Finite Group Databasebeta

← C5×#2829 #10616424

Subgroups — C5×#2829 #10616424

Order 640.

450 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#399C211yesmaximal, characteristic, complemented
2C5×#398C211yesmaximal, characteristic, complemented
3C5×#397C211yesmaximal, characteristic, complemented
4C5×#397C211yesmaximal, characteristic, complemented
5C5×#396C211yesmaximal, characteristic, complemented
6C5×#396C211yesmaximal, characteristic, complemented
7C5×#394C211yesmaximal, characteristic, complemented
8C5×#394C211yesmaximal, characteristic, complemented
9C5×#394C211yesmaximal, characteristic, complemented
10C5×#394C211yesmaximal, characteristic, complemented
11C5×#394C211yesmaximal, characteristic, complemented
12C5×#392C211yesmaximal, characteristic
13C5×#390C211yesmaximal, characteristic, complemented
14C5×#388C211yesmaximal, characteristic, complemented
15C5×#387C211yesmaximal, characteristic, complemented
16C22×C5×D4C2211yescharacteristic
17C22×C5×D4C2211yescharacteristic
18C22×C5×D4C2211yescharacteristic
19C2×C5×C4⋊C4C2211yescharacteristic
20C2×C5×C4⋊C4C2211yescharacteristic
21C2×C5×C4⋊C4C2211yescharacteristic
22C2×C5×C4⋊C4C2211yescharacteristic
23C2×C5×C4⋊C4C2211yescharacteristic
24C2×C5×C4⋊C4C2211yescharacteristic
25C2×C5×C4⋊C4C2211yescharacteristic
26C2×C5×C4⋊C4C2211yescharacteristic
27C2×C5×C22⋊C4C2211yescharacteristic
28C2×C5×C22⋊C4C2211yescharacteristic
29C2×C5×C22⋊C4C2211yescharacteristic
30C2×C5×C22⋊C4C2211yescharacteristic
31C2×C5×C22⋊C4C2211yescharacteristic
32C2×C5×C22⋊C4C2211yescharacteristic
33C2×C5×C22⋊C4C2211yescharacteristic
34C2×C5×C22⋊C4C2211yescharacteristic
35C2×C5×C22⋊C4C2211yescharacteristic
36C2×C5×C22⋊C4C2211yescharacteristic
37C2×C5×C22⋊C4C2211yescharacteristic
38C2×C5×C22⋊C4C2211yescharacteristic
39C2×C5×C22⋊C4C2211yescharacteristic
40C2×C5×C22⋊C4C2211yescharacteristic
41C2×C5×C22⋊C4C2211yescharacteristic
42C2×C42×C5C2211yescharacteristic
43C5×#95C2211yescharacteristic
44C5×#95C2211yescharacteristic
45C5×#95C2211yescharacteristic
46C5×#95C2211yescharacteristic
47C5×#95C2211yescharacteristic
48C5×#95C2211yescharacteristic
49C5×#95C2211yescharacteristic
50C5×#95C2211yescharacteristic
51#2829C511yesmaximal, characteristic, direct product factor, Sylow
52C24×C5C2311yescharacteristic
53C24×C5C2311yescharacteristic
54C24×C5C2311yescharacteristic
55C2×C5×D4—22no—
56C2×C5×D4—41no—
57C2×C5×D4—41no—
58C2×C5×D4—41no—
59C2×C5×D4—41no—
60C2×C5×D4—41no—
61C2×C5×D4—41no—
62C2×C5×D4—41no—
63C2×C5×D4—41no—
64C22×C4×C5C2311yescharacteristic
65C22×C4×C5C2311yescharacteristic
66C22×C4×C5C2311yescharacteristic
67C22×C4×C5C2311yescharacteristic
68C22×C4×C5C2311yescharacteristic
69C22×C4×C5C2311yescharacteristic
70C22×C4×C5C2311yescharacteristic
71C22×C4×C5C2311yescharacteristic
72C22×C4×C5C2311yescharacteristic
73C22×C4×C5C2311yescharacteristic
74C22×C4×C5C2311yescharacteristic
75C22×C4×C5C2311yescharacteristic
76C5×C4⋊C4—22no—
77C5×C4⋊C4—41no—
78C5×C4⋊C4—41no—
79C5×C4⋊C4—41no—
80C5×C4⋊C4—41no—
81C5×C4⋊C4—41no—
82C5×C4⋊C4—41no—
83C5×C4⋊C4—41no—
84C5×C22⋊C4—22no—
85C5×C22⋊C4—41no—
86C5×C22⋊C4—41no—
87C5×C22⋊C4—41no—
88C5×C22⋊C4—41no—
89C5×C22⋊C4—41no—
90C5×C22⋊C4—41no—
91C5×C22⋊C4—41no—
92C5×C22⋊C4—41no—
93C5×C22⋊C4—41no—
94C5×C22⋊C4—41no—
95C5×C22⋊C4—41no—
96C5×C22⋊C4—41no—
97C5×C22⋊C4—41no—
98C5×C22⋊C4—41no—
99C42×C5—41no—
100#399C2×C511yescharacteristic, complemented
101#398C2×C511yescharacteristic, complemented
102#397C2×C511yescharacteristic, complemented
103#397C2×C511yescharacteristic, complemented
104#396C2×C511yescharacteristic, complemented
105#396C2×C511yescharacteristic, complemented
106#394C2×C511yescharacteristic, complemented
107#394C2×C511yescharacteristic, complemented
108#394C2×C511yescharacteristic, complemented
109#394C2×C511yescharacteristic, complemented
110#394C2×C511yescharacteristic, complemented
111#392C2×C511yescharacteristic
112#390C2×C511yescharacteristic, complemented
113#388C2×C511yescharacteristic, complemented
114#387C2×C511yescharacteristic, complemented
115C23×C5—21no—
116C23×C5—21no—
117C23×C5—21no—
118C23×C5—21no—
119C23×C5—21no—
120C23×C5—21no—
121C23×C5—21no—
122C23×C5—21no—
123C23×C5—21no—
124C23×C5—21no—
125C23×C5—21no—
126C23×C5—21no—
127C23×C5—21no—
128C23×C5—21no—
129C23×C5—21no—
130C23×C5—21no—
131C23×C5—21no—
132C23×C5—21no—
133C23×C5—21no—
134C23×C5—21no—
135C23×C5—21no—
136C23×C5C2411yescharacteristic
137C5×D4—44no—
138C5×D4—44no—
139C5×D4—44no—
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—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—21no—
159C2×C4×C5—21no—
160C2×C4×C5—21no—
161C2×C4×C5—21no—
162C2×C4×C5—21no—
163C2×C4×C5—21no—
164C2×C4×C5—21no—
165C2×C4×C5—21no—
166C2×C4×C5—21no—
167C2×C4×C5—21no—
168C2×C4×C5—21no—
169C2×C4×C5—21no—
170C2×C4×C5—21no—
171C2×C4×C5—21no—
172C2×C4×C5—21no—
173C2×C4×C5—21no—
174C2×C4×C5—21no—
175C2×C4×C5#4112yes—
176C22×D4C22×C511yescharacteristic
177C22×D4C22×C511yescharacteristic
178C22×D4C22×C511yescharacteristic
179C2×C4⋊C4C22×C511yescharacteristic
180C2×C4⋊C4C22×C511yescharacteristic
181C2×C4⋊C4C22×C511yescharacteristic
182C2×C4⋊C4C22×C511yescharacteristic
183C2×C4⋊C4C22×C511yescharacteristic
184C2×C4⋊C4C22×C511yescharacteristic
185C2×C4⋊C4C22×C511yescharacteristic
186C2×C4⋊C4C22×C511yescharacteristic
187C2×C22⋊C4C22×C511yescharacteristic
188C2×C22⋊C4C22×C511yescharacteristic
189C2×C22⋊C4C22×C511yescharacteristic
190C2×C22⋊C4C22×C511yescharacteristic
191C2×C22⋊C4C22×C511yescharacteristic
192C2×C22⋊C4C22×C511yescharacteristic
193C2×C22⋊C4C22×C511yescharacteristic
194C2×C22⋊C4C22×C511yescharacteristic
195C2×C22⋊C4C22×C511yescharacteristic
196C2×C22⋊C4C22×C511yescharacteristic
197C2×C22⋊C4C22×C511yescharacteristic
198C2×C22⋊C4C22×C511yescharacteristic
199C2×C22⋊C4C22×C511yescharacteristic
200C2×C22⋊C4C22×C511yescharacteristic
201C2×C22⋊C4C22×C511yescharacteristic
202C2×C42C22×C511yescharacteristic
203#95C22×C511yescharacteristic
204#95C22×C511yescharacteristic
205#95C22×C511yescharacteristic
206#95C22×C511yescharacteristic
207#95C22×C511yescharacteristic
208#95C22×C511yescharacteristic
209#95C22×C511yescharacteristic
210#95C22×C511yescharacteristic
211C22×C5—41no—
212C22×C5—41no—
213C22×C5—41no—
214C22×C5—41no—
215C22×C5—41no—
216C22×C5—41no—
217C22×C5—41no—
218C22×C5—41no—
219C22×C5—41no—
220C22×C5—41no—
221C22×C5—41no—
222C22×C5—41no—
223C22×C5—41no—
224C22×C5—41no—
225C22×C5—41no—
226C22×C5—41no—
227C22×C5—41no—
228C22×C5—41no—
229C22×C5—41no—
230C22×C5—41no—
231C22×C5—41no—
232C22×C5C2×#4111yescharacteristic
233C22×C5H(5,𝔽2)11yescharacteristic
234C22×C5H(5,𝔽2)11yescharacteristic
235C22×C5H(5,𝔽2)11yescharacteristic
236C22×C5H(5,𝔽2)11yescharacteristic
237C22×C5H(5,𝔽2)11yescharacteristic
238C22×C52−1+411yescharacteristic
239C4×C5—22no—
240C4×C5—41no—
241C4×C5—41no—
242C4×C5—41no—
243C4×C5—41no—
244C4×C5—41no—
245C4×C5—41no—
246C4×C5—41no—
247C4×C5—41no—
248C4×C5—41no—
249C4×C5—41no—
250C4×C5—41no—
251C24C23×C511yescharacteristic
252C24C23×C511yescharacteristic
253C24C23×C511yescharacteristic
254C2×D4—22no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—41no—
263C22×C4C23×C511yescharacteristic
264C22×C4C23×C511yescharacteristic
265C22×C4C23×C511yescharacteristic
266C22×C4C23×C511yescharacteristic
267C22×C4C23×C511yescharacteristic
268C22×C4C23×C511yescharacteristic
269C22×C4C23×C511yescharacteristic
270C22×C4C23×C511yescharacteristic
271C22×C4C23×C511yescharacteristic
272C22×C4C23×C511yescharacteristic
273C22×C4C23×C511yescharacteristic
274C22×C4C23×C511yescharacteristic
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C22⋊C4—22no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C42—41no—
299C2×C5—81no—
300C2×C5—81no—
301C2×C5—81no—
302C2×C5#53811yescharacteristic
303C2×C5#54011yescharacteristic
304C2×C5#54211yescharacteristic
305C2×C5#56011yescharacteristic
306C2×C5#56011yescharacteristic
307C2×C5#56211yescharacteristic
308C2×C5#56211yescharacteristic
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23C24×C511yescharacteristic
331D4—44no—
332D4—44no—
333D4—44no—
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—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4C5×#4112yes—
370C5#282911yescharacteristic, direct product factor, Sylow
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22C2×C5×#4111yescharacteristic
393C22C5×H(5,𝔽2)11yescharacteristic
394C22C5×H(5,𝔽2)11yescharacteristic
395C22C5×H(5,𝔽2)11yescharacteristic
396C22C5×H(5,𝔽2)11yescharacteristic
397C22C5×H(5,𝔽2)11yescharacteristic
398C22C5×2−1+411yescharacteristic
399C4—22no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—41no—
411C2—81no—
412C2—81no—
413C2—81no—
414C2C5×#53811yescharacteristic
415C2C5×#54011yescharacteristic
416C2C5×#54211yescharacteristic
417C2C5×#56011yescharacteristic
418C2C5×#56011yescharacteristic
419C2C5×#56211yescharacteristic
420C2C5×#56211yescharacteristic
subgroupG/H
center, socleC23×C5C24
commutator, Frattini, cosocleC23C24×C5
prime radicalC5×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#399C2semidirect
2. C5×#398C2semidirect
3. C5×#397C2semidirect
4. C5×#397C2semidirect
5. C5×#396C2semidirect
6. C5×#396C2semidirect
7. C5×#394C2semidirect
8. C5×#394C2semidirect
9. C5×#394C2semidirect
10. C5×#394C2semidirect
11. C5×#394C2semidirect
13. C5×#390C2semidirect
14. C5×#388C2semidirect
15. C5×#387C2semidirect
51. #2829C5direct (N × H)
100. #399C2×C5semidirect
101. #398C2×C5semidirect
102. #397C2×C5semidirect
103. #397C2×C5semidirect
104. #396C2×C5semidirect
105. #396C2×C5semidirect
106. #394C2×C5semidirect
107. #394C2×C5semidirect
108. #394C2×C5semidirect
109. #394C2×C5semidirect
110. #394C2×C5semidirect
112. #390C2×C5semidirect
113. #388C2×C5semidirect
114. #387C2×C5semidirect
370. C5#2829direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#3992
C5×#3982
C5×#3972
C5×#3962
C5×#3942
C5×#3922
C5×#3902
C5×#3882
C5×#3872
#28295