Finite Group Databasebeta

← C4×#64928 #13025821

Subgroups — C4×#64928 #13025821

Order 1280.

584 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 106 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×#4093C211yesmaximal, characteristic
2C2×#64928C212yesmaximal
3C4×#3999C212yesmaximal
4#10598723C212yesmaximal
5C2×C4×C5×Q8C411yescharacteristic, complemented
6C2×#4093C2211yescharacteristic
7C2×C4×D20C2211yescharacteristic
8C4×C22⋊AGL(1,𝔽5)—22no—
9C2×#3999C2214yes—
10#65519C411yescharacteristic, complemented
11#65279—22no—
12#65277C2211yescharacteristic
13#65266C411yescharacteristic, complemented
14C4×#685—22no—
15C42×Dic5C411yescharacteristic, complemented
16#64928C418yesdirect product factor
17#64917—22no—
18C4×#354—51nomaximal, Sylow
19C22×C5×Q8C2×C411yescharacteristic
20C22×D20C2311yescharacteristic
21C22×C4×D5D412yes—
22C2×C22⋊AGL(1,𝔽5)—24no—
23C2×C4×AGL(1,𝔽5)—42no—
24C4×C5×Q8—41no—
25C4×C5×Q8—41no—
26C2×C5×C4⋊C4—21no—
27C2×C5×C4⋊C4C2×C411yescharacteristic
28C2×C42×C5—21no—
29C2×C42×C5C2×C411yescharacteristic
30#4093—22no—
31#4093C2×C414yes—
32C2×#685—22no—
33C2×#685—22no—
34C2×#685D412yes—
35C2×C4⋊Dic5C2×C411yescharacteristic
36C2×C4×Dic5—21no—
37C2×C4×Dic5—21no—
38C2×C4×Dic5C2×C411yescharacteristic
39C2×C4×Dic5C2×C411yescharacteristic
40C4×D20—41no—
41C4×D20—41no—
42(C2×AGL(1,𝔽5))⋊C4—42no—
43#3999—24no—
44#3999C2×C418yes—
45#3963—22no—
46#3963—22no—
47C4×#124—51no—
48C2×#354—52no—
49C4×#99—52no—
50#1393—52no—
51C23×D5C2×D412yes—
52C22×AGL(1,𝔽5)—44no—
53C2×C5×Q8—21no—
54C2×C5×Q8—41no—
55C2×C5×Q8—41no—
56C2×C5×Q8C4212yescomplemented
57C22×C4×C5—21no—
58C22×C4×C5—21no—
59C22×C4×C5C22⋊C411yescharacteristic
60C22×C4×C5C22⋊C411yescharacteristic
61C22×C4×C5C22×C411yescharacteristic
62C22×Dic5—21no—
63C22×Dic5—21no—
64C22×Dic5C22⋊C412yes—
65C2×D20—41no—
66C2×D20—41no—
67C2×D20C22×C412yes—
68C2×D20#4112yes—
69C2×C4×D5—22no—
70C2×C4×D5—22no—
71C2×C4×D5—44no—
72C22⋊AGL(1,𝔽5)—28no—
73C22⋊AGL(1,𝔽5)—44no—
74C4×AGL(1,𝔽5)—84no—
75C5×C4⋊C4—41no—
76C5×C4⋊C4—42no—
77C42×C5—21no—
78C42×C5—21no—
79C42×C5—41no—
80C42×C5—41no—
81#685—28no—
82#685—42no—
83#685—44no—
84C4⋊Dic5—41no—
85C4×Dic5—21no—
86C4×Dic5—42no—
87C4×Dic5—42no—
88C4×Dic5—41no—
89C4×Dic5C4212yescomplemented
90C2×#124—51no—
91C2×C4×Q8AGL(1,𝔽5)11yescharacteristic, complemented
92C2×C4×D4—51no—
93C2×#99—54no—
94#391—51no—
95#390—51no—
96#388—102no—
97#382—51no—
98C4×C22⋊C4—102no—
99C4×C22⋊C4—102no—
100C43—51no—
101#354—58no—
102#342—102no—
103C23×C5C2×C22⋊C411yescharacteristic
104C22×D5—22no—
105C22×D5—22no—
106C22×D5—42no—
107C22×D5—42no—
108C22×D5C4×D414yes—
109C2×AGL(1,𝔽5)—48no—
110C2×AGL(1,𝔽5)—84no—
111C2×AGL(1,𝔽5)—84no—
112C5×Q8—42no—
113C5×Q8—42no—
114C2×C4×C5—21no—
115C2×C4×C5—21no—
116C2×C4×C5—22no—
117C2×C4×C5—22no—
118C2×C4×C5—21no—
119C2×C4×C5—41no—
120C2×C4×C5—41no—
121C2×C4×C5—41no—
122C2×C4×C5—42no—
123C2×C4×C5—41no—
124C2×C4×C5#9911yescharacteristic
125C2×C4×C5#9911yescharacteristic
126C2×C4×C5C2×C4211yescharacteristic
127C2×C4×C5#11711yescharacteristic
128C2×Dic5—22no—
129C2×Dic5—22no—
130C2×Dic5—22no—
131C2×Dic5—41no—
132C2×Dic5—41no—
133C2×Dic5—41no—
134C2×Dic5—41no—
135C2×Dic5—42no—
136D20—42no—
137D20—42no—
138C4×D5—44no—
139C4×D5—82no—
140C22×Q8C2×AGL(1,𝔽5)11yescharacteristic
141C22×D4—51no—
142C23×C4—52no—
143#124—54no—
144#124—102no—
145C4×Q8—41no—
146C4×Q8—41no—
147C4×D4—201no—
148C4×D4—201no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—51no—
151C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
152C2×C22⋊C4—52no—
153C2×C22⋊C4—102no—
154C2×C22⋊C4—104no—
155C2×C22⋊C4—102no—
156C2×C42—21no—
157C2×C42—51no—
158C2×C42—51no—
159C2×C42—101no—
160C2×C42—101no—
161C2×C42—202no—
162C2×C42C2×AGL(1,𝔽5)11yescharacteristic
163#99—58no—
164#99—104no—
165#95—102no—
166#95—102no—
167#95—202no—
168C22×C5—21no—
169C22×C5—21no—
170C22×C5C4×C22⋊C411yescharacteristic
171C22×C5C2×#9911yescharacteristic
172C22×C5#41011yescharacteristic
173C2×D5—24no—
174C2×D5—42no—
175C2×D5—42no—
176C2×D5—44no—
177C2×D5—82no—
178AGL(1,𝔽5)—88no—
179C4×C5—21no—
180C4×C5—21no—
181C4×C5—21no—
182C4×C5—41no—
183C4×C5—42no—
184C4×C5—81no—
185C4×C5#35412yescomplemented
186Dic5—42no—
187Dic5—42no—
188Dic5—42no—
189C24—52no—
190C2×Q8—21no—
191C2×Q8—41no—
192C2×Q8—41no—
193C2×Q8C4×AGL(1,𝔽5)12yescomplemented
194C2×D4—52no—
195C2×D4—52no—
196C2×D4—201no—
197C2×D4—201no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—52no—
201C22×C4—101no—
202C22×C4—101no—
203C22×C4—102no—
204C22×C4—102no—
205C22×C4—204no—
206C22×C4—204no—
207C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
208C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
209C22×C4C22×AGL(1,𝔽5)11yescharacteristic
210C4⋊C4—41no—
211C4⋊C4—42no—
212C4⋊C4—201no—
213C22⋊C4—108no—
214C22⋊C4—108no—
215C22⋊C4—202no—
216C22⋊C4—204no—
217C22⋊C4—204no—
218C42—21no—
219C42—21no—
220C42—41no—
221C42—41no—
222C42—52no—
223C42—101no—
224C42—201no—
225C42—202no—
226C42—202no—
227C42—404no—
228C2×C5—21no—
229C2×C5—21no—
230C2×C5C4×#9911yescharacteristic
231C2×C5C2×#35411yescharacteristic
232C2×C5#212611yescharacteristic
233D5—44no—
234C23—54no—
235C23—102no—
236C23—102no—
237C23—202no—
238C23—202no—
239C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
240Q8—42no—
241Q8—42no—
242D4—202no—
243D4—202no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—102no—
255C2×C4—102no—
256C2×C4—102no—
257C2×C4—201no—
258C2×C4—201no—
259C2×C4—201no—
260C2×C4—201no—
261C2×C4—204no—
262C2×C4—202no—
263C2×C4—208no—
264C2×C4—402no—
265C2×C4—404no—
266C2×C4—404no—
267C2×C4#401111yescharacteristic
268C2×C4#401111yescharacteristic
269C2×C4C2×C4×AGL(1,𝔽5)11yescharacteristic
270C2×C4#413011yescharacteristic
271C5C4×#35411yescharacteristic, complemented, Sylow
272C22—21no—
273C22—21no—
274C22—104no—
275C22—204no—
276C22—202no—
277C22—202no—
278C22—402no—
279C22#6574511yescharacteristic
280C22C4×C22⋊AGL(1,𝔽5)11yescharacteristic
281C22C2×#401111yescharacteristic
282C4—21no—
283C4—21no—
284C4—21no—
285C4—42no—
286C4—41no—
287C4—81no—
288C4—202no—
289C4—202no—
290C4—202no—
291C4—408no—
292C4#6492812yesdirect product factor
293C2—21no—
294C2—21no—
295C2—204no—
296C2C4×#401111yescharacteristic
297C2C2×#6492811yescharacteristic
298C2#1060499611yescharacteristic
subgroupG/H
centerC2×C4#4011
commutatorC2×C4×C5C2×C42
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C4×C5×Q8C4
socleC22×C5C2×#99
prime radical, cosocleC22×D20C23
hypercenterC2×C4×Q8AGL(1,𝔽5)
hypocenterC5C4×#354
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
5. C2×C4×C5×Q8C4semidirect
10. #65519C4semidirect
13. #65266C4semidirect
15. C42×Dic5C4semidirect
16. #64928C4direct (N × H)
56. C2×C5×Q8C42semidirect
89. C4×Dic5C42semidirect
91. C2×C4×Q8AGL(1,𝔽5)semidirect
185. C4×C5#354semidirect
193. C2×Q8C4×AGL(1,𝔽5)semidirect
271. C5C4×#354semidirect
292. C4#64928direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#40932
C2×#649282
C4×#39992
#105987232
C4×#3545