Finite Group Databasebeta

← C5×#13089 #11935809

Subgroups — C5×#13089 #11935809

Order 1280.

782 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#410C211yesmaximal, characteristic, complemented
2C5×#2431C211yesmaximal, characteristic
3C2×C5×#353C212yesmaximal, complemented
4C5×#1782C211yesmaximal, characteristic, complemented
5C5×#1393C212yesmaximal, complemented
6C22×C5×#41C2211yescharacteristic
7C2×C5×#127C2211yescharacteristic
8C2×C5×#124C411yescharacteristic, complemented
9C2×C5×#121C411yescharacteristic, complemented
10C2×C5×#117—21no—
11C5×#410—24no—
12C2×C5×#99—21no—
13C2×C5×#99—21no—
14C2×C5×#99C2212yes—
15C2×C5×#99C2212yes—
16C5×#392—21no—
17C5×#392—21no—
18C5×#391C411yescharacteristic, complemented
19C5×#390C2211yescharacteristic
20C5×#386—21no—
21C5×#386—21no—
22C5×#381—21no—
23C4×C5×C22⋊C4C411yescharacteristic, complemented
24C5×#353—24no—
25#13089C511yesmaximal, characteristic, direct product factor, Sylow
26C2×C5×#41—22no—
27C2×C5×#41—22no—
28C2×C5×#41—41no—
29C2×C5×#41—41no—
30C2×C5×#41—42no—
31C22×C5×Q8C2×C411yescharacteristic
32C22×C5×D4—21no—
33C22×C5×D4—21no—
34C22×C5×D4—21no—
35C22×C5×D4C2×C411yescharacteristic
36C22×C5×D4D411yescharacteristic
37C22×C5×D4D411yescharacteristic
38C22×C5×D4C2311yescharacteristic
39C23×C4×C5C2×C411yescharacteristic
40C23×C4×C5D411yescharacteristic
41C23×C4×C5D411yescharacteristic
42C5×#127—22no—
43C5×#127—22no—
44C5×#124—42no—
45C5×#121—41no—
46C5×#121—41no—
47C5×#117—24no—
48C5×#117—42no—
49C2×C5×C4⋊C4—41no—
50C2×C5×C4⋊C4C2×C411yescharacteristic
51C2×C5×C22⋊C4—22no—
52C2×C5×C22⋊C4—21no—
53C2×C5×C22⋊C4—21no—
54C2×C5×C22⋊C4—21no—
55C2×C5×C22⋊C4—21no—
56C2×C5×C22⋊C4—22no—
57C2×C5×C22⋊C4—21no—
58C2×C5×C22⋊C4—21no—
59C2×C42×C5—41no—
60C2×C42×C5C2×C411yescharacteristic
61C2×C42×C5C2×C411yescharacteristic
62C5×#99—24no—
63C5×#99—22no—
64C5×#99—22no—
65C5×#99—22no—
66C5×#99—42no—
67C5×#99D414yescomplemented
68C5×#95—21no—
69C5×#95—21no—
70C5×#95—21no—
71C5×#95—41no—
72C5×#95—41no—
73C2×#410C2×C511yescharacteristic, complemented
74#2431C2×C511yescharacteristic
75C2×#353C2×C512yescomplemented
76#1782C2×C511yescharacteristic, complemented
77#1393C2×C512yescomplemented
78C24×C5—21no—
79C24×C5C22⋊C411yescharacteristic
80C24×C5C2×D411yescharacteristic
81C24×C5C2×D411yescharacteristic
82C5×#41—44no—
83C5×#41—44no—
84C5×#41—44no—
85C5×#41—44no—
86C2×C5×Q8—22no—
87C2×C5×Q8—22no—
88C2×C5×Q8—41no—
89C2×C5×D4—21no—
90C2×C5×D4—22no—
91C2×C5×D4—21no—
92C2×C5×D4—22no—
93C2×C5×D4—22no—
94C2×C5×D4—41no—
95C2×C5×D4—41no—
96C2×C5×D4—41no—
97C2×C5×D4—41no—
98C2×C5×D4—41no—
99C2×C5×D4—41no—
100C2×C5×D4—41no—
101C2×C5×D4—42no—
102C2×C5×D4—42no—
103C2×C5×D4—42no—
104C2×C5×D4—41no—
105C2×C5×D4—42no—
106C2×C5×D4—41no—
107C2×C5×D4—81no—
108C2×C5×D4—81no—
109C2×C5×D4—81no—
110C2×C5×D4—81no—
111C2×C5×D4C2×D412yes—
112C2×C5×D4#4112yes—
113C22×C4×C5—21no—
114C22×C4×C5—21no—
115C22×C4×C5—21no—
116C22×C4×C5—21no—
117C22×C4×C5—22no—
118C22×C4×C5—21no—
119C22×C4×C5—22no—
120C22×C4×C5—21no—
121C22×C4×C5—21no—
122C22×C4×C5—21no—
123C22×C4×C5—21no—
124C22×C4×C5—22no—
125C22×C4×C5—21no—
126C22×C4×C5—21no—
127C22×C4×C5—41no—
128C22×C4×C5—41no—
129C22×C4×C5—42no—
130C22×C4×C5—42no—
131C22×C4×C5C22⋊C411yescharacteristic
132C22×C4×C5C22⋊C411yescharacteristic
133C22×C4×C5C22⋊C411yescharacteristic
134C22×C4×C5C22×C411yescharacteristic
135C5×C4⋊C4—41no—
136C5×C4⋊C4—44no—
137C5×C22⋊C4—24no—
138C5×C22⋊C4—42no—
139C5×C22⋊C4—42no—
140C5×C22⋊C4—42no—
141C5×C22⋊C4—41no—
142C5×C22⋊C4—41no—
143C5×C22⋊C4—42no—
144C5×C22⋊C4—42no—
145C5×C22⋊C4—42no—
146C5×C22⋊C4—81no—
147C5×C22⋊C4—81no—
148C42×C5—22no—
149C42×C5—41no—
150C42×C5—44no—
151C22×#41C22×C511yescharacteristic
152C2×#127C22×C511yescharacteristic
153C2×#124C4×C511yescharacteristic, complemented
154C2×#121C4×C511yescharacteristic, complemented
155C2×#117—21no—
156#410—24no—
157C2×#99—21no—
158C2×#99—21no—
159C2×#99C22×C512yes—
160C2×#99C22×C512yes—
161#392—21no—
162#392—21no—
163#391C4×C511yescharacteristic, complemented
164#390C22×C511yescharacteristic
165#386—21no—
166#386—21no—
167#381—21no—
168C4×C22⋊C4C4×C511yescharacteristic, complemented
169#353—24no—
170C23×C5—21no—
171C23×C5—21no—
172C23×C5—21no—
173C23×C5—21no—
174C23×C5—21no—
175C23×C5—21no—
176C23×C5—21no—
177C23×C5—41no—
178C23×C5—41no—
179C23×C5—41no—
180C23×C5—41no—
181C23×C5—41no—
182C23×C5—41no—
183C23×C5—41no—
184C23×C5—41no—
185C23×C5—41no—
186C23×C5—41no—
187C23×C5—41no—
188C23×C5—41no—
189C23×C5—41no—
190C23×C5C2×C22⋊C411yescharacteristic
191C23×C5#12011yescharacteristic
192C23×C5#12112yes—
193C23×C5#12311yescharacteristic
194C5×Q8—44no—
195C5×D4—42no—
196C5×D4—42no—
197C5×D4—44no—
198C5×D4—42no—
199C5×D4—42no—
200C5×D4—82no—
201C5×D4—82no—
202C5×D4—84no—
203C5×D4—82no—
204C5×D4—84no—
205C2×C4×C5—22no—
206C2×C4×C5—22no—
207C2×C4×C5—22no—
208C2×C4×C5—22no—
209C2×C4×C5—21no—
210C2×C4×C5—21no—
211C2×C4×C5—21no—
212C2×C4×C5—21no—
213C2×C4×C5—21no—
214C2×C4×C5—21no—
215C2×C4×C5—22no—
216C2×C4×C5—21no—
217C2×C4×C5—21no—
218C2×C4×C5—21no—
219C2×C4×C5—42no—
220C2×C4×C5—42no—
221C2×C4×C5—42no—
222C2×C4×C5—42no—
223C2×C4×C5—41no—
224C2×C4×C5—41no—
225C2×C4×C5—44no—
226C2×C4×C5—41no—
227C2×C4×C5—41no—
228C2×C4×C5—41no—
229C2×C4×C5—41no—
230C2×C4×C5—41no—
231C2×C4×C5—41no—
232C2×C4×C5—82no—
233C2×C4×C5—82no—
234C2×C4×C5—82no—
235C2×C4×C5—82no—
236C2×C4×C5—82no—
237C2×C4×C5#9912yes—
238C2×C4×C5#9911yescharacteristic
239C2×C4×C5#9911yescharacteristic
240C2×C4×C5C4×D412yes—
241C2×#41—22no—
242C2×#41—22no—
243C2×#41—41no—
244C2×#41—41no—
245C2×#41—42no—
246C22×Q8C2×C4×C511yescharacteristic
247C22×D4—21no—
248C22×D4—21no—
249C22×D4—21no—
250C22×D4C2×C4×C511yescharacteristic
251C22×D4C5×D411yescharacteristic
252C22×D4C5×D411yescharacteristic
253C22×D4C23×C511yescharacteristic
254C23×C4C2×C4×C511yescharacteristic
255C23×C4C5×D411yescharacteristic
256C23×C4C5×D411yescharacteristic
257#127—22no—
258#127—22no—
259#124—42no—
260#121—41no—
261#121—41no—
262#117—24no—
263#117—42no—
264C2×C4⋊C4—41no—
265C2×C4⋊C4C2×C4×C511yescharacteristic
266C2×C22⋊C4—22no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C42—41no—
275C2×C42C2×C4×C511yescharacteristic
276C2×C42C2×C4×C511yescharacteristic
277#99—24no—
278#99—22no—
279#99—22no—
280#99—22no—
281#99—42no—
282#99C5×D414yescomplemented
283#95—21no—
284#95—21no—
285#95—21no—
286#95—41no—
287#95—41no—
288C22×C5—21no—
289C22×C5—21no—
290C22×C5—21no—
291C22×C5—21no—
292C22×C5—22no—
293C22×C5—41no—
294C22×C5—42no—
295C22×C5—41no—
296C22×C5—41no—
297C22×C5—41no—
298C22×C5—41no—
299C22×C5—41no—
300C22×C5—41no—
301C22×C5—41no—
302C22×C5—41no—
303C22×C5—81no—
304C22×C5—81no—
305C22×C5—81no—
306C22×C5—81no—
307C22×C5—81no—
308C22×C5—81no—
309C22×C5—81no—
310C22×C5—81no—
311C22×C5—81no—
312C22×C5—81no—
313C22×C5—81no—
314C22×C5#38611yescharacteristic
315C22×C5C2×#9911yescharacteristic
316C22×C5C2×#9911yescharacteristic
317C4×C5—21no—
318C4×C5—21no—
319C4×C5—22no—
320C4×C5—22no—
321C4×C5—42no—
322C4×C5—41no—
323C4×C5—81no—
324C4×C5—84no—
325C4×C5—81no—
326C4×C5—162no—
327C24—21no—
328C24C5×C22⋊C411yescharacteristic
329C24C2×C5×D411yescharacteristic
330C24C2×C5×D411yescharacteristic
331#41—44no—
332#41—44no—
333#41—44no—
334#41—44no—
335C2×Q8—22no—
336C2×Q8—22no—
337C2×Q8—41no—
338C2×D4—21no—
339C2×D4—22no—
340C2×D4—21no—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—42no—
351C2×D4—42no—
352C2×D4—42no—
353C2×D4—41no—
354C2×D4—42no—
355C2×D4—41no—
356C2×D4—81no—
357C2×D4—81no—
358C2×D4—81no—
359C2×D4—81no—
360C2×D4C2×C5×D412yes—
361C2×D4C5×#4112yes—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4C5×C22⋊C411yescharacteristic
381C22×C4C5×C22⋊C411yescharacteristic
382C22×C4C5×C22⋊C411yescharacteristic
383C22×C4C22×C4×C511yescharacteristic
384C4⋊C4—41no—
385C4⋊C4—44no—
386C22⋊C4—24no—
387C22⋊C4—42no—
388C22⋊C4—42no—
389C22⋊C4—42no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—42no—
393C22⋊C4—42no—
394C22⋊C4—42no—
395C22⋊C4—81no—
396C22⋊C4—81no—
397C42—22no—
398C42—41no—
399C42—44no—
400C2×C5—21no—
401C2×C5—21no—
402C2×C5—41no—
403C2×C5—42no—
404C2×C5—41no—
405C2×C5—81no—
406C2×C5—161no—
407C2×C5#189811yescharacteristic
408C2×C5#212611yescharacteristic
409C2×C5#212811yescharacteristic
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23C2×C5×C22⋊C411yescharacteristic
431C23C5×#12011yescharacteristic
432C23C5×#12112yes—
433C23C5×#12311yescharacteristic
434Q8—44no—
435D4—42no—
436D4—42no—
437D4—44no—
438D4—42no—
439D4—42no—
440D4—82no—
441D4—82no—
442D4—84no—
443D4—82no—
444D4—84no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—22no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—44no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—82no—
473C2×C4—82no—
474C2×C4—82no—
475C2×C4—82no—
476C2×C4—82no—
477C2×C4C5×#9911yescharacteristic
478C2×C4C5×#9911yescharacteristic
479C2×C4C5×#9912yes—
480C2×C4C4×C5×D412yes—
481C5#1308911yescharacteristic, direct product factor, Sylow
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—22no—
487C22—41no—
488C22—42no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—81no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22C5×#38611yescharacteristic
509C22C2×C5×#9911yescharacteristic
510C22C2×C5×#9911yescharacteristic
511C4—21no—
512C4—21no—
513C4—22no—
514C4—22no—
515C4—42no—
516C4—41no—
517C4—81no—
518C4—84no—
519C4—81no—
520C4—162no—
521C2—21no—
522C2—21no—
523C2—41no—
524C2—42no—
525C2—41no—
526C2—81no—
527C2—161no—
528C2C5×#189811yescharacteristic
529C2C5×#212611yescharacteristic
530C2C5×#212811yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC22×D4C23×C5
prime radicalC5×#2431C2
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C22×C5×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#410C2semidirect
3. C2×C5×#353C2semidirect
4. C5×#1782C2semidirect
5. C5×#1393C2semidirect
8. C2×C5×#124C4semidirect
9. C2×C5×#121C4semidirect
18. C5×#391C4semidirect
23. C4×C5×C22⋊C4C4semidirect
25. #13089C5direct (N × H)
67. C5×#99D4semidirect
73. C2×#410C2×C5semidirect
75. C2×#353C2×C5semidirect
76. #1782C2×C5semidirect
77. #1393C2×C5semidirect
153. C2×#124C4×C5semidirect
154. C2×#121C4×C5semidirect
163. #391C4×C5semidirect
168. C4×C22⋊C4C4×C5semidirect
282. #99C5×D4semidirect
481. C5#13089direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4102
C5×#24312
C2×C5×#3532
C5×#17822
C5×#13932
#130895