Finite Group Databasebeta

← C5×#12965 #11935685

Subgroups — C5×#12965 #11935685

Order 1280.

536 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2372C211yesmaximal, characteristic
2C2×C5×#354C211yesmaximal, characteristic
3C5×#1885C211yesmaximal, characteristic
4C5×#1867C212yesmaximal
5C5×#1390C212yesmaximal
6C2×C5×#124C2211yescharacteristic
7C5×#518C2211yescharacteristic
8C5×#419—21no—
9C2×C5×#100C2211yescharacteristic
10C2×C5×#99C2212yes—
11C5×#391—21no—
12C5×#388—22no—
13C5×#386C2212yes—
14C5×#385—22no—
15C4×C5×C22⋊C4—22no—
16C5×#376—21no—
17C5×#354C414yescomplemented
18C5×#342—22no—
19C5×#339—21no—
20#12965C511yesmaximal, characteristic, direct product factor, Sylow
21C22×C5×Q8D411yescharacteristic
22C22×C5×D4C2311yescharacteristic
23C23×C4×C5D412yes—
24C2×C5×M16—21no—
25C5×#124—22no—
26C5×#124C2×C412yes—
27C5×#124Q812yes—
28C4×C5×D4—42no—
29C5×#117—21no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4—42no—
32C2×C5×C22⋊C4—22no—
33C2×C5×C22⋊C4—22no—
34C2×C5×C22⋊C4—22no—
35C2×C5×C22⋊C4—22no—
36C2×C5×C22⋊C4D412yes—
37C2×C42×C5—22no—
38C2×C42×C5—21no—
39C2×C42×C5D411yescharacteristic
40C5×#103—42no—
41C5×#100—22no—
42C5×#99—22no—
43C5×#99C2×C414yes—
44C5×#95—21no—
45C5×#95—21no—
46C5×#95—22no—
47C5×#95—22no—
48C5×#95—42no—
49#2372C2×C511yescharacteristic
50C2×#354C2×C511yescharacteristic
51#1885C2×C511yescharacteristic
52#1867C2×C512yes—
53#1390C2×C512yes—
54C24×C5C2×D412yes—
55C2×C5×Q8—21no—
56C2×C5×Q8—41no—
57C2×C5×Q8—41no—
58C2×C5×Q8C4⋊C412yescomplemented
59C2×C5×D4—41no—
60C2×C5×D4—41no—
61C2×C5×D4C22×C411yescharacteristic
62C2×C5×D4C2×Q811yescharacteristic
63C2×C5×D4#4112yes—
64C22×C4×C5—21no—
65C22×C4×C5—22no—
66C22×C4×C5—21no—
67C22×C4×C5—22no—
68C22×C4×C5—22no—
69C22×C4×C5—22no—
70C22×C4×C5—44no—
71C22×C4×C5—42no—
72C22×C4×C5—42no—
73C22×C4×C5C2×D411yescharacteristic
74C5×M16—41no—
75C5×M16—41no—
76C2×C5×C8—41no—
77C5×C4⋊C4—22no—
78C5×C4⋊C4—81no—
79C5×C4⋊C4—84no—
80C5×C22⋊C4—24no—
81C5×C22⋊C4—24no—
82C5×C22⋊C4—24no—
83C5×C22⋊C4—44no—
84C5×C22⋊C4—42no—
85C5×C22⋊C4—42no—
86C5×C22⋊C4—41no—
87C5×C22⋊C4—42no—
88C42×C5—21no—
89C42×C5—44no—
90C42×C5—41no—
91C42×C5—81no—
92C42×C5C4⋊C412yescomplemented
93C2×#124C22×C511yescharacteristic
94#518C22×C511yescharacteristic
95#419—21no—
96C2×#100C22×C511yescharacteristic
97C2×#99C22×C512yes—
98#391—21no—
99#388—22no—
100#386C22×C512yes—
101#385—22no—
102C4×C22⋊C4—22no—
103#376—21no—
104#354C4×C514yescomplemented
105#342—22no—
106#339—21no—
107C23×C5—22no—
108C23×C5—22no—
109C23×C5—42no—
110C23×C5—42no—
111C23×C5C4×D412yes—
112C23×C5#12011yescharacteristic
113C23×C5C22⋊Q812yes—
114C5×Q8—42no—
115C5×Q8—81no—
116C5×D4—41no—
117C5×D4—41no—
118C5×D4—42no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—24no—
122C2×C4×C5—22no—
123C2×C4×C5—22no—
124C2×C4×C5—42no—
125C2×C4×C5—42no—
126C2×C4×C5—42no—
127C2×C4×C5—41no—
128C2×C4×C5—41no—
129C2×C4×C5—44no—
130C2×C4×C5—42no—
131C2×C4×C5—44no—
132C2×C4×C5—42no—
133C2×C4×C5—42no—
134C2×C4×C5—42no—
135C2×C4×C5—82no—
136C2×C4×C5—82no—
137C2×C4×C5—82no—
138C2×C4×C5—82no—
139C2×C4×C5—82no—
140C2×C4×C5C2×C4⋊C411yescharacteristic
141C2×C4×C5#12311yescharacteristic
142C5×C8—81no—
143C22×Q8C5×D411yescharacteristic
144C22×D4C23×C511yescharacteristic
145C23×C4C5×D412yes—
146C2×M16—21no—
147#124—22no—
148#124C2×C4×C512yes—
149#124C5×Q812yes—
150C4×D4—42no—
151#117—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—42no—
154C2×C22⋊C4—22no—
155C2×C22⋊C4—22no—
156C2×C22⋊C4—22no—
157C2×C22⋊C4—22no—
158C2×C22⋊C4C5×D412yes—
159C2×C42—22no—
160C2×C42—21no—
161C2×C42C5×D411yescharacteristic
162#103—42no—
163#100—22no—
164#99—22no—
165#99C2×C4×C514yes—
166#95—21no—
167#95—21no—
168#95—22no—
169#95—22no—
170#95—42no—
171C22×C5—22no—
172C22×C5—22no—
173C22×C5—22no—
174C22×C5—42no—
175C22×C5—42no—
176C22×C5—42no—
177C22×C5—42no—
178C22×C5—82no—
179C22×C5#38511yescharacteristic
180C22×C5B(4,𝔽2)11yescharacteristic
181C22×C5#45811yescharacteristic
182C4×C5—21no—
183C4×C5—21no—
184C4×C5—42no—
185C4×C5—42no—
186C4×C5—44no—
187C4×C5—82no—
188C4×C5—84no—
189C4×C5—82no—
190C24C2×C5×D412yes—
191C2×Q8—21no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8C5×C4⋊C412yescomplemented
195C2×D4—41no—
196C2×D4—41no—
197C2×D4C22×C4×C511yescharacteristic
198C2×D4C2×C5×Q811yescharacteristic
199C2×D4C5×#4112yes—
200C22×C4—22no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—44no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4C2×C5×D411yescharacteristic
210M16—41no—
211M16—41no—
212C2×C8—41no—
213C4⋊C4—22no—
214C4⋊C4—81no—
215C4⋊C4—84no—
216C22⋊C4—24no—
217C22⋊C4—24no—
218C22⋊C4—24no—
219C22⋊C4—44no—
220C22⋊C4—42no—
221C22⋊C4—42no—
222C22⋊C4—41no—
223C22⋊C4—42no—
224C42—21no—
225C42—44no—
226C42—41no—
227C42—81no—
228C42C5×C4⋊C412yescomplemented
229C2×C5—21no—
230C2×C5—21no—
231C2×C5—42no—
232C2×C5—42no—
233C2×C5#186711yescharacteristic
234C2×C5#219712yes—
235C23—22no—
236C23—22no—
237C23—42no—
238C23—42no—
239C23C4×C5×D412yes—
240C23C5×#12011yescharacteristic
241C23C5×C22⋊Q812yes—
242Q8—42no—
243Q8—81no—
244D4—41no—
245D4—41no—
246D4—42no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—24no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—44no—
258C2×C4—42no—
259C2×C4—44no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—82no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4—82no—
267C2×C4—82no—
268C2×C4C2×C5×C4⋊C411yescharacteristic
269C2×C4C5×#12311yescharacteristic
270C8—81no—
271C5#1296511yescharacteristic, direct product factor, Sylow
272C22—22no—
273C22—22no—
274C22—22no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—82no—
280C22C5×#38511yescharacteristic
281C22C5×B(4,𝔽2)11yescharacteristic
282C22C5×#45811yescharacteristic
283C4—21no—
284C4—21no—
285C4—42no—
286C4—42no—
287C4—44no—
288C4—82no—
289C4—84no—
290C4—82no—
291C2—21no—
292C2—21no—
293C2—42no—
294C2—42no—
295C2C5×#186711yescharacteristic
296C2C5×#219712yes—
subgroupG/H
center, socleC22×C5B(4,𝔽2)
commutatorC2×D4C22×C4×C5
Frattini, cosocleC22×D4C23×C5
prime radicalC22×C5×D4C23
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C5 ◁ C22×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
17. C5×#354C4semidirect
20. #12965C5direct (N × H)
58. C2×C5×Q8C4⋊C4semidirect
92. C42×C5C4⋊C4semidirect
104. #354C4×C5semidirect
194. C2×Q8C5×C4⋊C4semidirect
228. C42C5×C4⋊C4semidirect
271. C5#12965direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#23722
C2×C5×#3542
C5×#18852
C5×#18672
C5×#13902
#129655