Finite Group Databasebeta

← C5×#36695 #11959415

Subgroups — C5×#36695 #11959415

Order 1280.

1664 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2845C211yesmaximal, characteristic, complemented
2C5×#2837C214yesmaximal, complemented
3C5×#2831C214yesmaximal, complemented
4C5×#2829C214yesmaximal, complemented
5C5×#2820C212yesmaximal, complemented
6C5×#2819C211yesmaximal, characteristic
7C5×#2396C214yesmaximal, complemented
8C5×#2395C214yesmaximal, complemented
9C5×#2392C214yesmaximal, complemented
10C4×C5×#125C211yesmaximal, characteristic, complemented
11C4×C5×#124C212yesmaximal, complemented
12C2×C5×#125C2211yescharacteristic
13C2×C5×#124C2212yes—
14C2×C4×C5×Q8C2212yes—
15C2×C4×C5×D4C2212yes—
16C2×C4×C5×D4C2214yes—
17C2×C5×#117C2214yes—
18C5×#400C2214yes—
19C5×#400C2214yes—
20C5×#399C2214yes—
21C5×#399C2214yes—
22C5×#398C2214yes—
23C5×#398C2214yes—
24C5×#398C2214yes—
25C5×#398C2214yes—
26C5×#397C2214yes—
27C5×#397C2214yes—
28C5×#397C2214yes—
29C5×#397C2214yes—
30C5×#396C2214yes—
31C5×#396C2214yes—
32C5×#396C2214yes—
33C5×#396C2214yes—
34C5×#395C2214yes—
35C5×#394C2214yes—
36C5×#394C2214yes—
37C5×#394C2214yes—
38C5×#394C2214yes—
39C5×#394C2214yes—
40C5×#393C2214yes—
41C5×#392C2214yes—
42C5×#391C2212yes—
43C5×#390C2212yes—
44C5×#389C2212yes—
45C5×#388C2214yes—
46C5×#388C2214yes—
47C5×#387C2214yes—
48C5×#382C2212yes—
49C5×#382C2211yescharacteristic
50C4×C5×C4⋊C4C2214yes—
51C4×C5×C4⋊C4C2212yes—
52C4×C5×C4⋊C4C2214yes—
53C4×C5×C22⋊C4C2214yes—
54C4×C5×C22⋊C4C2214yes—
55C4×C5×C22⋊C4C2214yes—
56C43×C5C2211yescharacteristic
57#36695C511yesmaximal, characteristic, direct product factor, Sylow
58C22×C5×Q8C2312yes—
59C22×C5×D4C2312yes—
60C22×C5×D4C2314yes—
61C23×C4×C5C2314yes—
62C5×#125—24no—
63C5×#124—28no—
64C4×C5×Q8—44no—
65C4×C5×D4—48no—
66C4×C5×D4—44no—
67C5×#117—48no—
68C2×C5×C4⋊C4C2314yes—
69C2×C5×C4⋊C4C2312yes—
70C2×C5×C4⋊C4C2312yes—
71C2×C5×C4⋊C4C2314yes—
72C2×C5×C4⋊C4C2314yes—
73C2×C5×C4⋊C4C2314yes—
74C2×C5×C4⋊C4C2312yes—
75C2×C5×C4⋊C4C2312yes—
76C2×C5×C4⋊C4C2314yes—
77C2×C5×C4⋊C4C2314yes—
78C2×C5×C4⋊C4C2314yes—
79C2×C5×C4⋊C4C2314yes—
80C2×C5×C22⋊C4C2314yes—
81C2×C5×C22⋊C4C2314yes—
82C2×C5×C22⋊C4C2314yes—
83C2×C5×C22⋊C4C2314yes—
84C2×C5×C22⋊C4C2314yes—
85C2×C5×C22⋊C4C2314yes—
86C2×C5×C22⋊C4C2314yes—
87C2×C5×C22⋊C4C2314yes—
88C2×C5×C22⋊C4C2314yes—
89C2×C5×C22⋊C4C2314yes—
90C2×C5×C22⋊C4C2314yes—
91C2×C42×C5C2311yescharacteristic
92C2×C42×C5C2312yes—
93C2×C42×C5C2314yes—
94C2×C42×C5C2314yes—
95C2×C42×C5C2312yes—
96C2×C42×C5C2311yescharacteristic
97C2×C42×C5C2311yescharacteristic
98C5×#95C2314yes—
99C5×#95C2314yes—
100C5×#95C2314yes—
101C5×#95C2314yes—
102C5×#95C2314yes—
103C5×#95C2314yes—
104C5×#95C2314yes—
105C5×#95C2314yes—
106C5×#95C2314yes—
107C5×#95C2314yes—
108C5×#95C2314yes—
109#2845C2×C511yescharacteristic, complemented
110#2837C2×C514yescomplemented
111#2831C2×C514yescomplemented
112#2829C2×C514yescomplemented
113#2820C2×C512yescomplemented
114#2819C2×C511yescharacteristic
115#2396C2×C514yescomplemented
116#2395C2×C514yescomplemented
117#2392C2×C514yescomplemented
118C4×#125C2×C511yescharacteristic, complemented
119C4×#124C2×C512yescomplemented
120C24×C5C2414yes—
121C2×C5×Q8—24no—
122C2×C5×Q8—42no—
123C2×C5×Q8—42no—
124C2×C5×D4—24no—
125C2×C5×D4—42no—
126C2×C5×D4—44no—
127C2×C5×D4—42no—
128C2×C5×D4—44no—
129C2×C5×D4—44no—
130C22×C4×C5—28no—
131C22×C4×C5—28no—
132C22×C4×C5—28no—
133C22×C4×C5C2412yes—
134C22×C4×C5C2411yescharacteristic
135C22×C4×C5C2414yes—
136C22×C4×C5C2414yes—
137C22×C4×C5C2414yes—
138C22×C4×C5C2414yes—
139C22×C4×C5C2414yes—
140C22×C4×C5C2411yescharacteristic
141C22×C4×C5C2412yes—
142C22×C4×C5C2411yescharacteristic
143C5×C4⋊C4—24no—
144C5×C4⋊C4—28no—
145C5×C4⋊C4—42no—
146C5×C4⋊C4—44no—
147C5×C4⋊C4—44no—
148C5×C4⋊C4—44no—
149C5×C4⋊C4—44no—
150C5×C4⋊C4—44no—
151C5×C4⋊C4—42no—
152C5×C4⋊C4—44no—
153C5×C4⋊C4—42no—
154C5×C4⋊C4—44no—
155C5×C22⋊C4—28no—
156C5×C22⋊C4—28no—
157C5×C22⋊C4—44no—
158C5×C22⋊C4—44no—
159C5×C22⋊C4—44no—
160C5×C22⋊C4—44no—
161C5×C22⋊C4—44no—
162C5×C22⋊C4—44no—
163C5×C22⋊C4—44no—
164C5×C22⋊C4—44no—
165C5×C22⋊C4—44no—
166C42×C5—28no—
167C42×C5—28no—
168C42×C5—24no—
169C42×C5—22no—
170C42×C5—41no—
171C42×C5—42no—
172C42×C5#4114yes—
173C2×#125C22×C511yescharacteristic
174C2×#124C22×C512yes—
175C2×C4×Q8C22×C512yes—
176C2×C4×D4C22×C514yes—
177C2×C4×D4C22×C512yes—
178C2×#117C22×C514yes—
179#400C22×C514yes—
180#400C22×C514yes—
181#399C22×C514yes—
182#399C22×C514yes—
183#398C22×C514yes—
184#398C22×C514yes—
185#398C22×C514yes—
186#398C22×C514yes—
187#397C22×C514yes—
188#397C22×C514yes—
189#397C22×C514yes—
190#397C22×C514yes—
191#396C22×C514yes—
192#396C22×C514yes—
193#396C22×C514yes—
194#396C22×C514yes—
195#395C22×C514yes—
196#394C22×C514yes—
197#394C22×C514yes—
198#394C22×C514yes—
199#394C22×C514yes—
200#394C22×C514yes—
201#393C22×C514yes—
202#392C22×C514yes—
203#391C22×C512yes—
204#390C22×C512yes—
205#389C22×C512yes—
206#388C22×C514yes—
207#388C22×C514yes—
208#387C22×C514yes—
209#382C22×C511yescharacteristic
210#382C22×C512yes—
211C4×C4⋊C4C22×C514yes—
212C4×C4⋊C4C22×C512yes—
213C4×C4⋊C4C22×C514yes—
214C4×C22⋊C4C22×C514yes—
215C4×C22⋊C4C22×C514yes—
216C4×C22⋊C4C22×C514yes—
217C43C22×C511yescharacteristic
218C23×C5—24no—
219C23×C5—24no—
220C23×C5—24no—
221C23×C5—24no—
222C23×C5—24no—
223C23×C5—24no—
224C23×C5—24no—
225C23×C5C2511yescharacteristic
226C5×Q8—48no—
227C5×D4—48no—
228C5×D4—416no—
229C2×C4×C5—22no—
230C2×C4×C5—21no—
231C2×C4×C5—21no—
232C2×C4×C5—22no—
233C2×C4×C5—24no—
234C2×C4×C5—24no—
235C2×C4×C5—24no—
236C2×C4×C5—22no—
237C2×C4×C5—24no—
238C2×C4×C5—24no—
239C2×C4×C5—24no—
240C2×C4×C5—24no—
241C2×C4×C5—24no—
242C2×C4×C5—21no—
243C2×C4×C5—24no—
244C2×C4×C5—22no—
245C2×C4×C5—22no—
246C2×C4×C5—22no—
247C2×C4×C5—24no—
248C2×C4×C5—24no—
249C2×C4×C5—24no—
250C2×C4×C5—24no—
251C2×C4×C5—24no—
252C2×C4×C5—24no—
253C2×C4×C5—416no—
254C2×C4×C5C2×#4112yes—
255C2×C4×C5C2×#4114yes—
256C2×C4×C5H(5,𝔽2)14yes—
257C2×C4×C52−1+412yes—
258C22×Q8C23×C512yes—
259C22×D4C23×C512yes—
260C22×D4C23×C514yes—
261C23×C4C23×C514yes—
262#125—24no—
263#124—28no—
264C4×Q8—44no—
265C4×D4—48no—
266C4×D4—44no—
267#117—48no—
268C2×C4⋊C4C23×C514yes—
269C2×C4⋊C4C23×C512yes—
270C2×C4⋊C4C23×C514yes—
271C2×C4⋊C4C23×C514yes—
272C2×C4⋊C4C23×C512yes—
273C2×C4⋊C4C23×C514yes—
274C2×C4⋊C4C23×C512yes—
275C2×C4⋊C4C23×C514yes—
276C2×C4⋊C4C23×C512yes—
277C2×C4⋊C4C23×C514yes—
278C2×C4⋊C4C23×C514yes—
279C2×C4⋊C4C23×C514yes—
280C2×C22⋊C4C23×C514yes—
281C2×C22⋊C4C23×C514yes—
282C2×C22⋊C4C23×C514yes—
283C2×C22⋊C4C23×C514yes—
284C2×C22⋊C4C23×C514yes—
285C2×C22⋊C4C23×C514yes—
286C2×C22⋊C4C23×C514yes—
287C2×C22⋊C4C23×C514yes—
288C2×C22⋊C4C23×C514yes—
289C2×C22⋊C4C23×C514yes—
290C2×C22⋊C4C23×C514yes—
291C2×C42C23×C514yes—
292C2×C42C23×C514yes—
293C2×C42C23×C512yes—
294C2×C42C23×C511yescharacteristic
295C2×C42C23×C512yes—
296C2×C42C23×C511yescharacteristic
297C2×C42C23×C511yescharacteristic
298#95C23×C514yes—
299#95C23×C514yes—
300#95C23×C514yes—
301#95C23×C514yes—
302#95C23×C514yes—
303#95C23×C514yes—
304#95C23×C514yes—
305#95C23×C514yes—
306#95C23×C514yes—
307#95C23×C514yes—
308#95C23×C514yes—
309C22×C5—44no—
310C22×C5—44no—
311C22×C5—44no—
312C22×C5—44no—
313C22×C5—44no—
314C22×C5—44no—
315C22×C5—44no—
316C22×C5C22×#4111yescharacteristic
317C22×C5C2×H(5,𝔽2)12yes—
318C22×C5C2×2−1+411yescharacteristic
319C22×C5#58512yes—
320C22×C5#58511yescharacteristic
321C4×C5—24no—
322C4×C5—22no—
323C4×C5—44no—
324C4×C5—44no—
325C4×C5—44no—
326C4×C5—42no—
327C4×C5—44no—
328C4×C5—44no—
329C4×C5—41no—
330C4×C5#56214yes—
331C24C24×C514yes—
332C2×Q8—24no—
333C2×Q8—42no—
334C2×Q8—42no—
335C2×D4—24no—
336C2×D4—42no—
337C2×D4—44no—
338C2×D4—42no—
339C2×D4—44no—
340C2×D4—44no—
341C22×C4—28no—
342C22×C4—28no—
343C22×C4—28no—
344C22×C4C24×C511yescharacteristic
345C22×C4C24×C514yes—
346C22×C4C24×C514yes—
347C22×C4C24×C514yes—
348C22×C4C24×C512yes—
349C22×C4C24×C514yes—
350C22×C4C24×C514yes—
351C22×C4C24×C511yescharacteristic
352C22×C4C24×C512yes—
353C22×C4C24×C511yescharacteristic
354C4⋊C4—24no—
355C4⋊C4—28no—
356C4⋊C4—44no—
357C4⋊C4—44no—
358C4⋊C4—42no—
359C4⋊C4—44no—
360C4⋊C4—42no—
361C4⋊C4—44no—
362C4⋊C4—42no—
363C4⋊C4—44no—
364C4⋊C4—44no—
365C4⋊C4—44no—
366C22⋊C4—28no—
367C22⋊C4—28no—
368C22⋊C4—44no—
369C22⋊C4—44no—
370C22⋊C4—44no—
371C22⋊C4—44no—
372C22⋊C4—44no—
373C22⋊C4—44no—
374C22⋊C4—44no—
375C22⋊C4—44no—
376C22⋊C4—44no—
377C42—28no—
378C42—28no—
379C42—24no—
380C42—22no—
381C42—41no—
382C42—42no—
383C42C5×#4114yes—
384C2×C5—84no—
385C2×C5#346012yes—
386C2×C5#346111yescharacteristic
387C2×C5C2×#56211yescharacteristic
388C2×C5#352912yes—
389C2×C5#353111yescharacteristic
390C23—24no—
391C23—24no—
392C23—24no—
393C23—24no—
394C23—24no—
395C23—24no—
396C23—24no—
397C23C25×C511yescharacteristic
398Q8—48no—
399D4—48no—
400D4—416no—
401C2×C4—22no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—22no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—21no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—416no—
426C2×C4C2×C5×#4112yes—
427C2×C4C2×C5×#4114yes—
428C2×C4C5×H(5,𝔽2)14yes—
429C2×C4C5×2−1+412yes—
430C5#3669511yescharacteristic, direct product factor, Sylow
431C22—44no—
432C22—44no—
433C22—44no—
434C22—44no—
435C22—44no—
436C22—44no—
437C22—44no—
438C22C22×C5×#4111yescharacteristic
439C22C2×C5×H(5,𝔽2)12yes—
440C22C2×C5×2−1+411yescharacteristic
441C22C5×#58512yes—
442C22C5×#58511yescharacteristic
443C4—24no—
444C4—22no—
445C4—44no—
446C4—44no—
447C4—44no—
448C4—44no—
449C4—42no—
450C4—44no—
451C4—41no—
452C4C5×#56214yes—
453C2—84no—
454C2C5×#346012yes—
455C2C5×#346111yescharacteristic
456C2C2×C5×#56211yescharacteristic
457C2C5×#352912yes—
458C2C5×#353111yescharacteristic
subgroupG/H
centerC22×C4×C5C24
commutator, Frattini, cosocleC23C25×C5
socleC23×C5C25
prime radicalC5×#2819C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#2845C2semidirect
2. C5×#2837C2semidirect
3. C5×#2831C2semidirect
4. C5×#2829C2semidirect
5. C5×#2820C2semidirect
7. C5×#2396C2semidirect
8. C5×#2395C2semidirect
9. C5×#2392C2semidirect
10. C4×C5×#125C2semidirect
11. C4×C5×#124C2semidirect
57. #36695C5direct (N × H)
109. #2845C2×C5semidirect
110. #2837C2×C5semidirect
111. #2831C2×C5semidirect
112. #2829C2×C5semidirect
113. #2820C2×C5semidirect
115. #2396C2×C5semidirect
116. #2395C2×C5semidirect
117. #2392C2×C5semidirect
118. C4×#125C2×C5semidirect
119. C4×#124C2×C5semidirect
430. C5#36695direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#28452
C5×#28372
C5×#28312
C5×#28292
C5×#28202
C5×#28192
C5×#23962
C5×#23952
C5×#23922
C4×C5×#1252
C4×C5×#1242
#366955