41⋊C3—102no—
52C2×#41⋊C3AGL(1,𝔽5)11yescharacteristic, complemented
53C22×SL(2,𝔽3)—51no—
54C4×SL(2,𝔽3)—102no—
55C3×#95—201no—
56C23×D5—31no—
57C22×AGL(1,𝔽5)—32no—
58C22×AGL(1,𝔽5)C2×A412yes—
59C5×#41—21no—
60C5×#41—61no—
61C2×C5×Q8C2×C3×C411yescharacteristic
62C2×C5×D4—31no—
63C22×C4×C5—31no—
64C2×C22⋊D5—32no—
65C22×Dic5—31no—
66#713—21no—
67#713—61no—
68Q8×D5—32no—
69Q8×D5C3×D412yes—
70#711—62no—
71#711—62no—
72D4×D5—62no—
73D4×D5—62no—
74#709—62no—
75#709—62no—
76C2×D20—31no—
77C2×C4×D5—31no—
78C2×C4×D5—31no—
79C2×C4×D5—31no—
80C2×C4×D5—62no—
81C2×C4×D5—62no—
82C2×C4×D5C2×A411yescharacteristic
83C2×Dic10—31no—
84C22⋊AGL(1,𝔽5)—64no—
85C22⋊AGL(1,𝔽5)—122no—
86C4⋊AGL(1,𝔽5)—62no—
87C4⋊AGL(1,𝔽5)—62no—
88C4×AGL(1,𝔽5)—62no—
89C4×AGL(1,𝔽5)—62no—
90C22×#41—51no—
91C2×C4×Q8—52no—
92#390—152no—
93#380—151no—
94C4×C22⋊C4—151no—
95C22×C3×C5—41no—
96C2×C3×D5—42no—
97C2×C3×D5—42no—
98C2×C3×D5—41no—
99C2×C3×D5—41no—
100C3×AGL(1,𝔽5)—84no—
101C3×C4×C5—81no—
102C3×Dic5—81no—
103C22×C3×C4—201no—
104C22×C3×C4—202no—
105#41⋊C3—21no—
106#41⋊C3—101no—
107C2×SL(2,𝔽3)—52no—
108C2×SL(2,𝔽3)C2×AGL(1,𝔽5)11yescharacteristic
109C23×C5—31no—
110C22×D5—31no—
111C22×D5—62no—
112C22×D5—62no—
113C22×D5—61no—
114C22×D5—61no—
115C22×D5C22×A411yescharacteristic
116C2×AGL(1,𝔽5)—22no—
117C2×AGL(1,𝔽5)—22no—
118C2×AGL(1,𝔽5)—62no—
119C2×AGL(1,𝔽5)—62no—
120C2×AGL(1,𝔽5)—62no—
121C2×AGL(1,𝔽5)#41⋊C314yescomplemented
122C5×Q8—31no—
123C5×Q8C3×C22⋊C411yescharacteristic
124C5×D4—61no—
125C5×D4—61no—
126C2×C4×C5—31no—
127C2×C4×C5—61no—
128C2×C4×C5—61no—
129C2×C4×C5C4×A411yescharacteristic
130C22⋊D5—64no—
131C2×Dic5—31no—
132C2×Dic5—62no—
133C2×Dic5C4×A411yescharacteristic
134D20—61no—
135D20—61no—
136C4×D5—22no—
137C4×D5—32no—
138C4×D5—32no—
139C4×D5—61no—
140C4×D5—61no—
141C4×D5—62no—
142Dic10—32no—
143Dic10—32no—
144C2×#41—51no—
145C2×#41—102no—
146C2×#41—151no—
147C2×#41—151no—
148C2×#41—302no—
149C2×#41C3×AGL(1,𝔽5)11yescharacteristic, complemented
150C22×Q8—51no—
151C22×D4—151no—
152C23×C4—151no—
153C4×Q8—102no—
154C4×Q8—302no—
155C2×C4⋊C4—152no—
156C2×C22⋊C4—152no—
157C2×C22⋊C4—152no—
158C2×C42—152no—
159#95—51no—
160#95—151no—
161C2×C3×C5—41no—
162C2×C3×C5—41no—
163C2×C3×C5—41no—
164C3×D5—42no—
165C3×D5—42no—
166C23×C3—201no—
167C2×C3×C4—41no—
168C2×C3×C4—201no—
169C2×C3×C4—204no—
170C2×C3×C4—402no—
171C2×C3×C4—402no—
172C2×C3×C4—402no—
173SL(2,𝔽3)C22⋊AGL(1,𝔽5)11yescharacteristic, complemented
174C22×C5—61no—
175C22×C5—61no—
176C22×C5—61no—
177C22×C5C2×C4×A411yescharacteristic
178C2×D5—61no—
179C2×D5—61no—
180C2×D5—61no—
181C2×D5—122no—
182C2×D5—122no—
183C2×D5D4×A412yes—
184C2×D5C2×#41⋊C312yes—
185C2×D5#99411yescharacteristic
186C2×D52−1+4⋊C311yescharacteristic
187AGL(1,𝔽5)—24no—
188AGL(1,𝔽5)—122no—
189C4×C5—21no—
190C4×C5—31no—
191C4×C5—31no—
192Dic5—21no—
193Dic5—32no—
194C24—151no—
195#41—21no—
196#41—61no—
197#41—101no—
198#41—302no—
199#41—302no—
200#41—302no—
201#41—302no—
202#41—301no—
203C2×Q8—52no—
204C2×Q8—151no—
205C2×Q8—152no—
206C2×Q8C2×C3×AGL(1,𝔽5)11yescharacteristic
207C2×D4—31no—
208C2×D4—151no—
209C2×D4—152no—
210C2×D4—302no—
211C2×D4—302no—
212C22×C4—31no—
213C22×C4—52no—
214C22×C4—51no—
215C22×C4—151no—
216C22×C4—151no—
217C22×C4—151no—
218C22×C4—151no—
219C22×C4—152no—
220C22×C4—302no—
221C22×C4—302no—
222C4⋊C4—302no—
223C4⋊C4—302no—
224C22⋊C4—304no—
225C22⋊C4—602no—
226C42—302no—
227C42—302no—
228C3×C5—41noHall
229C22×C3—41no—
230C22×C3—202no—
231C22×C3—201no—
232C22×C3—202no—
233C22×C3—201no—
234C3×C4—81no—
235C3×C4—401no—
236C3×C4—404no—
237C2×C5—121no—
238C2×C5A4×C22⋊C411yescharacteristic
239C2×C5C4×#41⋊C311yescharacteristic
240C2×C5#520⋊C311yescharacteristic
241D5—121no—
242D5#548⋊C312yes—
243D5C4⋊(#41⋊C3)12yes—
244C23—31no—
245C23—51no—
246C23—151no—
247C23—302no—
248C23—301no—
249C23—302no—
250C23—301no—
251Q8—31no—
252Q8—152no—
253Q8—152no—
254Q8C3×C22⋊AGL(1,𝔽5)11yescharacteristic
255D4—61no—
256D4—61no—
257D4—301no—
258D4—301no—
259D4—304no—
260C2×C4—31no—
261C2×C4—54no—
262C2×C4—51no—
263C2×C4—61no—
264C2×C4—61no—
265C2×C4—102no—
266C2×C4—102no—
267C2×C4—102no—
268C2×C4—152no—
269C2×C4—152no—
270C2×C4—151no—
271C2×C4—302no—
272C2×C4—301no—
273C2×C4—301no—
274C2×C4—302no—
275C2×C4—302no—
276C2×C4—302no—
277C2×C4—302no—
278C2×C4A4×AGL(1,𝔽5)11yescharacteristic
279C2×C3—41no—
280C2×C3—41no—
281C2×C3—41no—
282C2×C3—202no—
283C2×C3—202no—
284C5#2341⋊C311yescharacteristic, complemented, Sylow
285C22—52no—
286C22—51no—
287C22—51no—
288C22—52no—
289C22—61no—
290C22—61no—
291C22—61no—
292C22—301no—
293C22—301no—
294C22—301no—
295C22—602no—
296C22—602no—
297C22C2×A4×AGL(1,𝔽5)11yescharacteristic
298C4—21no—
299C4—31no—
300C4—31no—
301C4—104no—
302C4—101no—
303C4—152no—
304C4—602no—
305C3—41noSylow
306C2—52no—
307C2—52no—
308C2—121no—
309C2—601no—
310C2AGL(1,𝔽5)×#41⋊C311yescharacteristic
311C2#66266⋊C311yescharacteristic
312C2A4×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C2×A4×AGL(1,𝔽5)
commutatorC2×C5×Q8C2×C3×C4
FittingC2×C5×#41C3×C4
socleC22×C5C2×C4×A4
prime radicalC2×D5×#41⋊C3C2
cosocleC2×Q8×D5C22×C3
hypercenterC2×C4A4×AGL(1,𝔽5)
hypocenterC5×Q8C3×C22⋊C4
LCSG ▷ C2×C5×Q8 ▷ C5×Q8
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×AGL(1,𝔽5)×SL(2,𝔽3)C2semidirect
3. #10617558C3semidirect
4. C2×C5×#41⋊C3C4semidirect
7. C2×C5⋊(#41⋊C3)C4semidirect
24. C2×C5×#41C3×C4semidirect
27. C2×#713C3×C4semidirect
49. C5×SL(2,𝔽3)C22⋊C4semidirect
52. C2×#41⋊C3AGL(1,𝔽5)semidirect
121. C2×AGL(1,𝔽5)#41⋊C3semidirect
149. C2×#41C3×AGL(1,𝔽5)semidirect
173. SL(2,𝔽3)C22⋊AGL(1,𝔽5)semidirect
284. C5#2341⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#41⋊C32
C2×AGL(1,𝔽5)×SL(2,𝔽3)2
#106175583
C3×(C2×AGL(1,𝔽5))⋊C44
#2341⋊C35