Finite Group Databasebeta

← C5×#13225 #11935945

Subgroups — C5×#13225 #11935945

Order 1280.

602 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2544C211yesmaximal, characteristic
2C2×C5×#354C212yesmaximal, complemented
3C2×C5×#353C212yesmaximal
4C5×#1799C211yesmaximal, characteristic, complemented
5C4×C5×#99C211yesmaximal, characteristic, complemented
6C2×C5×#127C2211yescharacteristic
7C2×C5×#124C411yescharacteristic, complemented
8C2×C5×#124C2211yescharacteristic
9C2×C4×C5×D4C2211yescharacteristic
10C2×C5×#99C2212yes—
11C2×C5×#99C2212yes—
12C5×#394—21no—
13C5×#394—21no—
14C5×#391C411yescharacteristic, complemented
15C5×#390C411yescharacteristic, complemented
16C5×#386—21no—
17C5×#386—21no—
18C5×#380—21no—
19C4×C5×C4⋊C4C411yescharacteristic, complemented
20C4×C5×C22⋊C4—21no—
21C5×#354—24no—
22C5×#353—24no—
23C5×#342—21no—
24C5×#342—21no—
25#13225C511yesmaximal, characteristic, direct product factor, Sylow
26C22×C5×Q8C2×C411yescharacteristic
27C22×C5×D4—21no—
28C22×C5×D4—21no—
29C22×C5×D4C2×C411yescharacteristic
30C22×C5×D4C2311yescharacteristic
31C23×C4×C5D411yescharacteristic
32C23×C4×C5D411yescharacteristic
33C5×#127—22no—
34C5×#127—22no—
35C5×#124—22no—
36C5×#124—22no—
37C5×#124—41no—
38C5×#124—41no—
39C4×C5×D4—41no—
40C4×C5×D4—41no—
41C2×C5×C4⋊C4—21no—
42C2×C5×C4⋊C4—41no—
43C2×C5×C4⋊C4C2×C411yescharacteristic
44C2×C5×C22⋊C4—22no—
45C2×C5×C22⋊C4—21no—
46C2×C5×C22⋊C4—21no—
47C2×C5×C22⋊C4—21no—
48C2×C5×C22⋊C4—21no—
49C2×C5×C22⋊C4—22no—
50C2×C5×C22⋊C4—21no—
51C2×C5×C22⋊C4—21no—
52C2×C5×C22⋊C4D411yescharacteristic
53C2×C5×C22⋊C4D411yescharacteristic
54C2×C42×C5—41no—
55C2×C42×C5C2×C411yescharacteristic
56C2×C42×C5C2×C411yescharacteristic
57C2×C42×C5C2×C411yescharacteristic
58C5×#99—22no—
59C5×#99—22no—
60C5×#99—22no—
61C5×#99D414yes—
62C5×#95—21no—
63C5×#95—21no—
64C5×#95—21no—
65C5×#95—41no—
66C5×#95—41no—
67#2544C2×C511yescharacteristic
68C2×#354C2×C512yescomplemented
69C2×#353C2×C512yes—
70#1799C2×C511yescharacteristic, complemented
71C4×#99C2×C511yescharacteristic, complemented
72C24×C5—21no—
73C24×C5C2×D411yescharacteristic
74C24×C5C2×D411yescharacteristic
75C2×C5×Q8—22no—
76C2×C5×Q8—41no—
77C2×C5×Q8—41no—
78C2×C5×D4—22no—
79C2×C5×D4—41no—
80C2×C5×D4—41no—
81C2×C5×D4—41no—
82C2×C5×D4—41no—
83C2×C5×D4—42no—
84C2×C5×D4—42no—
85C2×C5×D4—42no—
86C2×C5×D4—41no—
87C2×C5×D4—41no—
88C2×C5×D4—81no—
89C2×C5×D4—81no—
90C2×C5×D4C2×D412yes—
91C2×C5×D4#4112yes—
92C22×C4×C5—21no—
93C22×C4×C5—21no—
94C22×C4×C5—21no—
95C22×C4×C5—21no—
96C22×C4×C5—21no—
97C22×C4×C5—21no—
98C22×C4×C5—21no—
99C22×C4×C5—42no—
100C22×C4×C5—42no—
101C22×C4×C5—81no—
102C22×C4×C5—81no—
103C22×C4×C5C22⋊C411yescharacteristic
104C22×C4×C5C22⋊C411yescharacteristic
105C22×C4×C5C22⋊C411yescharacteristic
106C22×C4×C5C22⋊C411yescharacteristic
107C22×C4×C5C22×C411yescharacteristic
108C5×C4⋊C4—41no—
109C5×C4⋊C4—42no—
110C5×C4⋊C4—82no—
111C5×C22⋊C4—24no—
112C5×C22⋊C4—41no—
113C5×C22⋊C4—41no—
114C5×C22⋊C4—42no—
115C5×C22⋊C4—42no—
116C5×C22⋊C4—42no—
117C5×C22⋊C4—41no—
118C5×C22⋊C4—41no—
119C5×C22⋊C4—41no—
120C5×C22⋊C4—41no—
121C5×C22⋊C4—42no—
122C5×C22⋊C4—42no—
123C5×C22⋊C4—81no—
124C5×C22⋊C4—81no—
125C42×C5—21no—
126C42×C5—21no—
127C42×C5—22no—
128C42×C5—22no—
129C42×C5—82no—
130C2×#127C22×C511yescharacteristic
131C2×#124C4×C511yescharacteristic, complemented
132C2×#124C22×C511yescharacteristic
133C2×C4×D4C22×C511yescharacteristic
134C2×#99C22×C512yes—
135C2×#99C22×C512yes—
136#394—21no—
137#394—21no—
138#391C4×C511yescharacteristic, complemented
139#390C4×C511yescharacteristic, complemented
140#386—21no—
141#386—21no—
142#380—21no—
143C4×C4⋊C4C4×C511yescharacteristic, complemented
144C4×C22⋊C4—21no—
145#354—24no—
146#353—24no—
147#342—21no—
148#342—21no—
149C23×C5—21no—
150C23×C5—21no—
151C23×C5—21no—
152C23×C5—21no—
153C23×C5—41no—
154C23×C5—41no—
155C23×C5—41no—
156C23×C5—41no—
157C23×C5—41no—
158C23×C5—41no—
159C23×C5—41no—
160C23×C5—41no—
161C23×C5—41no—
162C23×C5—41no—
163C23×C5—41no—
164C23×C5C2×C22⋊C411yescharacteristic
165C23×C5#12112yes—
166C23×C5#12411yescharacteristic
167C23×C5#12711yescharacteristic
168C5×Q8—82no—
169C5×D4—42no—
170C5×D4—42no—
171C5×D4—82no—
172C5×D4—84no—
173C5×D4—82no—
174C5×D4—82no—
175C2×C4×C5—21no—
176C2×C4×C5—21no—
177C2×C4×C5—22no—
178C2×C4×C5—21no—
179C2×C4×C5—21no—
180C2×C4×C5—21no—
181C2×C4×C5—41no—
182C2×C4×C5—42no—
183C2×C4×C5—42no—
184C2×C4×C5—41no—
185C2×C4×C5—41no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C2×C4×C5—41no—
189C2×C4×C5—44no—
190C2×C4×C5—41no—
191C2×C4×C5—41no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5—41no—
195C2×C4×C5—41no—
196C2×C4×C5—81no—
197C2×C4×C5—81no—
198C2×C4×C5—82no—
199C2×C4×C5—82no—
200C2×C4×C5—82no—
201C2×C4×C5—82no—
202C2×C4×C5—82no—
203C2×C4×C5#9911yescharacteristic
204C2×C4×C5#9911yescharacteristic
205C2×C4×C5C4×D412yes—
206C22×Q8C2×C4×C511yescharacteristic
207C22×D4—21no—
208C22×D4—21no—
209C22×D4C2×C4×C511yescharacteristic
210C22×D4C23×C511yescharacteristic
211C23×C4C5×D411yescharacteristic
212C23×C4C5×D411yescharacteristic
213#127—22no—
214#127—22no—
215#124—22no—
216#124—22no—
217#124—41no—
218#124—41no—
219C4×D4—41no—
220C4×D4—41no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—41no—
223C2×C4⋊C4C2×C4×C511yescharacteristic
224C2×C22⋊C4—22no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4C5×D411yescharacteristic
233C2×C22⋊C4C5×D411yescharacteristic
234C2×C42—41no—
235C2×C42C2×C4×C511yescharacteristic
236C2×C42C2×C4×C511yescharacteristic
237C2×C42C2×C4×C511yescharacteristic
238#99—22no—
239#99—22no—
240#99—22no—
241#99C5×D414yes—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—41no—
246#95—41no—
247C22×C5—21no—
248C22×C5—21no—
249C22×C5—22no—
250C22×C5—21no—
251C22×C5—21no—
252C22×C5—42no—
253C22×C5—41no—
254C22×C5—41no—
255C22×C5—41no—
256C22×C5—41no—
257C22×C5—41no—
258C22×C5—41no—
259C22×C5—81no—
260C22×C5—81no—
261C22×C5—81no—
262C22×C5—81no—
263C22×C5—81no—
264C22×C5—81no—
265C22×C5—81no—
266C22×C5—81no—
267C22×C5—81no—
268C22×C5#39011yescharacteristic
269C22×C5C2×#9911yescharacteristic
270C22×C5#41011yescharacteristic
271C4×C5—21no—
272C4×C5—21no—
273C4×C5—22no—
274C4×C5—42no—
275C4×C5—41no—
276C4×C5—41no—
277C4×C5—41no—
278C4×C5—81no—
279C4×C5—84no—
280C4×C5—81no—
281C4×C5—162no—
282C24—21no—
283C24C2×C5×D411yescharacteristic
284C24C2×C5×D411yescharacteristic
285C2×Q8—22no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×D4—22no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—42no—
294C2×D4—42no—
295C2×D4—42no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—81no—
299C2×D4—81no—
300C2×D4C2×C5×D412yes—
301C2×D4C5×#4112yes—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—81no—
312C22×C4—81no—
313C22×C4C5×C22⋊C411yescharacteristic
314C22×C4C5×C22⋊C411yescharacteristic
315C22×C4C5×C22⋊C411yescharacteristic
316C22×C4C5×C22⋊C411yescharacteristic
317C22×C4C22×C4×C511yescharacteristic
318C4⋊C4—41no—
319C4⋊C4—42no—
320C4⋊C4—82no—
321C22⋊C4—24no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—42no—
325C22⋊C4—42no—
326C22⋊C4—42no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—42no—
332C22⋊C4—42no—
333C22⋊C4—81no—
334C22⋊C4—81no—
335C42—21no—
336C42—21no—
337C42—22no—
338C42—22no—
339C42—82no—
340C2×C5—21no—
341C2×C5—21no—
342C2×C5—42no—
343C2×C5—41no—
344C2×C5—41no—
345C2×C5—161no—
346C2×C5#196411yescharacteristic
347C2×C5#212611yescharacteristic
348C2×C5#212711yescharacteristic
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23C2×C5×C22⋊C411yescharacteristic
365C23C5×#12112yes—
366C23C5×#12411yescharacteristic
367C23C5×#12711yescharacteristic
368Q8—82no—
369D4—42no—
370D4—42no—
371D4—82no—
372D4—84no—
373D4—82no—
374D4—82no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—22no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—44no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—82no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4C5×#9911yescharacteristic
404C2×C4C5×#9911yescharacteristic
405C2×C4C4×C5×D412yes—
406C5#1322511yescharacteristic, direct product factor, Sylow
407C22—21no—
408C22—21no—
409C22—22no—
410C22—21no—
411C22—21no—
412C22—42no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22C5×#39011yescharacteristic
429C22C2×C5×#9911yescharacteristic
430C22C5×#41011yescharacteristic
431C4—21no—
432C4—21no—
433C4—22no—
434C4—42no—
435C4—41no—
436C4—41no—
437C4—41no—
438C4—81no—
439C4—84no—
440C4—81no—
441C4—162no—
442C2—21no—
443C2—21no—
444C2—42no—
445C2—41no—
446C2—41no—
447C2—161no—
448C2C5×#196411yescharacteristic
449C2C5×#212611yescharacteristic
450C2C5×#212711yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC22×D4C23×C5
prime radicalC2×C5×#127C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#354C2semidirect
4. C5×#1799C2semidirect
5. C4×C5×#99C2semidirect
7. C2×C5×#124C4semidirect
14. C5×#391C4semidirect
15. C5×#390C4semidirect
19. C4×C5×C4⋊C4C4semidirect
25. #13225C5direct (N × H)
68. C2×#354C2×C5semidirect
70. #1799C2×C5semidirect
71. C4×#99C2×C5semidirect
131. C2×#124C4×C5semidirect
138. #391C4×C5semidirect
139. #390C4×C5semidirect
143. C4×C4⋊C4C4×C5semidirect
406. C5#13225direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#25442
C2×C5×#3542
C2×C5×#3532
C5×#17992
C4×C5×#992
#132255