Finite Group Databasebeta

← C5×#9478 #11932198

Subgroups — C5×#9478 #11932198

Order 1280.

610 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 130 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×#2484C211yesmaximal, characteristic
2C5×#2274C211yesmaximal, characteristic
3C5×#1826C212yesmaximal
4C5×#1463C211yesmaximal, characteristic
5C5×#1284C212yesmaximal
6C2×C5×#117—21no—
7C2×C5×#117C2211yescharacteristic
8C22×C5×C4⋊C4C2211yescharacteristic
9C5×#407C2212yes—
10C5×#400C412yescomplemented
11C5×#398C412yescomplemented
12C5×#387—22no—
13C5×#385—21no—
14C5×#381—21no—
15C5×#381C2211yescharacteristic
16C4×C5×C4⋊C4—24no—
17C4×C5×C22⋊C4—21no—
18C4×C5×C22⋊C4C2212yes—
19C5×#339—24no—
20C5×#324—22no—
21#9478C511yesmaximal, characteristic, direct product factor, Sylow
22C23×C4×C5D411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C23×C4×C5C2311yescharacteristic
25C2×C5×M16—22no—
26C5×#117—28no—
27C5×#117—22no—
28C5×#117—22no—
29C2×C5×C4⋊C4—22no—
30C2×C5×C4⋊C4—22no—
31C2×C5×C4⋊C4—22no—
32C2×C5×C4⋊C4—22no—
33C2×C5×C4⋊C4C2×C411yescharacteristic
34C2×C5×C4⋊C4C2×C411yescharacteristic
35C2×C5×C4⋊C4C2×C412yes—
36C2×C5×C4⋊C4D412yes—
37C2×C5×C22⋊C4—22no—
38C2×C5×C22⋊C4—21no—
39C2×C5×C22⋊C4—21no—
40C2×C42×C5—22no—
41C2×C42×C5—21no—
42C2×C42×C5—22no—
43C2×C42×C5D414yes—
44C5×C22⋊C8—22no—
45C5×C22⋊C8—22no—
46C5×#95—22no—
47C5×#95—22no—
48C5×#95—22no—
49C5×#95—22no—
50C5×#95—22no—
51C5×#95—21no—
52C5×#95C2×C412yes—
53#2484C2×C511yescharacteristic
54#2274C2×C511yescharacteristic
55#1826C2×C512yes—
56#1463C2×C511yescharacteristic
57#1284C2×C512yes—
58C24×C5C2×D411yescharacteristic
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—24no—
62C22×C4×C5—24no—
63C22×C4×C5—21no—
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5—22no—
68C22×C4×C5—42no—
69C22×C4×C5—42no—
70C22×C4×C5C22⋊C412yes—
71C22×C4×C5C22⋊C412yes—
72C22×C4×C5C22×C411yescharacteristic
73C22×C4×C5C2×D412yes—
74C22×C4×C5C2×D411yescharacteristic
75C22×C4×C5#4112yes—
76C5×M16—44no—
77C2×C5×C8—42no—
78C5×C4⋊C4—28no—
79C5×C4⋊C4—24no—
80C5×C4⋊C4—24no—
81C5×C4⋊C4—22no—
82C5×C4⋊C4—22no—
83C5×C4⋊C4—44no—
84C5×C22⋊C4—28no—
85C5×C22⋊C4—42no—
86C5×C22⋊C4—41no—
87C5×C22⋊C4—41no—
88C42×C5—28no—
89C42×C5—44no—
90C42×C5—42no—
91C42×C5—82no—
92C2×#117—21no—
93C2×#117C22×C511yescharacteristic
94C22×C4⋊C4C22×C511yescharacteristic
95#407C22×C512yes—
96#400C4×C512yescomplemented
97#398C4×C512yescomplemented
98#387—22no—
99#385—21no—
100#381—21no—
101#381C22×C511yescharacteristic
102C4×C4⋊C4—24no—
103C4×C22⋊C4—21no—
104C4×C22⋊C4C22×C512yes—
105#339—24no—
106#324—22no—
107C23×C5—22no—
108C23×C5—22no—
109C23×C5—41no—
110C23×C5C2×C22⋊C411yescharacteristic
111C23×C5#12011yescharacteristic
112C23×C5#12311yescharacteristic
113C2×C4×C5—22no—
114C2×C4×C5—22no—
115C2×C4×C5—24no—
116C2×C4×C5—22no—
117C2×C4×C5—22no—
118C2×C4×C5—24no—
119C2×C4×C5—28no—
120C2×C4×C5—22no—
121C2×C4×C5—41no—
122C2×C4×C5—41no—
123C2×C4×C5—42no—
124C2×C4×C5—44no—
125C2×C4×C5—44no—
126C2×C4×C5—42no—
127C2×C4×C5—42no—
128C2×C4×C5—42no—
129C2×C4×C5—42no—
130C2×C4×C5—42no—
131C2×C4×C5—41no—
132C2×C4×C5—41no—
133C2×C4×C5—42no—
134C2×C4×C5—42no—
135C2×C4×C5—81no—
136C2×C4×C5#10414yes—
137C2×C4×C5C4×D412yes—
138C2×C4×C5#12112yes—
139C5×C8—82no—
140C23×C4C5×D411yescharacteristic
141C23×C4C5×D411yescharacteristic
142C23×C4C23×C511yescharacteristic
143C2×M16—22no—
144#117—28no—
145#117—22no—
146#117—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4C2×C4×C511yescharacteristic
152C2×C4⋊C4C2×C4×C511yescharacteristic
153C2×C4⋊C4C2×C4×C512yes—
154C2×C4⋊C4C5×D412yes—
155C2×C22⋊C4—22no—
156C2×C22⋊C4—21no—
157C2×C22⋊C4—21no—
158C2×C42—22no—
159C2×C42—21no—
160C2×C42—22no—
161C2×C42C5×D414yes—
162C22⋊C8—22no—
163C22⋊C8—22no—
164#95—22no—
165#95—22no—
166#95—22no—
167#95—22no—
168#95—22no—
169#95—21no—
170#95C2×C4×C512yes—
171C22×C5—21no—
172C22×C5—21no—
173C22×C5—21no—
174C22×C5—21no—
175C22×C5—21no—
176C22×C5—21no—
177C22×C5—21no—
178C22×C5—44no—
179C22×C5#38611yescharacteristic
180C22×C5C2×#10412yes—
181C22×C5#45812yes—
182C4×C5—22no—
183C4×C5—22no—
184C4×C5—24no—
185C4×C5—48no—
186C4×C5—42no—
187C4×C5—82no—
188C4×C5—81no—
189C4×C5—81no—
190C24C2×C5×D411yescharacteristic
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—24no—
194C22×C4—24no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—22no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4C5×C22⋊C412yes—
203C22×C4C5×C22⋊C412yes—
204C22×C4C22×C4×C511yescharacteristic
205C22×C4C2×C5×D412yes—
206C22×C4C2×C5×D411yescharacteristic
207C22×C4C5×#4112yes—
208M16—44no—
209C2×C8—42no—
210C4⋊C4—28no—
211C4⋊C4—24no—
212C4⋊C4—24no—
213C4⋊C4—22no—
214C4⋊C4—22no—
215C4⋊C4—44no—
216C22⋊C4—28no—
217C22⋊C4—42no—
218C22⋊C4—41no—
219C22⋊C4—41no—
220C42—28no—
221C42—44no—
222C42—42no—
223C42—82no—
224C2×C5—22no—
225C2×C5—22no—
226C2×C5—41no—
227C2×C5#189011yescharacteristic
228C2×C5#189611yescharacteristic
229C2×C5#191211yescharacteristic
230C23—22no—
231C23—22no—
232C23—41no—
233C23C2×C5×C22⋊C411yescharacteristic
234C23C5×#12011yescharacteristic
235C23C5×#12311yescharacteristic
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—24no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—24no—
242C2×C4—28no—
243C2×C4—22no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—44no—
248C2×C4—44no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—81no—
259C2×C4C5×#10414yes—
260C2×C4C4×C5×D412yes—
261C2×C4C5×#12112yes—
262C8—82no—
263C5#947811yescharacteristic, direct product factor, Sylow
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—44no—
272C22C5×#38611yescharacteristic
273C22C2×C5×#10412yes—
274C22C5×#45812yes—
275C4—22no—
276C4—22no—
277C4—24no—
278C4—48no—
279C4—42no—
280C4—82no—
281C4—81no—
282C4—81no—
283C2—22no—
284C2—22no—
285C2—41no—
286C2C5×#189011yescharacteristic
287C2C5×#189611yescharacteristic
288C2C5×#191211yescharacteristic
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×#400C4semidirect
11. C5×#398C4semidirect
21. #9478C5direct (N × H)
96. #400C4×C5semidirect
97. #398C4×C5semidirect
263. C5#9478direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#24842
C5×#22742
C5×#18262
C5×#14632
C5×#12842
#94785