Finite Group Databasebeta

← C5×#9886 #11932606

Subgroups — C5×#9886 #11932606

Order 1280.

566 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2851C211yesmaximal, characteristic
2C4×C5×C22⋊C8C211yesmaximal, characteristic
3C5×#1434C211yesmaximal, characteristic
4C5×#1294C212yesmaximal
5C5×#1294C212yesmaximal
6C2×C5×#125C411yescharacteristic, complemented
7C22×C42×C5C2211yescharacteristic
8C2×C5×C22⋊C8C2212yes—
9C2×C4×C5×C8—21no—
10C5×#389C411yescharacteristic, complemented
11C5×#389C411yescharacteristic, complemented
12C5×#387—21no—
13C5×#387—21no—
14C5×#385—21no—
15C5×#385—21no—
16C5×#382C411yescharacteristic, complemented
17C5×#380C2211yescharacteristic
18C5×#380C2211yescharacteristic
19C2×C5×#95—21no—
20C2×C5×#95—21no—
21C2×C5×#95C2212yes—
22C5×#336—21no—
23#9886C511yesmaximal, characteristic, direct product factor, Sylow
24C23×C4×C5—22no—
25C23×C4×C5D411yescharacteristic
26C23×C4×C5D411yescharacteristic
27C23×C4×C5C2311yescharacteristic
28C22×C5×C8—22no—
29C5×#125—42no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4C2×C411yescharacteristic
35C2×C5×C4⋊C4C2×C411yescharacteristic
36C2×C5×C4⋊C4C2×C411yescharacteristic
37C2×C5×C4⋊C4C2×C411yescharacteristic
38C2×C5×C22⋊C4—21no—
39C2×C5×C22⋊C4—21no—
40C2×C42×C5—42no—
41C2×C42×C5C2×C411yescharacteristic
42C2×C42×C5C2×C411yescharacteristic
43C2×C42×C5D411yescharacteristic
44C2×C42×C5D411yescharacteristic
45C5×C22⋊C8—22no—
46C5×C22⋊C8Q814yes—
47C4×C5×C8—42no—
48C5×#95—24no—
49C5×#95—21no—
50C5×#95—21no—
51C5×#95—21no—
52C5×#95—21no—
53C5×#95—21no—
54C5×#95—21no—
55C5×#95—24no—
56C5×#95—42no—
57#2851C2×C511yescharacteristic
58C4×C22⋊C8C2×C511yescharacteristic
59#1434C2×C511yescharacteristic
60#1294C2×C512yes—
61#1294C2×C512yes—
62C24×C5C2×D411yescharacteristic
63C22×C4×C5—22no—
64C22×C4×C5—22no—
65C22×C4×C5—22no—
66C22×C4×C5—22no—
67C22×C4×C5—24no—
68C22×C4×C5—21no—
69C22×C4×C5—21no—
70C22×C4×C5—21no—
71C22×C4×C5—21no—
72C22×C4×C5—41no—
73C22×C4×C5—41no—
74C22×C4×C5—41no—
75C22×C4×C5—41no—
76C22×C4×C5—42no—
77C22×C4×C5—42no—
78C22×C4×C5—42no—
79C22×C4×C5—42no—
80C22×C4×C5—42no—
81C22×C4×C5—42no—
82C22×C4×C5C22⋊C411yescharacteristic
83C22×C4×C5C22⋊C411yescharacteristic
84C22×C4×C5C22⋊C411yescharacteristic
85C22×C4×C5C22⋊C411yescharacteristic
86C22×C4×C5C22×C411yescharacteristic
87C22×C4×C5C2×D411yescharacteristic
88C22×C4×C5C2×Q812yes—
89C22×C4×C5#4112yes—
90C2×C5×C8—24no—
91C2×C5×C8—42no—
92C2×C5×C8—42no—
93C5×C4⋊C4—41no—
94C5×C4⋊C4—41no—
95C5×C4⋊C4—41no—
96C5×C4⋊C4—41no—
97C5×C4⋊C4—42no—
98C5×C4⋊C4—42no—
99C5×C4⋊C4—42no—
100C5×C4⋊C4—42no—
101C5×C22⋊C4—42no—
102C5×C22⋊C4—42no—
103C42×C5—22no—
104C42×C5—22no—
105C42×C5—41no—
106C42×C5—41no—
107C2×#125C4×C511yescharacteristic, complemented
108C22×C42C22×C511yescharacteristic
109C2×C22⋊C8C22×C512yes—
110C2×C4×C8—21no—
111#389C4×C511yescharacteristic, complemented
112#389C4×C511yescharacteristic, complemented
113#387—21no—
114#387—21no—
115#385—21no—
116#385—21no—
117#382C4×C511yescharacteristic, complemented
118#380C22×C511yescharacteristic
119#380C22×C511yescharacteristic
120C2×#95—21no—
121C2×#95—21no—
122C2×#95C22×C512yes—
123#336—21no—
124C23×C5—21no—
125C23×C5—21no—
126C23×C5—21no—
127C23×C5—21no—
128C23×C5C2×C22⋊C411yescharacteristic
129C23×C5#12411yescharacteristic
130C23×C5C4⋊Q811yescharacteristic
131C23×C5#13512yes—
132C23×C5#13512yes—
133C2×C4×C5—21no—
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
139C2×C4×C5—21no—
140C2×C4×C5—21no—
141C2×C4×C5—21no—
142C2×C4×C5—21no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—42no—
148C2×C4×C5—42no—
149C2×C4×C5—44no—
150C2×C4×C5—44no—
151C2×C4×C5—44no—
152C2×C4×C5—44no—
153C2×C4×C5—44no—
154C2×C4×C5—41no—
155C2×C4×C5—41no—
156C2×C4×C5—41no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—41no—
161C2×C4×C5—41no—
162C2×C4×C5—41no—
163C2×C4×C5—41no—
164C2×C4×C5—41no—
165C2×C4×C5—41no—
166C2×C4×C5—82no—
167C2×C4×C5—82no—
168C2×C4×C5—82no—
169C2×C4×C5—82no—
170C2×C4×C5#9912yes—
171C2×C4×C5#10412yes—
172C2×C4×C5C4×Q812yes—
173C2×C4×C5C22⋊Q812yes—
174C5×C8—44no—
175C23×C4—22no—
176C23×C4C5×D411yescharacteristic
177C23×C4C5×D411yescharacteristic
178C23×C4C23×C511yescharacteristic
179C22×C8—22no—
180#125—42no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4C2×C4×C511yescharacteristic
186C2×C4⋊C4C2×C4×C511yescharacteristic
187C2×C4⋊C4C2×C4×C511yescharacteristic
188C2×C4⋊C4C2×C4×C511yescharacteristic
189C2×C22⋊C4—21no—
190C2×C22⋊C4—21no—
191C2×C42—42no—
192C2×C42C2×C4×C511yescharacteristic
193C2×C42C2×C4×C511yescharacteristic
194C2×C42C5×D411yescharacteristic
195C2×C42C5×D411yescharacteristic
196C22⋊C8—22no—
197C22⋊C8C5×Q814yes—
198C4×C8—42no—
199#95—24no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—24no—
207#95—42no—
208C22×C5—21no—
209C22×C5—21no—
210C22×C5—21no—
211C22×C5—21no—
212C22×C5—22no—
213C22×C5—22no—
214C22×C5—22no—
215C22×C5—22no—
216C22×C5#39111yescharacteristic
217C22×C5C2×#9911yescharacteristic
218C22×C5#41011yescharacteristic
219C22×C5#41611yescharacteristic
220C22×C5#41611yescharacteristic
221C22×C5C2×#10411yescharacteristic
222C22×C5#42111yescharacteristic
223C22×C5#48812yes—
224C22×C5#49912yes—
225C4×C5—22no—
226C4×C5—22no—
227C4×C5—22no—
228C4×C5—22no—
229C4×C5—41no—
230C4×C5—41no—
231C4×C5—84no—
232C4×C5—81no—
233C4×C5—81no—
234C4×C5—81no—
235C4×C5—81no—
236C24C2×C5×D411yescharacteristic
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—24no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4C5×C22⋊C411yescharacteristic
257C22×C4C5×C22⋊C411yescharacteristic
258C22×C4C5×C22⋊C411yescharacteristic
259C22×C4C5×C22⋊C411yescharacteristic
260C22×C4C22×C4×C511yescharacteristic
261C22×C4C2×C5×D411yescharacteristic
262C22×C4C2×C5×Q812yes—
263C22×C4C5×#4112yes—
264C2×C8—24no—
265C2×C8—42no—
266C2×C8—42no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C22⋊C4—42no—
276C22⋊C4—42no—
277C42—22no—
278C42—22no—
279C42—41no—
280C42—41no—
281C2×C5—22no—
282C2×C5—22no—
283C2×C5#150011yescharacteristic
284C2×C5#150111yescharacteristic
285C2×C5#151611yescharacteristic
286C2×C5#152111yescharacteristic
287C2×C5#198611yescharacteristic
288C2×C5#199111yescharacteristic
289C2×C5#199611yescharacteristic
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23C2×C5×C22⋊C411yescharacteristic
295C23C5×#12411yescharacteristic
296C23C5×C4⋊Q811yescharacteristic
297C23C5×#13512yes—
298C23C5×#13512yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—44no—
319C2×C4—44no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4C5×#9912yes—
337C2×C4C5×#10412yes—
338C2×C4C4×C5×Q812yes—
339C2×C4C5×C22⋊Q812yes—
340C8—44no—
341C5#988611yescharacteristic, direct product factor, Sylow
342C22—22no—
343C22—22no—
344C22—22no—
345C22—22no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22C5×#39111yescharacteristic
351C22C2×C5×#9911yescharacteristic
352C22C5×#41011yescharacteristic
353C22C5×#41611yescharacteristic
354C22C5×#41611yescharacteristic
355C22C2×C5×#10411yescharacteristic
356C22C5×#42111yescharacteristic
357C22C5×#48812yes—
358C22C5×#49912yes—
359C4—22no—
360C4—22no—
361C4—22no—
362C4—22no—
363C4—41no—
364C4—41no—
365C4—84no—
366C4—81no—
367C4—81no—
368C4—81no—
369C4—81no—
370C2—22no—
371C2—22no—
372C2C5×#150011yescharacteristic
373C2C5×#150111yescharacteristic
374C2C5×#151611yescharacteristic
375C2C5×#152111yescharacteristic
376C2C5×#198611yescharacteristic
377C2C5×#199111yescharacteristic
378C2C5×#199611yescharacteristic
subgroupG/H
center, socleC23×C5C2×C22⋊C4
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC24×C5C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C22×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×C5×#125C4semidirect
10. C5×#389C4semidirect
11. C5×#389C4semidirect
16. C5×#382C4semidirect
23. #9886C5direct (N × H)
107. C2×#125C4×C5semidirect
111. #389C4×C5semidirect
112. #389C4×C5semidirect
117. #382C4×C5semidirect
341. C5#9886direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#28512
C4×C5×C22⋊C82
C5×#14342
C5×#12942
#98865