Finite Group Databasebeta

← C5×#19045 #11941765

Subgroups — C5×#19045 #11941765

Order 1280.

870 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3559C211yesmaximal, characteristic
2C5×#3236C211yesmaximal, characteristic, complemented
3C5×#3181C211yesmaximal, characteristic, complemented
4C5×#3135C211yesmaximal, characteristic, complemented
5C5×#1664C212yesmaximal, complemented
6C5×#1664C212yesmaximal, complemented
7C5×#1662C212yesmaximal, complemented
8C5×#1661C212yesmaximal, complemented
9C5×#1532C211yesmaximal, characteristic, complemented
10C5×#1530C211yesmaximal, characteristic, complemented
11C2×C5×#330C211yesmaximal, characteristic, complemented
12C5×#563C2212yes—
13C5×#562C2212yes—
14C5×#554—21no—
15C5×#553—21no—
16C5×#553—21no—
17C5×#547—22no—
18C5×#547—21no—
19C5×#544—21no—
20C5×#540—21no—
21C5×#539—22no—
22C5×#539—21no—
23C5×#537—21no—
24C5×#533C2211yescharacteristic
25C5×#532C2211yescharacteristic
26C5×#529C2211yescharacteristic
27C2×C5×#125C2211yescharacteristic
28C5×#501C2212yes—
29C5×#501C2211yescharacteristic
30C5×#497C2211yescharacteristic
31C5×#491—21no—
32C5×#491C2212yes—
33C5×#491C2211yescharacteristic
34C5×#490—21no—
35C5×#489C2212yes—
36C5×#489C2212yes—
37C5×#489C2211yescharacteristic
38C5×#484—21no—
39C5×#483—21no—
40C5×#479—22no—
41C5×#467—21no—
42C5×#465—21no—
43C5×#441—21no—
44C5×#440—21no—
45C5×#432C2211yescharacteristic
46C5×#416—22no—
47C2×C5×#97C2211yescharacteristic
48C2×C5×#97C2211yescharacteristic
49C5×#330C2212yes—
50C5×#330C2212yes—
51C5×#330C2212yes—
52C5×#329C2212yes—
53C5×#329C2212yes—
54C5×#329C2212yes—
55#19045C511yesmaximal, characteristic, direct product factor, Sylow
56C2×C5×#41—22no—
57C2×C5×#41D412yes—
58C2×C5×Q16—21no—
59C2×C5×SD16—21no—
60C22×C5×C8—21no—
61C22×C5×C8—21no—
62C5×C4⋊Q8—21no—
63C5×C4⋊Q8—22no—
64C5×C4⋊Q8D411yescharacteristic
65C5×C4⋊Q8C2311yescharacteristic
66C5×C4⋊Q8C2311yescharacteristic
67C5×#127D411yescharacteristic
68C5×#126—22no—
69C5×#126—22no—
70C5×#126—21no—
71C5×#125—22no—
72C5×#125—21no—
73C5×#125—21no—
74C5×#125—21no—
75C5×#125—21no—
76C5×#125D412yes—
77C5×#125C2312yes—
78C5×#125C2311yescharacteristic
79C5×#124C2312yes—
80C5×#124C2311yescharacteristic
81C5×#123—22no—
82C5×#123—22no—
83C5×#123—22no—
84C5×#123—22no—
85C5×#123—21no—
86C5×#123—22no—
87C5×#123—22no—
88C5×C22⋊Q8—22no—
89C5×C22⋊Q8—22no—
90C5×C22⋊Q8—22no—
91C5×C22⋊Q8—22no—
92C5×C22⋊Q8—22no—
93C5×C22⋊Q8—22no—
94C5×C22⋊Q8—21no—
95C5×C22⋊Q8—21no—
96C5×C22⋊Q8D411yescharacteristic
97C5×#121—22no—
98C5×#121—22no—
99C5×#121—21no—
100C5×#121—21no—
101C5×#121—22no—
102C5×#121—22no—
103C5×#121—21no—
104C5×#121—21no—
105C5×#121D411yescharacteristic
106C4×C5×Q8—21no—
107C4×C5×Q8—21no—
108C4×C5×Q8D411yescharacteristic
109C4×C5×D4—22no—
110C4×C5×D4—22no—
111C4×C5×D4—21no—
112C4×C5×D4—21no—
113C4×C5×D4—21no—
114C4×C5×D4—21no—
115C4×C5×D4—21no—
116C4×C5×D4D411yescharacteristic
117C5×#117—21no—
118C5×#117—21no—
119C5×#117—21no—
120C2×C5×C4⋊C4—22no—
121C2×C5×C4⋊C4—21no—
122C2×C5×C4⋊C4—21no—
123C2×C5×C4⋊C4—21no—
124C2×C5×C4⋊C4D411yescharacteristic
125C2×C5×C4⋊C4D411yescharacteristic
126C2×C42×C5C2311yescharacteristic
127C5×#107—21no—
128C5×#107—22no—
129C5×#106—21no—
130C5×#106—22no—
131C5×C4⋊C8—21no—
132C5×#103—22no—
133C5×#103—22no—
134C5×#103—21no—
135C5×#103—21no—
136C5×#103—21no—
137C5×#103—22no—
138C5×#103—22no—
139C5×#102—22no—
140C5×#102—22no—
141C5×#102—21no—
142C5×C22⋊C8—21no—
143C5×#97—21no—
144C5×#97—21no—
145C5×#97C2312yes—
146C5×#97C2311yescharacteristic
147C5×#97C2311yescharacteristic
148C5×#97C2312yes—
149#3559C2×C511yescharacteristic
150#3236C2×C511yescharacteristic, complemented
151#3181C2×C511yescharacteristic, complemented
152#3135C2×C511yescharacteristic, complemented
153#1664C2×C512yescomplemented
154#1664C2×C512yescomplemented
155#1662C2×C512yescomplemented
156#1661C2×C512yescomplemented
157#1532C2×C511yescharacteristic, complemented
158#1530C2×C511yescharacteristic, complemented
159C2×#330C2×C511yescharacteristic, complemented
160C5×#41—44no—
161C5×#41—84no—
162C2×C5×Q8—22no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8C2×D411yescharacteristic
166C2×C5×Q8C2×D412yes—
167C2×C5×D4—22no—
168C2×C5×D4—21no—
169C2×C5×D4—22no—
170C2×C5×D4—22no—
171C2×C5×D4—21no—
172C2×C5×D4—21no—
173C2×C5×D4C2×D411yescharacteristic
174C2×C5×D4C2×D412yes—
175C22×C4×C5—21no—
176C22×C4×C5—22no—
177C22×C4×C5—22no—
178C22×C4×C5—22no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—22no—
182C22×C4×C5C2×D411yescharacteristic
183C22×C4×C5C2×D411yescharacteristic
184C22×C4×C5C2×D411yescharacteristic
185C5×Q16—42no—
186C5×SD16—42no—
187C2×C5×C8—21no—
188C2×C5×C8—22no—
189C2×C5×C8—21no—
190C2×C5×C8—22no—
191C2×C5×C8—42no—
192C2×C5×C8—42no—
193C5×C4⋊C4—22no—
194C5×C4⋊C4—22no—
195C5×C4⋊C4—22no—
196C5×C4⋊C4—22no—
197C5×C4⋊C4—22no—
198C5×C4⋊C4—21no—
199C5×C4⋊C4—21no—
200C5×C4⋊C4—21no—
201C5×C4⋊C4—22no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—21no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—22no—
206C5×C4⋊C4—22no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—21no—
210C5×C4⋊C4—21no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—21no—
213C5×C4⋊C4—41no—
214C5×C4⋊C4—41no—
215C5×C4⋊C4C2×D412yes—
216C5×C4⋊C4C2×D412yes—
217C5×C4⋊C4C2×D411yescharacteristic
218C5×C4⋊C4C2×D411yescharacteristic
219C5×C22⋊C4—22no—
220C5×C22⋊C4—22no—
221C5×C22⋊C4—22no—
222C5×C22⋊C4—22no—
223C5×C22⋊C4—22no—
224C5×C22⋊C4—21no—
225C5×C22⋊C4—21no—
226C5×C22⋊C4—21no—
227C5×C22⋊C4—21no—
228C5×C22⋊C4—22no—
229C5×C22⋊C4—22no—
230C5×C22⋊C4—21no—
231C5×C22⋊C4—41no—
232C42×C5—22no—
233C42×C5—21no—
234C42×C5—41no—
235C42×C5C2×D411yescharacteristic
236C42×C5C2×D411yescharacteristic
237C42×C5C2×D411yescharacteristic
238C42×C5C2411yescharacteristic
239#563C22×C512yes—
240#562C22×C512yes—
241#554—21no—
242#553—21no—
243#553—21no—
244#547—22no—
245#547—21no—
246#544—21no—
247#540—21no—
248#539—22no—
249#539—21no—
250#537—21no—
251#533C22×C511yescharacteristic
252#532C22×C511yescharacteristic
253#529C22×C511yescharacteristic
254C2×#125C22×C511yescharacteristic
255#501C22×C511yescharacteristic
256#501C22×C512yes—
257#497C22×C511yescharacteristic
258#491—21no—
259#491C22×C511yescharacteristic
260#491C22×C512yes—
261#490—21no—
262#489C22×C512yes—
263#489C22×C512yes—
264#489C22×C511yescharacteristic
265#484—21no—
266#483—21no—
267#479—22no—
268#467—21no—
269#465—21no—
270#441—21no—
271#440—21no—
272#432C22×C511yescharacteristic
273#416—22no—
274C2×#97C22×C511yescharacteristic
275C2×#97C22×C511yescharacteristic
276#330C22×C512yes—
277#330C22×C512yes—
278#330C22×C512yes—
279#329C22×C512yes—
280#329C22×C512yes—
281#329C22×C512yes—
282C23×C5—22no—
283C23×C5—21no—
284C23×C5#12011yescharacteristic
285C5×Q8—41no—
286C5×Q8—42no—
287C5×Q8—41no—
288C5×Q8—41no—
289C5×Q8—42no—
290C5×Q8—82no—
291C5×D4—41no—
292C5×D4—42no—
293C5×D4—42no—
294C5×D4—44no—
295C5×D4—42no—
296C5×D4—81no—
297C5×D4—82no—
298C5×D4—82no—
299C2×C4×C5—22no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—21no—
305C2×C4×C5—22no—
306C2×C4×C5—41no—
307C2×C4×C5—41no—
308C2×C4×C5—42no—
309C2×C4×C5—42no—
310C2×C4×C5—41no—
311C2×C4×C5—41no—
312C2×C4×C5—82no—
313C2×C4×C5—81no—
314C2×C4×C5—82no—
315C2×C4×C5—82no—
316C2×C4×C5—82no—
317C2×C4×C5#12011yescharacteristic
318C2×C4×C5#12011yescharacteristic
319C2×C4×C5#12011yescharacteristic
320C2×C4×C5C22×D411yescharacteristic
321C2×C4×C5C22×D411yescharacteristic
322C2×C4×C5C22×D411yescharacteristic
323C5×C8—22no—
324C5×C8—42no—
325C5×C8—42no—
326C5×C8—41no—
327C2×#41—22no—
328C2×#41C5×D412yes—
329C2×Q16—21no—
330C2×SD16—21no—
331C22×C8—21no—
332C22×C8—21no—
333C4⋊Q8—21no—
334C4⋊Q8—22no—
335C4⋊Q8C5×D411yescharacteristic
336C4⋊Q8C23×C511yescharacteristic
337C4⋊Q8C23×C511yescharacteristic
338#127C5×D411yescharacteristic
339#126—22no—
340#126—22no—
341#126—21no—
342#125—22no—
343#125—21no—
344#125—21no—
345#125—21no—
346#125—21no—
347#125C5×D412yes—
348#125C23×C512yes—
349#125C23×C511yescharacteristic
350#124C23×C511yescharacteristic
351#124C23×C512yes—
352#123—22no—
353#123—22no—
354#123—22no—
355#123—22no—
356#123—21no—
357#123—22no—
358#123—22no—
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364C22⋊Q8—22no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8C5×D411yescharacteristic
368#121—22no—
369#121—22no—
370#121—21no—
371#121—21no—
372#121—22no—
373#121—22no—
374#121—21no—
375#121—21no—
376#121C5×D411yescharacteristic
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8C5×D411yescharacteristic
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4C5×D411yescharacteristic
388#117—21no—
389#117—21no—
390#117—21no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4C5×D411yescharacteristic
396C2×C4⋊C4C5×D411yescharacteristic
397C2×C42C23×C511yescharacteristic
398#107—21no—
399#107—22no—
400#106—21no—
401#106—22no—
402C4⋊C8—21no—
403#103—22no—
404#103—22no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—22no—
409#103—22no—
410#102—22no—
411#102—22no—
412#102—21no—
413C22⋊C8—21no—
414#97—21no—
415#97—21no—
416#97C23×C512yes—
417#97C23×C511yescharacteristic
418#97C23×C511yescharacteristic
419#97C23×C512yes—
420C22×C5—21no—
421C22×C5—21no—
422C22×C5—42no—
423C22×C5—41no—
424C22×C5—42no—
425C22×C5—41no—
426C22×C5—41no—
427C22×C5—42no—
428C22×C5#45512yes—
429C22×C5C2×#12011yescharacteristic
430C4×C5—21no—
431C4×C5—21no—
432C4×C5—21no—
433C4×C5—21no—
434C4×C5—21no—
435C4×C5—21no—
436C4×C5—42no—
437C4×C5—42no—
438C4×C5—41no—
439C4×C5—42no—
440C4×C5—41no—
441C4×C5—41no—
442C4×C5—81no—
443C4×C5—81no—
444#41—44no—
445#41—84no—
446C2×Q8—22no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8C2×C5×D412yes—
450C2×Q8C2×C5×D411yescharacteristic
451C2×D4—22no—
452C2×D4—21no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4C2×C5×D412yes—
458C2×D4C2×C5×D411yescharacteristic
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4C2×C5×D411yescharacteristic
467C22×C4C2×C5×D411yescharacteristic
468C22×C4C2×C5×D411yescharacteristic
469Q16—42no—
470SD16—42no—
471C2×C8—21no—
472C2×C8—22no—
473C2×C8—21no—
474C2×C8—22no—
475C2×C8—42no—
476C2×C8—42no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—22no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4C2×C5×D412yes—
500C4⋊C4C2×C5×D411yescharacteristic
501C4⋊C4C2×C5×D412yes—
502C4⋊C4C2×C5×D411yescharacteristic
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—21no—
515C22⋊C4—41no—
516C42—22no—
517C42—21no—
518C42—41no—
519C42C2×C5×D411yescharacteristic
520C42C2×C5×D411yescharacteristic
521C42C2×C5×D411yescharacteristic
522C42C24×C511yescharacteristic
523C2×C5—22no—
524C2×C5—82no—
525C2×C5—81no—
526C2×C5C2×#45511yescharacteristic
527C2×C5#301811yescharacteristic
528C2×C5#302011yescharacteristic
529C23—22no—
530C23—21no—
531C23C5×#12011yescharacteristic
532Q8—41no—
533Q8—42no—
534Q8—41no—
535Q8—41no—
536Q8—42no—
537Q8—82no—
538D4—41no—
539D4—42no—
540D4—42no—
541D4—44no—
542D4—42no—
543D4—81no—
544D4—82no—
545D4—82no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—82no—
560C2×C4—81no—
561C2×C4—82no—
562C2×C4—82no—
563C2×C4—82no—
564C2×C4C5×#12011yescharacteristic
565C2×C4C5×#12011yescharacteristic
566C2×C4C5×#12011yescharacteristic
567C2×C4C22×C5×D411yescharacteristic
568C2×C4C22×C5×D411yescharacteristic
569C2×C4C22×C5×D411yescharacteristic
570C8—22no—
571C8—42no—
572C8—41no—
573C8—42no—
574C5#1904511yescharacteristic, direct product factor, Sylow
575C22—21no—
576C22—21no—
577C22—42no—
578C22—41no—
579C22—42no—
580C22—41no—
581C22—41no—
582C22—42no—
583C22C5×#45512yes—
584C22C2×C5×#12011yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—42no—
592C4—42no—
593C4—41no—
594C4—42no—
595C4—41no—
596C4—41no—
597C4—81no—
598C4—81no—
599C2—22no—
600C2—82no—
601C2—81no—
602C2C2×C5×#45511yescharacteristic
603C2C5×#301811yescharacteristic
604C2C5×#302011yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3559C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#3236C2semidirect
3. C5×#3181C2semidirect
4. C5×#3135C2semidirect
5. C5×#1664C2semidirect
6. C5×#1664C2semidirect
7. C5×#1662C2semidirect
8. C5×#1661C2semidirect
9. C5×#1532C2semidirect
10. C5×#1530C2semidirect
11. C2×C5×#330C2semidirect
55. #19045C5direct (N × H)
150. #3236C2×C5semidirect
151. #3181C2×C5semidirect
152. #3135C2×C5semidirect
153. #1664C2×C5semidirect
154. #1664C2×C5semidirect
155. #1662C2×C5semidirect
156. #1661C2×C5semidirect
157. #1532C2×C5semidirect
158. #1530C2×C5semidirect
159. C2×#330C2×C5semidirect
574. C5#19045direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35592
C5×#32362
C5×#31812
C5×#31352
C5×#16642
C5×#16622
C5×#16612
C5×#15322
C5×#15302
C2×C5×#3302
#190455