Finite Group Databasebeta

← C5×#9887 #11932607

Subgroups — C5×#9887 #11932607

Order 1280.

598 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2851C211yesmaximal, characteristic
2C5×#1749C211yesmaximal, characteristic
3C5×C4⋊#95C211yesmaximal, characteristic
4C5×#1294C212yesmaximal
5C5×#1294C212yesmaximal
6C2×C5×#125C411yescharacteristic, complemented
7C22×C5×C4⋊C4—21no—
8C22×C42×C5C2211yescharacteristic
9C2×C5×C22⋊C8C2212yes—
10C2×C5×#97—21no—
11C5×#389C411yescharacteristic, complemented
12C5×#389C411yescharacteristic, complemented
13C5×#387—21no—
14C5×#387—21no—
15C5×#385—21no—
16C5×#385—21no—
17C5×#382C411yescharacteristic, complemented
18C5×#380C2211yescharacteristic
19C5×#380C2211yescharacteristic
20C2×C5×#95—21no—
21C2×C5×#95C2212yes—
22C5×#336—21no—
23#9887C511yesmaximal, 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—24no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—42no—
36C2×C5×C4⋊C4—42no—
37C2×C5×C4⋊C4C2×C411yescharacteristic
38C2×C5×C4⋊C4C2×C411yescharacteristic
39C2×C5×C4⋊C4C2×C411yescharacteristic
40C2×C5×C4⋊C4C2×C411yescharacteristic
41C2×C5×C22⋊C4—21no—
42C2×C5×C22⋊C4—21no—
43C2×C42×C5—42no—
44C2×C42×C5C2×C411yescharacteristic
45C2×C42×C5C2×C411yescharacteristic
46C2×C42×C5D411yescharacteristic
47C2×C42×C5D411yescharacteristic
48C5×C22⋊C8—22no—
49C5×C22⋊C8Q814yes—
50C5×#97—42no—
51C5×#95—21no—
52C5×#95—21no—
53C5×#95—21no—
54C5×#95—21no—
55C5×#95—21no—
56C5×#95—21no—
57C5×#95—24no—
58C5×#95—42no—
59#2851C2×C511yescharacteristic
60#1749C2×C511yescharacteristic
61C4⋊#95C2×C511yescharacteristic
62#1294C2×C512yes—
63#1294C2×C512yes—
64C24×C5C2×D411yescharacteristic
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5—22no—
68C22×C4×C5—22no—
69C22×C4×C5—21no—
70C22×C4×C5—21no—
71C22×C4×C5—24no—
72C22×C4×C5—21no—
73C22×C4×C5—21no—
74C22×C4×C5—21no—
75C22×C4×C5—21no—
76C22×C4×C5—41no—
77C22×C4×C5—41no—
78C22×C4×C5—41no—
79C22×C4×C5—41no—
80C22×C4×C5—42no—
81C22×C4×C5—42no—
82C22×C4×C5—42no—
83C22×C4×C5—42no—
84C22×C4×C5—42no—
85C22×C4×C5—42no—
86C22×C4×C5C22⋊C411yescharacteristic
87C22×C4×C5C22⋊C411yescharacteristic
88C22×C4×C5C22⋊C411yescharacteristic
89C22×C4×C5C22⋊C411yescharacteristic
90C22×C4×C5C22×C411yescharacteristic
91C22×C4×C5C2×D411yescharacteristic
92C22×C4×C5C2×Q812yes—
93C22×C4×C5#4112yes—
94C2×C5×C8—24no—
95C2×C5×C8—42no—
96C2×C5×C8—42no—
97C5×C4⋊C4—41no—
98C5×C4⋊C4—41no—
99C5×C4⋊C4—41no—
100C5×C4⋊C4—41no—
101C5×C4⋊C4—42no—
102C5×C4⋊C4—48no—
103C5×C4⋊C4—42no—
104C5×C4⋊C4—42no—
105C5×C4⋊C4—42no—
106C5×C22⋊C4—41no—
107C5×C22⋊C4—41no—
108C5×C22⋊C4—41no—
109C5×C22⋊C4—41no—
110C42×C5—22no—
111C42×C5—22no—
112C42×C5—41no—
113C42×C5—41no—
114C2×#125C4×C511yescharacteristic, complemented
115C22×C4⋊C4—21no—
116C22×C42C22×C511yescharacteristic
117C2×C22⋊C8C22×C512yes—
118C2×#97—21no—
119#389C4×C511yescharacteristic, complemented
120#389C4×C511yescharacteristic, complemented
121#387—21no—
122#387—21no—
123#385—21no—
124#385—21no—
125#382C4×C511yescharacteristic, complemented
126#380C22×C511yescharacteristic
127#380C22×C511yescharacteristic
128C2×#95—21no—
129C2×#95C22×C512yes—
130#336—21no—
131C23×C5—21no—
132C23×C5—21no—
133C23×C5—21no—
134C23×C5—21no—
135C23×C5C2×C22⋊C411yescharacteristic
136C23×C5#12411yescharacteristic
137C23×C5C4⋊Q811yescharacteristic
138C23×C5AGL(1,ℤ/8)11yescharacteristic
139C23×C5AGL(1,ℤ/8)11yescharacteristic
140C23×C5#13711yescharacteristic
141C23×C5#13711yescharacteristic
142C2×C4×C5—24no—
143C2×C4×C5—24no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5—21no—
149C2×C4×C5—21no—
150C2×C4×C5—21no—
151C2×C4×C5—21no—
152C2×C4×C5—21no—
153C2×C4×C5—21no—
154C2×C4×C5—21no—
155C2×C4×C5—21no—
156C2×C4×C5—21no—
157C2×C4×C5—21no—
158C2×C4×C5—42no—
159C2×C4×C5—42no—
160C2×C4×C5—42no—
161C2×C4×C5—42no—
162C2×C4×C5—44no—
163C2×C4×C5—44no—
164C2×C4×C5—44no—
165C2×C4×C5—41no—
166C2×C4×C5—41no—
167C2×C4×C5—41no—
168C2×C4×C5—41no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5—41no—
172C2×C4×C5—41no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5—41no—
176C2×C4×C5—41no—
177C2×C4×C5—82no—
178C2×C4×C5—82no—
179C2×C4×C5—82no—
180C2×C4×C5—82no—
181C2×C4×C5#9912yes—
182C2×C4×C5#10412yes—
183C2×C4×C5C4×Q812yes—
184C2×C4×C5C22⋊Q812yes—
185C5×C8—44no—
186C23×C4—22no—
187C23×C4C5×D411yescharacteristic
188C23×C4C5×D411yescharacteristic
189C23×C4C23×C511yescharacteristic
190C22×C8—22no—
191#125—42no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—42no—
198C2×C4⋊C4—42no—
199C2×C4⋊C4C2×C4×C511yescharacteristic
200C2×C4⋊C4C2×C4×C511yescharacteristic
201C2×C4⋊C4C2×C4×C511yescharacteristic
202C2×C4⋊C4C2×C4×C511yescharacteristic
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C42—42no—
206C2×C42C2×C4×C511yescharacteristic
207C2×C42C2×C4×C511yescharacteristic
208C2×C42C5×D411yescharacteristic
209C2×C42C5×D411yescharacteristic
210C22⋊C8—22no—
211C22⋊C8C5×Q814yes—
212#97—42no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—24no—
220#95—42no—
221C22×C5—21no—
222C22×C5—21no—
223C22×C5—21no—
224C22×C5—21no—
225C22×C5—21no—
226C22×C5—21no—
227C22×C5—21no—
228C22×C5—21no—
229C22×C5—21no—
230C22×C5—21no—
231C22×C5—21no—
232C22×C5—21no—
233C22×C5#39111yescharacteristic
234C22×C5C2×#9911yescharacteristic
235C22×C5#41011yescharacteristic
236C22×C5#41711yescharacteristic
237C22×C5#41711yescharacteristic
238C22×C5C2×#10411yescharacteristic
239C22×C5#42111yescharacteristic
240C22×C5#49011yescharacteristic
241C22×C5#49111yescharacteristic
242C22×C5#50111yescharacteristic
243C22×C5#50111yescharacteristic
244C4×C5—22no—
245C4×C5—22no—
246C4×C5—22no—
247C4×C5—22no—
248C4×C5—41no—
249C4×C5—41no—
250C4×C5—84no—
251C4×C5—81no—
252C4×C5—81no—
253C4×C5—81no—
254C4×C5—81no—
255C24C2×C5×D411yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—24no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4C5×C22⋊C411yescharacteristic
278C22×C4C5×C22⋊C411yescharacteristic
279C22×C4C5×C22⋊C411yescharacteristic
280C22×C4C5×C22⋊C411yescharacteristic
281C22×C4C22×C4×C511yescharacteristic
282C22×C4C2×C5×D411yescharacteristic
283C22×C4C2×C5×Q812yes—
284C22×C4C5×#4112yes—
285C2×C8—24no—
286C2×C8—42no—
287C2×C8—42no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—48no—
293C4⋊C4—42no—
294C4⋊C4—42no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C42—22no—
302C42—22no—
303C42—41no—
304C42—41no—
305C2×C5—21no—
306C2×C5—21no—
307C2×C5—21no—
308C2×C5—21no—
309C2×C5#150411yescharacteristic
310C2×C5#150911yescharacteristic
311C2×C5#151211yescharacteristic
312C2×C5#151311yescharacteristic
313C2×C5#198611yescharacteristic
314C2×C5#199211yescharacteristic
315C2×C5#199611yescharacteristic
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23C2×C5×C22⋊C411yescharacteristic
321C23C5×#12411yescharacteristic
322C23C5×C4⋊Q811yescharacteristic
323C23C5×AGL(1,ℤ/8)11yescharacteristic
324C23C5×AGL(1,ℤ/8)11yescharacteristic
325C23C5×#13711yescharacteristic
326C23C5×#13711yescharacteristic
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—44no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—82no—
363C2×C4—82no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4C5×#9912yes—
367C2×C4C5×#10412yes—
368C2×C4C4×C5×Q812yes—
369C2×C4C5×C22⋊Q812yes—
370C8—44no—
371C5#988711yescharacteristic, direct product factor, Sylow
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22C5×#39111yescharacteristic
385C22C2×C5×#9911yescharacteristic
386C22C5×#41011yescharacteristic
387C22C5×#41711yescharacteristic
388C22C5×#41711yescharacteristic
389C22C2×C5×#10411yescharacteristic
390C22C5×#42111yescharacteristic
391C22C5×#49011yescharacteristic
392C22C5×#49111yescharacteristic
393C22C5×#50111yescharacteristic
394C22C5×#50111yescharacteristic
395C4—22no—
396C4—22no—
397C4—22no—
398C4—22no—
399C4—41no—
400C4—41no—
401C4—84no—
402C4—81no—
403C4—81no—
404C4—81no—
405C4—81no—
406C2—21no—
407C2—21no—
408C2—21no—
409C2—21no—
410C2C5×#150411yescharacteristic
411C2C5×#150911yescharacteristic
412C2C5×#151211yescharacteristic
413C2C5×#151311yescharacteristic
414C2C5×#198611yescharacteristic
415C2C5×#199211yescharacteristic
416C2C5×#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
11. C5×#389C4semidirect
12. C5×#389C4semidirect
17. C5×#382C4semidirect
23. #9887C5direct (N × H)
114. C2×#125C4×C5semidirect
119. #389C4×C5semidirect
120. #389C4×C5semidirect
125. #382C4×C5semidirect
371. C5#9887direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#28512
C5×#17492
C5×C4⋊#952
C5×#12942
#98875