Finite Group Databasebeta

← C5×#18299 #11941019

Subgroups — C5×#18299 #11941019

Order 1280.

974 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3460C211yesmaximal, characteristic
2C5×#3190C212yesmaximal, complemented
3C5×#2638C211yesmaximal, characteristic, complemented
4C5×#1612C212yesmaximal, complemented
5C5×#1611C211yesmaximal, characteristic, complemented
6C5×#1610C211yesmaximal, characteristic, complemented
7C5×#1606C212yesmaximal, complemented
8C5×#1605C211yesmaximal, characteristic, complemented
9C5×#1604C211yesmaximal, characteristic, complemented
10C5×#1516C212yesmaximal, complemented
11C5×#1459C211yesmaximal, characteristic, complemented
12C5×#544C2211yescharacteristic
13C5×#542—22no—
14C5×#540—22no—
15C5×#538—21no—
16C5×#538C2212yes—
17C5×#537C2211yescharacteristic
18C5×#535—21no—
19C5×#532—22no—
20C5×#529—22no—
21C5×#525—21no—
22C5×#525C2212yes—
23C2×C5×C22⋊Q8C2211yescharacteristic
24C4×C5×#41—21no—
25C2×C4×C5×D4C2211yescharacteristic
26C5×#485—22no—
27C5×#483C2212yes—
28C5×#480C2212yes—
29C5×#467—22no—
30C5×#465—22no—
31C5×#452—22no—
32C5×#451C2212yes—
33C5×#448C2212yes—
34C2×C5×C22⋊C8C2212yes—
35C5×#398C2211yescharacteristic
36C5×#397—21no—
37C5×#397C2211yescharacteristic
38C5×#395C2211yescharacteristic
39C5×#394—21no—
40C5×#393C2211yescharacteristic
41C5×#387—21no—
42C5×#385—21no—
43C5×#381C2211yescharacteristic
44C5×#328C2212yes—
45C5×#328C2212yes—
46C5×#327C2212yes—
47C5×#327C2212yes—
48C5×#324C2211yescharacteristic
49C5×#324C2211yescharacteristic
50C5×#323C2212yes—
51#18299C511yesmaximal, characteristic, direct product factor, Sylow
52C2×C5×#41—21no—
53C2×C5×#41—21no—
54C2×C5×#41D412yes—
55C22×C5×Q8C2311yescharacteristic
56C22×C5×D4D411yescharacteristic
57C23×C4×C5D411yescharacteristic
58C23×C4×C5C2311yescharacteristic
59C2×C5×Q16—22no—
60C2×C5×SD16—22no—
61C22×C5×C8—22no—
62C5×C4⋊Q8—22no—
63C5×#127—22no—
64C5×#126—22no—
65C5×#126—22no—
66C5×#125—22no—
67C5×#124—22no—
68C5×#124—22no—
69C5×#124—22no—
70C5×#123—22no—
71C5×#123—22no—
72C5×#123—22no—
73C5×#123—22no—
74C5×C22⋊Q8—21no—
75C5×C22⋊Q8—21no—
76C5×C22⋊Q8—22no—
77C5×C22⋊Q8—22no—
78C5×C22⋊Q8—22no—
79C5×C22⋊Q8D412yes—
80C5×C22⋊Q8C2312yes—
81C5×#121—21no—
82C5×#121—22no—
83C5×#121—22no—
84C5×#121—22no—
85C5×#121—22no—
86C5×#121—22no—
87C5×#121—21no—
88C5×#121D412yes—
89C5×#121C2312yes—
90C5×#120—22no—
91C5×#120—22no—
92C4×C5×Q8—21no—
93C4×C5×Q8—21no—
94C4×C5×D4—21no—
95C4×C5×D4—21no—
96C4×C5×D4—22no—
97C4×C5×D4—22no—
98C4×C5×D4—22no—
99C4×C5×D4—22no—
100C4×C5×D4—22no—
101C4×C5×D4—22no—
102C5×#117—22no—
103C5×#117—21no—
104C5×#117—21no—
105C5×#117D412yes—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C22⋊C4—21no—
112C2×C5×C22⋊C4—21no—
113C2×C5×C22⋊C4—21no—
114C2×C5×C22⋊C4—21no—
115C2×C5×C22⋊C4D411yescharacteristic
116C2×C5×C22⋊C4C2311yescharacteristic
117C2×C42×C5—22no—
118C2×C42×C5D411yescharacteristic
119C5×#107—22no—
120C5×#106—22no—
121C5×#103—22no—
122C5×#103—22no—
123C5×#103—22no—
124C5×#102—22no—
125C5×C22⋊C8—22no—
126C5×C22⋊C8C2312yes—
127C5×C22⋊C8C2312yes—
128C5×#95—21no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95—21no—
133C5×#95C2311yescharacteristic
134C5×#95C2311yescharacteristic
135#3460C2×C511yescharacteristic
136#3190C2×C512yescomplemented
137#2638C2×C511yescharacteristic, complemented
138#1612C2×C512yescomplemented
139#1611C2×C511yescharacteristic, complemented
140#1610C2×C511yescharacteristic, complemented
141#1606C2×C512yescomplemented
142#1605C2×C511yescharacteristic, complemented
143#1604C2×C511yescharacteristic, complemented
144#1516C2×C512yescomplemented
145#1459C2×C511yescharacteristic, complemented
146C24×C5C2×D411yescharacteristic
147C24×C5C2×D411yescharacteristic
148C5×#41—42no—
149C5×#41—42no—
150C5×#41—82no—
151C5×#41—82no—
152C2×C5×Q8—21no—
153C2×C5×Q8—21no—
154C2×C5×Q8—22no—
155C2×C5×Q8—81no—
156C2×C5×Q8C2×D412yes—
157C2×C5×D4—21no—
158C2×C5×D4—22no—
159C2×C5×D4—22no—
160C2×C5×D4—22no—
161C2×C5×D4—22no—
162C2×C5×D4—21no—
163C2×C5×D4—22no—
164C2×C5×D4—22no—
165C2×C5×D4—22no—
166C2×C5×D4—41no—
167C2×C5×D4C2×D412yes—
168C22×C4×C5—22no—
169C22×C4×C5—22no—
170C22×C4×C5—22no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—81no—
178C22×C4×C5—81no—
179C22×C4×C5C2×D411yescharacteristic
180C22×C4×C5C2×D411yescharacteristic
181C22×C4×C5C2×D411yescharacteristic
182C22×C4×C5C2×D411yescharacteristic
183C22×C4×C5C2×D412yes—
184C22×C4×C5C2×D412yes—
185C22×C4×C5C2411yescharacteristic
186C5×Q16—82no—
187C5×SD16—82no—
188C2×C5×C8—22no—
189C2×C5×C8—22no—
190C2×C5×C8—82no—
191C5×C4⋊C4—21no—
192C5×C4⋊C4—21no—
193C5×C4⋊C4—22no—
194C5×C4⋊C4—21no—
195C5×C4⋊C4—21no—
196C5×C4⋊C4—22no—
197C5×C4⋊C4—22no—
198C5×C4⋊C4—22no—
199C5×C4⋊C4—22no—
200C5×C4⋊C4—22no—
201C5×C4⋊C4—41no—
202C5×C4⋊C4—41no—
203C5×C4⋊C4—42no—
204C5×C4⋊C4—81no—
205C5×C4⋊C4C2×D412yes—
206C5×C4⋊C4C2×D412yes—
207C5×C22⋊C4—22no—
208C5×C22⋊C4—22no—
209C5×C22⋊C4—22no—
210C5×C22⋊C4—22no—
211C5×C22⋊C4—22no—
212C5×C22⋊C4—22no—
213C5×C22⋊C4—22no—
214C5×C22⋊C4—22no—
215C5×C22⋊C4—22no—
216C5×C22⋊C4—22no—
217C5×C22⋊C4—22no—
218C5×C22⋊C4—42no—
219C5×C22⋊C4—42no—
220C5×C22⋊C4—81no—
221C5×C22⋊C4—81no—
222C42×C5—22no—
223C42×C5—22no—
224C42×C5—21no—
225C42×C5—22no—
226C42×C5—21no—
227#544C22×C511yescharacteristic
228#542—22no—
229#540—22no—
230#538—21no—
231#538C22×C512yes—
232#537C22×C511yescharacteristic
233#535—21no—
234#532—22no—
235#529—22no—
236#525—21no—
237#525C22×C512yes—
238C2×C22⋊Q8C22×C511yescharacteristic
239C4×#41—21no—
240C2×C4×D4C22×C511yescharacteristic
241#485—22no—
242#483C22×C512yes—
243#480C22×C512yes—
244#467—22no—
245#465—22no—
246#452—22no—
247#451C22×C512yes—
248#448C22×C512yes—
249C2×C22⋊C8C22×C512yes—
250#398C22×C511yescharacteristic
251#397—21no—
252#397C22×C511yescharacteristic
253#395C22×C511yescharacteristic
254#394—21no—
255#393C22×C511yescharacteristic
256#387—21no—
257#385—21no—
258#381C22×C511yescharacteristic
259#328C22×C512yes—
260#328C22×C512yes—
261#327C22×C512yes—
262#327C22×C512yes—
263#324C22×C511yescharacteristic
264#324C22×C511yescharacteristic
265#323C22×C512yes—
266C23×C5—21no—
267C23×C5—21no—
268C23×C5—21no—
269C23×C5—22no—
270C23×C5—21no—
271C23×C5—21no—
272C23×C5—41no—
273C23×C5—41no—
274C23×C5—41no—
275C23×C5—41no—
276C23×C5#12012yes—
277C23×C5C22×D411yescharacteristic
278C5×Q8—42no—
279C5×Q8—42no—
280C5×Q8—42no—
281C5×Q8—42no—
282C5×Q8—81no—
283C5×D4—44no—
284C5×D4—42no—
285C5×D4—42no—
286C5×D4—42no—
287C5×D4—42no—
288C5×D4—82no—
289C5×D4—82no—
290C5×D4—82no—
291C5×D4—81no—
292C5×D4—82no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—22no—
297C2×C4×C5—22no—
298C2×C4×C5—22no—
299C2×C4×C5—21no—
300C2×C4×C5—42no—
301C2×C4×C5—41no—
302C2×C4×C5—42no—
303C2×C4×C5—41no—
304C2×C4×C5—42no—
305C2×C4×C5—44no—
306C2×C4×C5—44no—
307C2×C4×C5—41no—
308C2×C4×C5—41no—
309C2×C4×C5—41no—
310C2×C4×C5—41no—
311C2×C4×C5—41no—
312C2×C4×C5—41no—
313C2×C4×C5—41no—
314C2×C4×C5—41no—
315C2×C4×C5—41no—
316C2×C4×C5—41no—
317C2×C4×C5—41no—
318C2×C4×C5—41no—
319C2×C4×C5—41no—
320C2×C4×C5—41no—
321C2×C4×C5—81no—
322C2×C4×C5—82no—
323C2×C4×C5#12011yescharacteristic
324C2×C4×C5#12011yescharacteristic
325C2×C4×C5#13512yes—
326C2×C4×C5C22×D412yes—
327C5×C8—42no—
328C5×C8—42no—
329C2×#41—21no—
330C2×#41—21no—
331C2×#41C5×D412yes—
332C22×Q8C23×C511yescharacteristic
333C22×D4C5×D411yescharacteristic
334C23×C4C5×D411yescharacteristic
335C23×C4C23×C511yescharacteristic
336C2×Q16—22no—
337C2×SD16—22no—
338C22×C8—22no—
339C4⋊Q8—22no—
340#127—22no—
341#126—22no—
342#126—22no—
343#125—22no—
344#124—22no—
345#124—22no—
346#124—22no—
347#123—22no—
348#123—22no—
349#123—22no—
350#123—22no—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353C22⋊Q8—22no—
354C22⋊Q8—22no—
355C22⋊Q8—22no—
356C22⋊Q8C5×D412yes—
357C22⋊Q8C23×C512yes—
358#121—21no—
359#121—22no—
360#121—22no—
361#121—22no—
362#121—22no—
363#121—22no—
364#121—21no—
365#121C5×D412yes—
366#121C23×C512yes—
367#120—22no—
368#120—22no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—22no—
379#117—22no—
380#117—21no—
381#117—21no—
382#117C5×D412yes—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4C23×C511yescharacteristic
387C2×C4⋊C4C23×C511yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4C5×D411yescharacteristic
393C2×C22⋊C4C23×C511yescharacteristic
394C2×C42—22no—
395C2×C42C5×D411yescharacteristic
396#107—22no—
397#106—22no—
398#103—22no—
399#103—22no—
400#103—22no—
401#102—22no—
402C22⋊C8—22no—
403C22⋊C8C23×C512yes—
404C22⋊C8C23×C512yes—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95C23×C511yescharacteristic
411#95C23×C511yescharacteristic
412C22×C5—21no—
413C22×C5—21no—
414C22×C5—22no—
415C22×C5—22no—
416C22×C5—22no—
417C22×C5—42no—
418C22×C5—42no—
419C22×C5—41no—
420C22×C5—42no—
421C22×C5—41no—
422C22×C5—41no—
423C22×C5—42no—
424C22×C5—81no—
425C22×C5—81no—
426C22×C5—81no—
427C22×C5C2×#12011yescharacteristic
428C22×C5C2×#13511yescharacteristic
429C22×C5#57511yescharacteristic
430C4×C5—22no—
431C4×C5—22no—
432C4×C5—21no—
433C4×C5—21no—
434C4×C5—42no—
435C4×C5—41no—
436C4×C5—42no—
437C4×C5—41no—
438C4×C5—42no—
439C4×C5—81no—
440C4×C5—81no—
441C4×C5—81no—
442C4×C5—81no—
443C24C2×C5×D411yescharacteristic
444C24C2×C5×D411yescharacteristic
445#41—42no—
446#41—42no—
447#41—82no—
448#41—82no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—22no—
452C2×Q8—81no—
453C2×Q8C2×C5×D412yes—
454C2×D4—21no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—21no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—41no—
464C2×D4C2×C5×D412yes—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—81no—
475C22×C4—81no—
476C22×C4C2×C5×D411yescharacteristic
477C22×C4C2×C5×D411yescharacteristic
478C22×C4C2×C5×D411yescharacteristic
479C22×C4C2×C5×D411yescharacteristic
480C22×C4C2×C5×D412yes—
481C22×C4C2×C5×D412yes—
482C22×C4C24×C511yescharacteristic
483Q16—82no—
484SD16—82no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—82no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—42no—
501C4⋊C4—81no—
502C4⋊C4C2×C5×D412yes—
503C4⋊C4C2×C5×D412yes—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—81no—
518C22⋊C4—81no—
519C42—22no—
520C42—22no—
521C42—21no—
522C42—22no—
523C42—21no—
524C2×C5—21no—
525C2×C5—21no—
526C2×C5—42no—
527C2×C5—82no—
528C2×C5—81no—
529C2×C5#300211yescharacteristic
530C2×C5#302211yescharacteristic
531C2×C5#302611yescharacteristic
532C23—21no—
533C23—21no—
534C23—21no—
535C23—22no—
536C23—21no—
537C23—21no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23C5×#12012yes—
543C23C22×C5×D411yescharacteristic
544Q8—42no—
545Q8—42no—
546Q8—42no—
547Q8—42no—
548Q8—81no—
549D4—44no—
550D4—42no—
551D4—42no—
552D4—42no—
553D4—42no—
554D4—82no—
555D4—82no—
556D4—81no—
557D4—82no—
558D4—82no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—44no—
572C2×C4—44no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—81no—
588C2×C4—82no—
589C2×C4C5×#12011yescharacteristic
590C2×C4C5×#12011yescharacteristic
591C2×C4C5×#13512yes—
592C2×C4C22×C5×D412yes—
593C8—42no—
594C8—42no—
595C5#1829911yescharacteristic, direct product factor, Sylow
596C22—21no—
597C22—21no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—42no—
602C22—42no—
603C22—41no—
604C22—42no—
605C22—41no—
606C22—41no—
607C22—42no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22C2×C5×#12011yescharacteristic
612C22C2×C5×#13511yescharacteristic
613C22C5×#57511yescharacteristic
614C4—22no—
615C4—22no—
616C4—21no—
617C4—21no—
618C4—42no—
619C4—41no—
620C4—42no—
621C4—41no—
622C4—42no—
623C4—81no—
624C4—81no—
625C4—81no—
626C4—81no—
627C2—21no—
628C2—21no—
629C2—42no—
630C2—81no—
631C2—82no—
632C2C5×#300211yescharacteristic
633C2C5×#302211yescharacteristic
634C2C5×#302611yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3460C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#3190C2semidirect
3. C5×#2638C2semidirect
4. C5×#1612C2semidirect
5. C5×#1611C2semidirect
6. C5×#1610C2semidirect
7. C5×#1606C2semidirect
8. C5×#1605C2semidirect
9. C5×#1604C2semidirect
10. C5×#1516C2semidirect
11. C5×#1459C2semidirect
51. #18299C5direct (N × H)
136. #3190C2×C5semidirect
137. #2638C2×C5semidirect
138. #1612C2×C5semidirect
139. #1611C2×C5semidirect
140. #1610C2×C5semidirect
141. #1606C2×C5semidirect
142. #1605C2×C5semidirect
143. #1604C2×C5semidirect
144. #1516C2×C5semidirect
145. #1459C2×C5semidirect
595. C5#18299direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#34602
C5×#31902
C5×#26382
C5×#16122
C5×#16112
C5×#16102
C5×#16062
C5×#16052
C5×#16042
C5×#15162
C5×#14592
#182995