Finite Group Databasebeta

← C4×#64923 #13025836

Subgroups — C4×#64923 #13025836

Order 1280.

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

normal subgroups only

This group has 532 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×#4082C211yesmaximal, characteristic
2C2×#64923C212yesmaximal
3C4×#4005C212yesmaximal, complemented
4#10598724C212yesmaximal, complemented
5C2×C4×C5×D4C411yescharacteristic
6C2×#4082C2211yescharacteristic
7C2×C4×Dic10C2211yescharacteristic
8C2×#4005C2214yes—
9C4×#704—22no—
10#65510C411yescharacteristic
11C4×C22⋊Dic5—22no—
12#65266C411yescharacteristic
13#65263C2211yescharacteristic
14#65234—22no—
15C42×Dic5C411yescharacteristic
16#64923C418yesdirect product factor
17#64919—22no—
18C4×#355—51nomaximal, Sylow
19C22×C5×D4C2×C411yescharacteristic
20C23×C4×C5—21no—
21C22×Dic10C2311yescharacteristic
22C2×#704—24no—
23C4×C5×D4—41no—
24C4×C5×D4—41no—
25C2×C5×C4⋊C4C2×C411yescharacteristic
26C2×C5×C22⋊C4—21no—
27C2×C42×C5C2×C411yescharacteristic
28C2×C22⋊Dic5—22no—
29C2×C22⋊Dic5—22no—
30#4082—22no—
31#4082C2×C414yes—
32C2×C4⋊Dic5C2×C411yescharacteristic
33C2×#683D412yes—
34C2×C4×Dic5—21no—
35C2×C4×Dic5—21no—
36C2×C4×Dic5C2×C411yescharacteristic
37C2×C4×Dic5C2×C411yescharacteristic
38C2×C4×Dic5D412yes—
39C4×Dic10—41no—
40C4×Dic10—41no—
41#4005—24no—
42#4005C2×C418yescomplemented
43#4002—42no—
44C4×#170—42no—
45#3963—22no—
46#3963—22no—
47C4×#124—51no—
48C2×#355—52no—
49C4×#101—52no—
50#1394—52no—
51C24×C5—21no—
52C2×C5×D4—21no—
53C2×C5×D4—41no—
54C2×C5×D4—41no—
55C2×C5×D4C4212yes—
56C22×C4×C5—21no—
57C22×C4×C5—44no—
58C22×C4×C5—41no—
59C22×C4×C5—41no—
60C22×C4×C5C22⋊C411yescharacteristic
61C22×C4×C5C22⋊C411yescharacteristic
62C22×C4×C5C22×C411yescharacteristic
63C22×Dic5—21no—
64C22×Dic5—21no—
65C22×Dic5C22⋊C412yes—
66C22×Dic5C2×D412yes—
67C2×Dic10—41no—
68C2×Dic10—41no—
69C2×Dic10C22×C412yes—
70C2×Dic10#4112yes—
71#704—28no—
72#704—44no—
73C2×#170—44no—
74C5×C4⋊C4—41no—
75C5×C22⋊C4—42no—
76C42×C5—21no—
77C42×C5—21no—
78C22⋊Dic5—28no—
79C22⋊Dic5—44no—
80C4⋊Dic5—41no—
81#683—42no—
82C4×Dic5—22no—
83C4×Dic5—22no—
84C4×Dic5—21no—
85C4×Dic5—42no—
86C4×Dic5—42no—
87C4×Dic5—41no—
88C4×Dic5C4212yes—
89C2×#124—51no—
90C2×C4×Q8—51no—
91C2×C4×D4AGL(1,𝔽5)11yescharacteristic
92C2×#101—54no—
93C4×M16—102no—
94#391—51no—
95#390—51no—
96#388—102no—
97#382—51no—
98C4×C22⋊C4—102no—
99C43—51no—
100#355—58no—
101#343—102no—
102C23×C5—22no—
103C23×C5—42no—
104C23×C5—42no—
105C23×C5—41no—
106C23×C5—41no—
107C23×C5C2×C22⋊C411yescharacteristic
108C5×D4—42no—
109C5×D4—42no—
110C2×C4×C5—21no—
111C2×C4×C5—21no—
112C2×C4×C5—22no—
113C2×C4×C5—21no—
114C2×C4×C5—41no—
115C2×C4×C5—42no—
116C2×C4×C5—41no—
117C2×C4×C5—82no—
118C2×C4×C5—82no—
119C2×C4×C5#9911yescharacteristic
120C2×C4×C5#9911yescharacteristic
121C2×C4×C5C2×C4211yescharacteristic
122C2×C4×C5#11711yescharacteristic
123C2×Dic5—22no—
124C2×Dic5—22no—
125C2×Dic5—22no—
126C2×Dic5—22no—
127C2×Dic5—22no—
128C2×Dic5—41no—
129C2×Dic5—41no—
130C2×Dic5—41no—
131C2×Dic5—41no—
132C2×Dic5—42no—
133C2×Dic5C4×D414yes—
134Dic10—42no—
135Dic10—42no—
136#170—48no—
137C22×Q8—51no—
138C22×D4C2×AGL(1,𝔽5)11yescharacteristic
139C23×C4—21no—
140C2×M16—104no—
141#124—54no—
142#124—102no—
143C4×Q8—201no—
144C4×Q8—201no—
145C4×D4—41no—
146C4×D4—41no—
147C2×C4⋊C4—52no—
148C2×C4⋊C4—51no—
149C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
150C2×C22⋊C4—21no—
151C2×C22⋊C4—102no—
152C2×C22⋊C4—102no—
153C2×C42—51no—
154C2×C42—52no—
155C2×C42—51no—
156C2×C42—101no—
157C2×C42—101no—
158C2×C42C2×AGL(1,𝔽5)11yescharacteristic
159#101—58no—
160#101—104no—
161#97—202no—
162C4×C8—202no—
163#95—102no—
164#95—102no—
165C22×C5—21no—
166C22×C5—21no—
167C22×C5—44no—
168C22×C5—42no—
169C22×C5—82no—
170C22×C5—81no—
171C22×C5—81no—
172C22×C5C4×C22⋊C411yescharacteristic
173C22×C5C2×#9911yescharacteristic
174C22×C5#41011yescharacteristic
175C4×C5—21no—
176C4×C5—21no—
177C4×C5—21no—
178C4×C5—41no—
179C4×C5—81no—
180C4×C5#35512yescomplemented
181Dic5—24no—
182Dic5—42no—
183Dic5—42no—
184Dic5—42no—
185C24—21no—
186C2×Q8—52no—
187C2×Q8—52no—
188C2×Q8—201no—
189C2×Q8—201no—
190C2×D4—21no—
191C2×D4—41no—
192C2×D4—41no—
193C2×D4C4×AGL(1,𝔽5)12yes—
194C22×C4—21no—
195C22×C4—44no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—52no—
199C22×C4—52no—
200C22×C4—101no—
201C22×C4—101no—
202C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
203C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
204C22×C4C22×AGL(1,𝔽5)11yescharacteristic
205M16—108no—
206M16—204no—
207C2×C8—204no—
208C4⋊C4—41no—
209C4⋊C4—202no—
210C4⋊C4—201no—
211C22⋊C4—42no—
212C22⋊C4—108no—
213C22⋊C4—204no—
214C42—21no—
215C42—21no—
216C42—52no—
217C42—101no—
218C42—102no—
219C42—102no—
220C42—201no—
221C42—202no—
222C42—202no—
223C2×C5—21no—
224C2×C5—21no—
225C2×C5—82no—
226C2×C5C4×#9911yescharacteristic
227C2×C5C2×#35511yescharacteristic
228C2×C5#213211yescharacteristic
229C23—22no—
230C23—42no—
231C23—42no—
232C23—41no—
233C23—41no—
234C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
235Q8—202no—
236Q8—202no—
237D4—42no—
238D4—42no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—54no—
247C2×C4—82no—
248C2×C4—82no—
249C2×C4—102no—
250C2×C4—102no—
251C2×C4—102no—
252C2×C4—102no—
253C2×C4—102no—
254C2×C4—201no—
255C2×C4—201no—
256C2×C4—201no—
257C2×C4—201no—
258C2×C4—202no—
259C2×C4#401111yescharacteristic
260C2×C4#401111yescharacteristic
261C2×C4C2×C4×AGL(1,𝔽5)11yescharacteristic
262C2×C4#413011yescharacteristic
263C8—208no—
264C5C4×#35511yescharacteristic, complemented, Sylow
265C22—21no—
266C22—21no—
267C22—44no—
268C22—42no—
269C22—82no—
270C22—81no—
271C22—81no—
272C22#6574511yescharacteristic
273C22C4×C22⋊AGL(1,𝔽5)11yescharacteristic
274C22C2×#401111yescharacteristic
275C4—21no—
276C4—21no—
277C4—21no—
278C4—41no—
279C4—81no—
280C4—104no—
281C4—202no—
282C4—202no—
283C4—202no—
284C4#6492312yesdirect product factor
285C2—21no—
286C2—21no—
287C2—82no—
288C2C4×#401111yescharacteristic
289C2C2×#6492311yescharacteristic
290C2#1060499811yescharacteristic
subgroupG/H
centerC2×C4#4011
commutatorC2×C4×C5C2×C42
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C4×C5×D4C4
socleC22×C5C2×#99
prime radicalC22×C5×D4C2×C4
cosocleC22×Dic10C23
hypercenterC2×C4×D4AGL(1,𝔽5)
hypocenterC5C4×#355
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
3. C4×#4005C2semidirect
4. #10598724C2semidirect
16. #64923C4direct (N × H)
42. #4005C2×C4semidirect
180. C4×C5#355semidirect
264. C5C4×#355semidirect
284. C4#64923direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#40822
C2×#649232
C4×#40052
#105987242
C4×#3555