Finite Group Databasebeta

← C2×#11756725 #14514380

Subgroups — C2×#11756725 #14514380

Order 1920.

686 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 686 conjugacy classes of subgroups — too many to draw. Only its 88 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
2#11756725C214yesmaximal, direct product factor
3C2×#91886C212yesmaximal, complemented
4C2×#65794—31nomaximal, Hall
5C2×C5×#41⋊C3C411yescharacteristic, complemented
6C2×C4×ΓL(1,𝔽16)—41nomaximal
7D5×#41⋊C3C412yescomplemented
8D5×#41⋊C3C2212yes—
9C2×D5×SL(2,𝔽3)C2211yescharacteristic
10C2×C5⋊(#41⋊C3)C411yescharacteristic, complemented
11#91886C2214yescomplemented
12C2×#5424—51nomaximal, Hall
13C2×D5×#41D311yescharacteristic
14C2×#4130—31no—
15C22×D5⋊C8—31no—
16#65794—34no—
17#65794—34no—
18C2×#4009—32no—
19C2×#4007—32no—
20C22×ΓL(1,𝔽16)—42no—
21C2×C3×C4×D5—41no—
22C5×#41⋊C3C2×C412yescomplemented
23C2×C5×SL(2,𝔽3)C2×C411yescharacteristic
24C4×ΓL(1,𝔽16)—44no—
25D5×SL(2,𝔽3)C2×C411yescharacteristic
26D5×SL(2,𝔽3)C2311yescharacteristic
27C5⋊(#41⋊C3)C2×C412yescomplemented
28C22×#41⋊C3—51no—
29#5424—54no—
30C2×#859—52no—
31C2×C5×#41Dic311yescharacteristic, complemented
32D5×#41—32no—
33D5×#41—32no—
34D5×#41Dic312yescomplemented
35D5×#41C2×D312yes—
36C2×#713Dic311yescharacteristic, complemented
37C2×Q8×D5C2×D311yescharacteristic
38C2×#711—31no—
39C2×D4×D5—31no—
40C2×#709—31no—
41C22×C4×D5—31no—
42C2×C22⋊AGL(1,𝔽5)—61no—
43C22×#170—61no—
44#4130—34no—
45#4130—62no—
46C2×C4⋊AGL(1,𝔽5)—32no—
47C2×C4×AGL(1,𝔽5)—61no—
48C2×D5⋊C8—34no—
49C2×D5⋊C8—32no—
50C2×D5⋊C8—61no—
51C2×D5⋊C8—62no—
52#4009—34no—
53#4009—34no—
54#4007—38no—
55C2×#416—151noSylow
56C22×C3×D5—41no—
57C2×ΓL(1,𝔽16)—44no—
58C2×ΓL(1,𝔽16)—48no—
59C2×C3×C4×C5—41no—
60C2×C3×Dic5—41no—
61C3×C4×D5—42no—
62C3×C4×D5—42no—
63C5×SL(2,𝔽3)C22×C411yescharacteristic
64C2×#41⋊C3—52no—
65C2×#41⋊C3—52no—
66C2×#41⋊C3—51no—
67C2×#41⋊C3AGL(1,𝔽5)11yescharacteristic, complemented
68C22×SL(2,𝔽3)—51no—
69C2×C4×Dic3—201no—
70#859—54no—
71C23×D5—31no—
72C22×AGL(1,𝔽5)—62no—
73C5×#41—32no—
74C5×#41C2×Dic312yescomplemented
75C2×C5×Q8C2×Dic311yescharacteristic
76C2×C5×D4—31no—
77C22×C4×C5—31no—
78C2×C22⋊D5—61no—
79C22×Dic5—31no—
80#713—32no—
81#713C2×Dic312yescomplemented
82Q8×D5—31no—
83Q8×D5—31no—
84Q8×D5C2×Dic311yescharacteristic
85Q8×D5C22×D311yescharacteristic
86#711—32no—
87#711—32no—
88#711—62no—
89D4×D5—32no—
90D4×D5—32no—
91D4×D5—61no—
92D4×D5—61no—
93#709—32no—
94#709—32no—
95#709—62no—
96C2×D20—31no—
97C2×C4×D5—31no—
98C2×C4×D5—31no—
99C2×C4×D5—31no—
100C2×C4×D5—32no—
101C2×C4×D5—32no—
102C2×C4×D5—32no—
103C2×C4×D5—32no—
104C2×C4×D5S411yescharacteristic
105C2×Dic10—31no—
106C22⋊AGL(1,𝔽5)—64no—
107C2×#170—62no—
108C2×#170—64no—
109C4⋊AGL(1,𝔽5)—34no—
110C4⋊AGL(1,𝔽5)—62no—
111C4×AGL(1,𝔽5)—64no—
112D5⋊C8—34no—
113D5⋊C8—62no—
114D5⋊C8—64no—
115C22×#41—51no—
116C23×C8—151no—
117C2×#117—151no—
118#416—154no—
119#416—154no—
120C2×#103—152no—
121C2×#102—152no—
122C22×C3×C5—41no—
123C2×C3×D5—44no—
124C2×C3×D5—41no—
125C2×C3×D5—41no—
126ΓL(1,𝔽16)—48no—
127C3×C4×C5—42no—
128C3×Dic5—42no—
129C22×C3×C4—201no—
130C22×Dic3—202no—
131#41⋊C3—52no—
132#41⋊C3C2×AGL(1,𝔽5)12yescomplemented
133C2×SL(2,𝔽3)—51no—
134C2×SL(2,𝔽3)—51no—
135C2×SL(2,𝔽3)C2×AGL(1,𝔽5)11yescharacteristic
136C4×Dic3—204no—
137C23×C5—31no—
138C22×D5—31no—
139C22×D5—32no—
140C22×D5—32no—
141C22×D5—64no—
142C22×D5C2×S411yescharacteristic
143C2×AGL(1,𝔽5)—64no—
144C2×AGL(1,𝔽5)—124no—
145C5×Q8—31no—
146C5×Q8C22×Dic311yescharacteristic
147C5×D4—32no—
148C5×D4—61no—
149C2×C4×C5—31no—
150C2×C4×C5—32no—
151C2×C4×C5—32no—
152C2×C4×C5SL(2,ℤ/4)11yescharacteristic
153C22⋊D5—62no—
154C22⋊D5—62no—
155C2×Dic5—31no—
156C2×Dic5—32no—
157C2×Dic5—32no—
158C2×Dic5SL(2,ℤ/4)11yescharacteristic
159D20—32no—
160D20—61no—
161C4×D5—31no—
162C4×D5—31no—
163C4×D5—31no—
164C4×D5—31no—
165C4×D5—32no—
166C4×D5—32no—
167C4×D5—32no—
168C4×D5—32no—
169C4×D5SL(2,ℤ/4)12yes—
170C4×D5C2×S412yes—
171Dic10—31no—
172Dic10—31no—
173Dic10—61no—
174#170—64no—
175C2×#41—52no—
176C2×#41—52no—
177C2×#41—51no—
178C2×#41—151no—
179C2×#41—151no—
180C2×#41—152no—
181C2×#41—152no—
182C2×#41ΓL(1,𝔽16)11yescharacteristic, complemented
183C22×Q8—51no—
184C22×D4—151no—
185C23×C4—151no—
186C22×C8—152no—
187C22×C8—154no—
188C22×C8—302no—
189C22×C8—301no—
190C22×C8—301no—
191#117—154no—
192#117—302no—
193C2×C4⋊C4—152no—
194C2×C22⋊C4—301no—
195C2×C42—301no—
196#103—154no—
197#103—154no—
198#102—158no—
199C2×C3×C5—41no—
200C2×C3×C5—42no—
201C3×D5—42no—
202C3×D5—42no—
203C23×C3—201no—
204C2×C3×C4—41no—
205C2×C3×C4—202no—
206C2×C3×C4—202no—
207C2×C3×C4—201no—
208C2×Dic3—204no—
209C2×Dic3—208no—
210SL(2,𝔽3)C22×AGL(1,𝔽5)11yescharacteristic
211C22×C5—32no—
212C22×C5—62no—
213C22×C5C2×SL(2,ℤ/4)11yescharacteristic
214C2×D5—32no—
215C2×D5—62no—
216C2×D5—64no—
217C2×D5—64no—
218C2×D5#98514yes—
219C2×D5C2×SL(2,ℤ/4)11yescharacteristic
220C2×D5C22×S411yescharacteristic
221AGL(1,𝔽5)—124no—
222C4×C5—31no—
223C4×C5—31no—
224C4×C5C2×SL(2,ℤ/4)12yes—
225Dic5—31no—
226Dic5—31no—
227Dic5C2×SL(2,ℤ/4)12yes—
228C24—151no—
229#41—32no—
230#41—52no—
231#41—152no—
232#41—152no—
233#41—152no—
234#41—152no—
235#41—152no—
236#41—302no—
237#41—302no—
238#41C2×ΓL(1,𝔽16)12yescomplemented
239C2×Q8—51no—
240C2×Q8—51no—
241C2×Q8—151no—
242C2×Q8—151no—
243C2×Q8—151no—
244C2×Q8C2×ΓL(1,𝔽16)11yescharacteristic
245C2×D4—31no—
246C2×D4—151no—
247C2×D4—152no—
248C2×D4—152no—
249C2×D4—301no—
250C2×D4—301no—
251C2×D4—301no—
252C22×C4—31no—
253C22×C4—51no—
254C22×C4—152no—
255C22×C4—152no—
256C22×C4—152no—
257C22×C4—151no—
258C22×C4—152no—
259C22×C4—151no—
260C22×C4—151no—
261C22×C4—151no—
262C22×C4—302no—
263C2×C8—154no—
264C2×C8—302no—
265C2×C8—304no—
266C2×C8—304no—
267C2×C8—302no—
268C4⋊C4—154no—
269C4⋊C4—302no—
270C22⋊C4—304no—
271C42—304no—
272C3×C5—41noHall
273C22×C3—41no—
274C22×C3—201no—
275C22×C3—204no—
276C22×C3—201no—
277C3×C4—42no—
278C3×C4—202no—
279Dic3—208no—
280C2×C5—62no—
281C2×C5#542412yescomplemented
282C2×C5C22×SL(2,ℤ/4)11yescharacteristic
283D5—62no—
284D5#542412yescomplemented
285D5C2×#98512yes—
286C23—31no—
287C23—51no—
288C23—152no—
289C23—152no—
290C23—151no—
291C23—304no—
292Q8—31no—
293Q8—151no—
294Q8—151no—
295Q8—301no—
296Q8C22×ΓL(1,𝔽16)11yescharacteristic
297D4—32no—
298D4—61no—
299D4—152no—
300D4—301no—
301D4—302no—
302D4—302no—
303C2×C4—31no—
304C2×C4—32no—
305C2×C4—32no—
306C2×C4—51no—
307C2×C4—52no—
308C2×C4—52no—
309C2×C4—152no—
310C2×C4—152no—
311C2×C4—151no—
312C2×C4—151no—
313C2×C4—151no—
314C2×C4—151no—
315C2×C4—152no—
316C2×C4—152no—
317C2×C4—151no—
318C2×C4—152no—
319C2×C4—152no—
320C2×C4—304no—
321C2×C4—604no—
322C2×C4A4⋊AGL(1,𝔽5)11yescharacteristic
323C8—304no—
324C2×C3—41no—
325C2×C3—42no—
326C2×C3—202no—
327C2×C3—202no—
328C5C2×#542411yescharacteristic, complemented, Sylow
329C22—32no—
330C22—51no—
331C22—51no—
332C22—54no—
333C22—62no—
334C22—152no—
335C22—304no—
336C22—304no—
337C22—302no—
338C22C2×A4⋊AGL(1,𝔽5)11yescharacteristic
339C4—31no—
340C4—31no—
341C4—52no—
342C4—151no—
343C4—151no—
344C4—604no—
345C4C2×A4⋊AGL(1,𝔽5)12yes—
346C3—41noSylow
347C2—52no—
348C2—52no—
349C2—62no—
350C2—302no—
351C2#1175672512yesdirect product factor
352C2C22×A4⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, hypercenterC2×C4A4⋊AGL(1,𝔽5)
commutator, hypocenterC5×SL(2,𝔽3)C22×C4
FrattiniC2C22×A4⋊AGL(1,𝔽5)
FittingC2×C5×#41Dic3
socleC22×C5C2×SL(2,ℤ/4)
prime radicalC2×D5×#41⋊C3C2
cosocleD5×SL(2,𝔽3)C23
LCSG ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11756725C2direct (N × H)
3. C2×#91886C2semidirect
5. C2×C5×#41⋊C3C4semidirect
7. D5×#41⋊C3C4semidirect
10. C2×C5⋊(#41⋊C3)C4semidirect
11. #91886C22semidirect
22. C5×#41⋊C3C2×C4semidirect
27. C5⋊(#41⋊C3)C2×C4semidirect
31. C2×C5×#41Dic3semidirect
34. D5×#41Dic3semidirect
36. C2×#713Dic3semidirect
67. C2×#41⋊C3AGL(1,𝔽5)semidirect
74. C5×#41C2×Dic3semidirect
81. #713C2×Dic3semidirect
132. #41⋊C3C2×AGL(1,𝔽5)semidirect
182. C2×#41ΓL(1,𝔽16)semidirect
238. #41C2×ΓL(1,𝔽16)semidirect
281. C2×C5#5424semidirect
284. D5#5424semidirect
328. C5C2×#5424semidirect
351. C2#11756725direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×#41⋊C32
#117567252
C2×#918862
C2×#657943
C2×C4×ΓL(1,𝔽16)4
C2×#54245