Finite Group Databasebeta

← C5×#13090 #11935810

Subgroups — C5×#13090 #11935810

Order 1280.

910 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#99C211yesmaximal, characteristic
2C5×#2435C211yesmaximal, characteristic
3C2×C5×#354C212yesmaximal, complemented
4C5×#1781C211yesmaximal, characteristic
5C5×#1393C212yesmaximal, complemented
6C23×C5×D4C2211yescharacteristic
7C2×C5×#124C411yescharacteristic, complemented
8C2×C5×#124C2211yescharacteristic
9C2×C5×C22⋊Q8C411yescharacteristic, complemented
10C22×C5×C22⋊C4—21no—
11C2×C5×#99—24no—
12C2×C5×#99—21no—
13C2×C5×#99—21no—
14C2×C5×#99C2212yes—
15C2×C5×#99C2212yes—
16C5×#394—21no—
17C5×#394—21no—
18C5×#390C411yescharacteristic, complemented
19C5×#390C2211yescharacteristic
20C5×#379—21no—
21C5×#379—21no—
22C5×#379—21no—
23C4×C5×C22⋊C4C411yescharacteristic, complemented
24C5×#354—24no—
25#13090C511yesmaximal, characteristic, direct product factor, Sylow
26C25×C5D411yescharacteristic
27C25×C5D411yescharacteristic
28C22×C5×Q8C2×C411yescharacteristic, complemented
29C22×C5×D4—22no—
30C22×C5×D4—22no—
31C22×C5×D4—41no—
32C22×C5×D4—41no—
33C22×C5×D4—42no—
34C22×C5×D4C2×C411yescharacteristic
35C22×C5×D4D411yescharacteristic
36C22×C5×D4D411yescharacteristic
37C22×C5×D4C2311yescharacteristic
38C23×C4×C5—41no—
39C23×C4×C5C2×C411yescharacteristic
40C5×#124—22no—
41C5×#124—22no—
42C5×#124—42no—
43C5×C22⋊Q8—41no—
44C5×C22⋊Q8—41no—
45C2×C5×C4⋊C4—21no—
46C2×C5×C4⋊C4C2×C411yescharacteristic, complemented
47C2×C5×C22⋊C4—24no—
48C2×C5×C22⋊C4—22no—
49C2×C5×C22⋊C4—21no—
50C2×C5×C22⋊C4—21no—
51C2×C5×C22⋊C4—21no—
52C2×C5×C22⋊C4—21no—
53C2×C5×C22⋊C4—21no—
54C2×C5×C22⋊C4—21no—
55C2×C5×C22⋊C4—22no—
56C2×C5×C22⋊C4—21no—
57C2×C5×C22⋊C4—21no—
58C2×C5×C22⋊C4—21no—
59C2×C5×C22⋊C4—21no—
60C2×C5×C22⋊C4—41no—
61C2×C5×C22⋊C4—42no—
62C2×C5×C22⋊C4—41no—
63C2×C5×C22⋊C4—41no—
64C2×C42×C5C2×C411yescharacteristic, complemented
65C2×C42×C5C2×C411yescharacteristic, complemented
66C5×#99—24no—
67C5×#99—22no—
68C5×#99—22no—
69C5×#99—22no—
70C5×#99—42no—
71C5×#99D414yes—
72C5×#95—21no—
73C22×#99C2×C511yescharacteristic
74#2435C2×C511yescharacteristic
75C2×#354C2×C512yescomplemented
76#1781C2×C511yescharacteristic
77#1393C2×C512yescomplemented
78C24×C5—21no—
79C24×C5—22no—
80C24×C5—21no—
81C24×C5—21no—
82C24×C5—21no—
83C24×C5—21no—
84C24×C5—21no—
85C24×C5—22no—
86C24×C5—41no—
87C24×C5—42no—
88C24×C5—42no—
89C24×C5—81no—
90C24×C5—81no—
91C24×C5C22⋊C411yescharacteristic
92C24×C5C22⋊C411yescharacteristic
93C24×C5C22⋊C411yescharacteristic
94C24×C5C2×D411yescharacteristic
95C24×C5C2×D411yescharacteristic
96C2×C5×Q8—22no—
97C2×C5×Q8—41no—
98C2×C5×Q8—41no—
99C2×C5×D4—22no—
100C2×C5×D4—22no—
101C2×C5×D4—21no—
102C2×C5×D4—22no—
103C2×C5×D4—21no—
104C2×C5×D4—22no—
105C2×C5×D4—41no—
106C2×C5×D4—41no—
107C2×C5×D4—41no—
108C2×C5×D4—41no—
109C2×C5×D4—41no—
110C2×C5×D4—41no—
111C2×C5×D4—44no—
112C2×C5×D4—44no—
113C2×C5×D4—44no—
114C2×C5×D4—44no—
115C2×C5×D4C2×D412yes—
116C2×C5×D4#4112yes—
117C22×C4×C5—21no—
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—41no—
125C22×C4×C5—44no—
126C22×C4×C5—42no—
127C22×C4×C5—42no—
128C22×C4×C5—82no—
129C22×C4×C5—82no—
130C22×C4×C5C22⋊C411yescharacteristic
131C22×C4×C5C22×C411yescharacteristic
132C5×C4⋊C4—41no—
133C5×C4⋊C4—42no—
134C5×C22⋊C4—24no—
135C5×C22⋊C4—42no—
136C5×C22⋊C4—44no—
137C5×C22⋊C4—42no—
138C5×C22⋊C4—42no—
139C5×C22⋊C4—41no—
140C5×C22⋊C4—41no—
141C5×C22⋊C4—42no—
142C5×C22⋊C4—41no—
143C5×C22⋊C4—42no—
144C5×C22⋊C4—41no—
145C5×C22⋊C4—42no—
146C5×C22⋊C4—42no—
147C5×C22⋊C4—81no—
148C5×C22⋊C4—81no—
149C5×C22⋊C4—81no—
150C5×C22⋊C4—81no—
151C5×C22⋊C4—82no—
152C5×C22⋊C4—82no—
153C42×C5—22no—
154C42×C5—41no—
155C23×D4C22×C511yescharacteristic
156C2×#124C4×C511yescharacteristic, complemented
157C2×#124C22×C511yescharacteristic
158C2×C22⋊Q8C4×C511yescharacteristic, complemented
159C22×C22⋊C4—21no—
160C2×#99—21no—
161C2×#99—24no—
162C2×#99—21no—
163C2×#99C22×C512yes—
164C2×#99C22×C512yes—
165#394—21no—
166#394—21no—
167#390C4×C511yescharacteristic, complemented
168#390C22×C511yescharacteristic
169#379—21no—
170#379—21no—
171#379—21no—
172C4×C22⋊C4C4×C511yescharacteristic, complemented
173#354—24no—
174C23×C5—22no—
175C23×C5—22no—
176C23×C5—22no—
177C23×C5—22no—
178C23×C5—22no—
179C23×C5—21no—
180C23×C5—21no—
181C23×C5—21no—
182C23×C5—21no—
183C23×C5—21no—
184C23×C5—21no—
185C23×C5—21no—
186C23×C5—21no—
187C23×C5—21no—
188C23×C5—21no—
189C23×C5—21no—
190C23×C5—41no—
191C23×C5—42no—
192C23×C5—42no—
193C23×C5—42no—
194C23×C5—41no—
195C23×C5—41no—
196C23×C5—41no—
197C23×C5—41no—
198C23×C5—41no—
199C23×C5—41no—
200C23×C5—41no—
201C23×C5—41no—
202C23×C5—42no—
203C23×C5—42no—
204C23×C5—42no—
205C23×C5—81no—
206C23×C5—81no—
207C23×C5—81no—
208C23×C5—81no—
209C23×C5—84no—
210C23×C5—82no—
211C23×C5—82no—
212C23×C5—84no—
213C23×C5—84no—
214C23×C5#9911yescharacteristic
215C23×C5#9911yescharacteristic
216C23×C5#9912yes—
217C23×C5C2×C22⋊C411yescharacteristic
218C23×C5#12011yescharacteristic
219C23×C5#12112yes—
220C23×C5#12311yescharacteristic
221C5×Q8—82no—
222C5×D4—42no—
223C5×D4—42no—
224C5×D4—44no—
225C5×D4—44no—
226C5×D4—42no—
227C5×D4—42no—
228C2×C4×C5—21no—
229C2×C4×C5—21no—
230C2×C4×C5—21no—
231C2×C4×C5—21no—
232C2×C4×C5—21no—
233C2×C4×C5—42no—
234C2×C4×C5—42no—
235C2×C4×C5—44no—
236C2×C4×C5—41no—
237C2×C4×C5—41no—
238C2×C4×C5—41no—
239C2×C4×C5—41no—
240C2×C4×C5—41no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5—41no—
244C2×C4×C5—41no—
245C2×C4×C5—41no—
246C2×C4×C5—41no—
247C2×C4×C5—41no—
248C2×C4×C5—88no—
249C2×C4×C5—82no—
250C2×C4×C5—82no—
251C2×C4×C5—82no—
252C2×C4×C5—82no—
253C2×C4×C5—82no—
254C2×C4×C5C4×D412yes—
255C25C5×D411yescharacteristic
256C25C5×D411yescharacteristic
257C22×Q8C2×C4×C511yescharacteristic, complemented
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—41no—
261C22×D4—41no—
262C22×D4—42no—
263C22×D4C2×C4×C511yescharacteristic
264C22×D4C5×D411yescharacteristic
265C22×D4C5×D411yescharacteristic
266C22×D4C23×C511yescharacteristic
267C23×C4—41no—
268C23×C4C2×C4×C511yescharacteristic
269#124—22no—
270#124—22no—
271#124—42no—
272C22⋊Q8—41no—
273C22⋊Q8—41no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4C2×C4×C511yescharacteristic, complemented
276C2×C22⋊C4—24no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—22no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—41no—
290C2×C22⋊C4—42no—
291C2×C22⋊C4—41no—
292C2×C22⋊C4—41no—
293C2×C42C2×C4×C511yescharacteristic, complemented
294C2×C42C2×C4×C511yescharacteristic, complemented
295#99—24no—
296#99—22no—
297#99—22no—
298#99—22no—
299#99—42no—
300#99C5×D414yes—
301#95—21no—
302C22×C5—21no—
303C22×C5—21no—
304C22×C5—21no—
305C22×C5—21no—
306C22×C5—21no—
307C22×C5—21no—
308C22×C5—21no—
309C22×C5—21no—
310C22×C5—22no—
311C22×C5—22no—
312C22×C5—21no—
313C22×C5—42no—
314C22×C5—42no—
315C22×C5—42no—
316C22×C5—41no—
317C22×C5—42no—
318C22×C5—41no—
319C22×C5—44no—
320C22×C5—44no—
321C22×C5—42no—
322C22×C5—41no—
323C22×C5—41no—
324C22×C5—41no—
325C22×C5—41no—
326C22×C5—41no—
327C22×C5—41no—
328C22×C5—41no—
329C22×C5—41no—
330C22×C5—41no—
331C22×C5—81no—
332C22×C5—81no—
333C22×C5—81no—
334C22×C5—84no—
335C22×C5—81no—
336C22×C5—82no—
337C22×C5—82no—
338C22×C5—84no—
339C22×C5#35412yescomplemented
340C22×C5#38611yescharacteristic
341C22×C5C2×#9911yescharacteristic
342C22×C5C2×#9911yescharacteristic
343C4×C5—22no—
344C4×C5—41no—
345C4×C5—81no—
346C4×C5—81no—
347C4×C5—84no—
348C4×C5—81no—
349C4×C5—81no—
350C4×C5—162no—
351C24—21no—
352C24—21no—
353C24—21no—
354C24—22no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—22no—
359C24—41no—
360C24—42no—
361C24—42no—
362C24—81no—
363C24—81no—
364C24C5×C22⋊C411yescharacteristic
365C24C5×C22⋊C411yescharacteristic
366C24C5×C22⋊C411yescharacteristic
367C24C2×C5×D411yescharacteristic
368C24C2×C5×D411yescharacteristic
369C2×Q8—22no—
370C2×Q8—41no—
371C2×Q8—41no—
372C2×D4—21no—
373C2×D4—22no—
374C2×D4—21no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4—44no—
385C2×D4—44no—
386C2×D4—44no—
387C2×D4—44no—
388C2×D4C2×C5×D412yes—
389C2×D4C5×#4112yes—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—41no—
398C22×C4—44no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—82no—
402C22×C4—82no—
403C22×C4C5×C22⋊C411yescharacteristic
404C22×C4C22×C4×C511yescharacteristic
405C4⋊C4—41no—
406C4⋊C4—42no—
407C22⋊C4—24no—
408C22⋊C4—44no—
409C22⋊C4—42no—
410C22⋊C4—42no—
411C22⋊C4—42no—
412C22⋊C4—41no—
413C22⋊C4—42no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—42no—
418C22⋊C4—42no—
419C22⋊C4—42no—
420C22⋊C4—81no—
421C22⋊C4—81no—
422C22⋊C4—81no—
423C22⋊C4—81no—
424C22⋊C4—82no—
425C22⋊C4—82no—
426C42—22no—
427C42—41no—
428C2×C5—21no—
429C2×C5—21no—
430C2×C5—22no—
431C2×C5—41no—
432C2×C5—42no—
433C2×C5—41no—
434C2×C5—42no—
435C2×C5—41no—
436C2×C5—81no—
437C2×C5#189811yescharacteristic
438C2×C5C2×#35411yescharacteristic
439C2×C5#212711yescharacteristic
440C23—22no—
441C23—22no—
442C23—22no—
443C23—22no—
444C23—21no—
445C23—21no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—22no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—41no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—81no—
472C23—81no—
473C23—81no—
474C23—81no—
475C23—82no—
476C23—82no—
477C23—84no—
478C23—84no—
479C23—84no—
480C23C5×#9911yescharacteristic
481C23C5×#9911yescharacteristic
482C23C5×#9912yes—
483C23C2×C5×C22⋊C411yescharacteristic
484C23C5×#12011yescharacteristic
485C23C5×#12112yes—
486C23C5×#12311yescharacteristic
487Q8—82no—
488D4—42no—
489D4—42no—
490D4—44no—
491D4—44no—
492D4—42no—
493D4—42no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—44no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—88no—
515C2×C4—82no—
516C2×C4—82no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4—82no—
520C2×C4C4×C5×D412yes—
521C5#1309011yescharacteristic, direct product factor, Sylow
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—22no—
531C22—21no—
532C22—22no—
533C22—42no—
534C22—42no—
535C22—41no—
536C22—42no—
537C22—41no—
538C22—42no—
539C22—44no—
540C22—44no—
541C22—42no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—84no—
555C22—81no—
556C22—82no—
557C22—82no—
558C22—84no—
559C22C5×#35412yescomplemented
560C22C5×#38611yescharacteristic
561C22C2×C5×#9911yescharacteristic
562C22C2×C5×#9911yescharacteristic
563C4—22no—
564C4—41no—
565C4—81no—
566C4—81no—
567C4—84no—
568C4—81no—
569C4—81no—
570C4—162no—
571C2—21no—
572C2—21no—
573C2—22no—
574C2—41no—
575C2—42no—
576C2—41no—
577C2—41no—
578C2—42no—
579C2—81no—
580C2C5×#189811yescharacteristic
581C2C2×C5×#35411yescharacteristic
582C2C5×#212711yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC22×D4C23×C5
prime radicalC23×C5×D4C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C24×C5 ◁ C23×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C5×#354C2semidirect
5. C5×#1393C2semidirect
7. C2×C5×#124C4semidirect
9. C2×C5×C22⋊Q8C4semidirect
18. C5×#390C4semidirect
23. C4×C5×C22⋊C4C4semidirect
25. #13090C5direct (N × H)
28. C22×C5×Q8C2×C4semidirect
46. C2×C5×C4⋊C4C2×C4semidirect
64. C2×C42×C5C2×C4semidirect
65. C2×C42×C5C2×C4semidirect
75. C2×#354C2×C5semidirect
77. #1393C2×C5semidirect
156. C2×#124C4×C5semidirect
158. C2×C22⋊Q8C4×C5semidirect
167. #390C4×C5semidirect
172. C4×C22⋊C4C4×C5semidirect
257. C22×Q8C2×C4×C5semidirect
275. C2×C4⋊C4C2×C4×C5semidirect
293. C2×C42C2×C4×C5semidirect
294. C2×C42C2×C4×C5semidirect
339. C22×C5#354semidirect
521. C5#13090direct (N × H)
559. C22C5×#354semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#992
C5×#24352
C2×C5×#3542
C5×#17812
C5×#13932
#130905