Finite Group Databasebeta

← C5×#9461 #11932181

Subgroups — C5×#9461 #11932181

Order 1280.

528 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C5×#2502C211yesmaximal, characteristic
2C5×#2313C211yesmaximal, characteristic
3C5×#1821C211yesmaximal, characteristic
4C5×#1511C212yesmaximal
5C5×#1284C212yesmaximal
6C2×C5×C22⋊Q8C2211yescharacteristic
7C22×C5×C4⋊C4C2211yescharacteristic
8C5×#407C2212yes—
9C5×#398—22no—
10C5×#391C412yescomplemented
11C5×#387—24no—
12C5×#385—21no—
13C5×#385—21no—
14C5×#384C412yescomplemented
15C5×#381C2212yes—
16C5×#380—21no—
17C4×C5×C22⋊C4—21no—
18C4×C5×C22⋊C4C2211yescharacteristic
19C5×#343—22no—
20C5×#328—24no—
21#9461C511yesmaximal, characteristic, direct product factor, Sylow
22C22×C5×Q8C2×C411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C23×C4×C5D411yescharacteristic
25C23×C4×C5C2311yescharacteristic
26C2×C5×M16—22no—
27C5×C22⋊Q8—22no—
28C5×C22⋊Q8—22no—
29C2×C5×C4⋊C4—22no—
30C2×C5×C4⋊C4—22no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—22no—
33C2×C5×C4⋊C4—22no—
34C2×C5×C4⋊C4—22no—
35C2×C5×C4⋊C4C2×C411yescharacteristic
36C2×C5×C4⋊C4C2×C412yes—
37C2×C5×C4⋊C4D412yes—
38C2×C5×C22⋊C4—21no—
39C2×C5×C22⋊C4—22no—
40C2×C5×C22⋊C4—21no—
41C2×C42×C5—22no—
42C2×C42×C5C2×C412yes—
43C5×C22⋊C8—22no—
44C5×C22⋊C8—22no—
45C5×#95—22no—
46C5×#95—22no—
47C5×#95—22no—
48C5×#95—22no—
49C5×#95—21no—
50C5×#95—22no—
51C5×#95D414yes—
52#2502C2×C511yescharacteristic
53#2313C2×C511yescharacteristic
54#1821C2×C511yescharacteristic
55#1511C2×C512yes—
56#1284C2×C512yes—
57C24×C5C2×D411yescharacteristic
58C2×C5×Q8—22no—
59C2×C5×Q8—42no—
60C22×C4×C5—22no—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—21no—
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5—24no—
68C22×C4×C5—42no—
69C22×C4×C5—81no—
70C22×C4×C5—81no—
71C22×C4×C5C22⋊C412yes—
72C22×C4×C5C22⋊C412yes—
73C22×C4×C5C22×C411yescharacteristic
74C22×C4×C5C2×D411yescharacteristic
75C22×C4×C5C2×D412yes—
76C22×C4×C5#4112yes—
77C5×M16—44no—
78C2×C5×C8—42no—
79C5×C4⋊C4—24no—
80C5×C4⋊C4—24no—
81C5×C4⋊C4—22no—
82C5×C4⋊C4—42no—
83C5×C4⋊C4—82no—
84C5×C4⋊C4—82no—
85C5×C4⋊C4—82no—
86C5×C22⋊C4—24no—
87C5×C22⋊C4—44no—
88C5×C22⋊C4—41no—
89C5×C22⋊C4—41no—
90C42×C5—42no—
91C42×C5—82no—
92C2×C22⋊Q8C22×C511yescharacteristic
93C22×C4⋊C4C22×C511yescharacteristic
94#407C22×C512yes—
95#398—22no—
96#391C4×C512yescomplemented
97#387—24no—
98#385—21no—
99#385—21no—
100#384C4×C512yescomplemented
101#381C22×C512yes—
102#380—21no—
103C4×C22⋊C4—21no—
104C4×C22⋊C4C22×C511yescharacteristic
105#343—22no—
106#328—24no—
107C23×C5—22no—
108C23×C5—22no—
109C23×C5—41no—
110C23×C5C2×C22⋊C411yescharacteristic
111C23×C5#12011yescharacteristic
112C23×C5#12311yescharacteristic
113C5×Q8—82no—
114C2×C4×C5—22no—
115C2×C4×C5—22no—
116C2×C4×C5—24no—
117C2×C4×C5—22no—
118C2×C4×C5—22no—
119C2×C4×C5—42no—
120C2×C4×C5—42no—
121C2×C4×C5—42no—
122C2×C4×C5—42no—
123C2×C4×C5—42no—
124C2×C4×C5—42no—
125C2×C4×C5—42no—
126C2×C4×C5—42no—
127C2×C4×C5—44no—
128C2×C4×C5—44no—
129C2×C4×C5—42no—
130C2×C4×C5—41no—
131C2×C4×C5—41no—
132C2×C4×C5—42no—
133C2×C4×C5—44no—
134C2×C4×C5—81no—
135C2×C4×C5—81no—
136C2×C4×C5C4×D412yes—
137C2×C4×C5#12112yes—
138C5×C8—82no—
139C22×Q8C2×C4×C511yescharacteristic
140C23×C4C5×D411yescharacteristic
141C23×C4C5×D411yescharacteristic
142C23×C4C23×C511yescharacteristic
143C2×M16—22no—
144C22⋊Q8—22no—
145C22⋊Q8—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4C2×C4×C511yescharacteristic
153C2×C4⋊C4C2×C4×C512yes—
154C2×C4⋊C4C5×D412yes—
155C2×C22⋊C4—21no—
156C2×C22⋊C4—21no—
157C2×C22⋊C4—22no—
158C2×C42—22no—
159C2×C42C2×C4×C512yes—
160C22⋊C8—22no—
161C22⋊C8—22no—
162#95—22no—
163#95—22no—
164#95—22no—
165#95—22no—
166#95—21no—
167#95—22no—
168#95C5×D414yes—
169C22×C5—21no—
170C22×C5—21no—
171C22×C5—21no—
172C22×C5—21no—
173C22×C5—21no—
174C22×C5—21no—
175C22×C5—21no—
176C22×C5—44no—
177C22×C5#38611yescharacteristic
178C22×C5#41012yes—
179C22×C5#45612yes—
180C4×C5—22no—
181C4×C5—22no—
182C4×C5—44no—
183C4×C5—42no—
184C4×C5—42no—
185C4×C5—84no—
186C4×C5—81no—
187C4×C5—81no—
188C24C2×C5×D411yescharacteristic
189C2×Q8—22no—
190C2×Q8—42no—
191C22×C4—22no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—24no—
199C22×C4—42no—
200C22×C4—81no—
201C22×C4—81no—
202C22×C4C5×C22⋊C412yes—
203C22×C4C5×C22⋊C412yes—
204C22×C4C22×C4×C511yescharacteristic
205C22×C4C2×C5×D411yescharacteristic
206C22×C4C2×C5×D412yes—
207C22×C4C5×#4112yes—
208M16—44no—
209C2×C8—42no—
210C4⋊C4—24no—
211C4⋊C4—24no—
212C4⋊C4—22no—
213C4⋊C4—42no—
214C4⋊C4—82no—
215C4⋊C4—82no—
216C4⋊C4—82no—
217C22⋊C4—24no—
218C22⋊C4—44no—
219C22⋊C4—41no—
220C22⋊C4—41no—
221C42—42no—
222C42—82no—
223C2×C5—22no—
224C2×C5—22no—
225C2×C5—41no—
226C2×C5#188611yescharacteristic
227C2×C5#189911yescharacteristic
228C2×C5#191111yescharacteristic
229C23—22no—
230C23—22no—
231C23—41no—
232C23C2×C5×C22⋊C411yescharacteristic
233C23C5×#12011yescharacteristic
234C23C5×#12311yescharacteristic
235Q8—82no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—24no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—44no—
250C2×C4—44no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—44no—
256C2×C4—81no—
257C2×C4—81no—
258C2×C4C4×C5×D412yes—
259C2×C4C5×#12112yes—
260C8—82no—
261C5#946111yescharacteristic, direct product factor, Sylow
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—44no—
270C22C5×#38611yescharacteristic
271C22C5×#41012yes—
272C22C5×#45612yes—
273C4—22no—
274C4—22no—
275C4—44no—
276C4—42no—
277C4—42no—
278C4—84no—
279C4—81no—
280C4—81no—
281C2—22no—
282C2—22no—
283C2—41no—
284C2C5×#188611yescharacteristic
285C2C5×#189911yescharacteristic
286C2C5×#191111yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC24×C5C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
10. C5×#391C4semidirect
14. C5×#384C4semidirect
21. #9461C5direct (N × H)
96. #391C4×C5semidirect
100. #384C4×C5semidirect
261. C5#9461direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#25022
C5×#23132
C5×#18212
C5×#15112
C5×#12842
#94615