Finite Group Databasebeta

← C5×#19041 #11941761

Subgroups — C5×#19041 #11941761

Order 1280.

838 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3567C211yesmaximal, characteristic
2C5×#3240C211yesmaximal, characteristic, complemented
3C5×#3181C211yesmaximal, characteristic, complemented
4C5×#3172C211yesmaximal, characteristic, complemented
5C5×#1663C211yesmaximal, characteristic, complemented
6C5×#1663C211yesmaximal, characteristic, complemented
7C5×#1662C211yesmaximal, characteristic, complemented
8C5×#1662C211yesmaximal, characteristic, complemented
9C5×#1661C211yesmaximal, characteristic, complemented
10C5×#1661C211yesmaximal, characteristic, complemented
11C5×#1661C211yesmaximal, characteristic, complemented
12C5×#1661C211yesmaximal, characteristic, complemented
13C5×#1532C211yesmaximal, characteristic, complemented
14C5×#1529C211yesmaximal, characteristic, complemented
15C5×#1524C211yesmaximal, characteristic, complemented
16C5×#564C2211yescharacteristic
17C5×#562C2211yescharacteristic
18C5×#562C2211yescharacteristic
19C5×#562C2211yescharacteristic
20C5×#553—21no—
21C5×#553—21no—
22C5×#553—21no—
23C5×#552—21no—
24C5×#552—21no—
25C5×#552—21no—
26C5×#540—21no—
27C5×#540—21no—
28C5×#540—21no—
29C5×#539—21no—
30C5×#539—21no—
31C5×#539—21no—
32C5×#533C2211yescharacteristic
33C5×#529C2211yescharacteristic
34C5×#529C2211yescharacteristic
35C5×#529C2211yescharacteristic
36C5×#501C2211yescharacteristic
37C5×#501C2211yescharacteristic
38C5×#501C2211yescharacteristic
39C5×#501C2211yescharacteristic
40C5×#497C2211yescharacteristic
41C5×#497C2211yescharacteristic
42C5×#491C2211yescharacteristic
43C5×#491C2211yescharacteristic
44C5×#489C2211yescharacteristic
45C5×#489C2211yescharacteristic
46C5×#489C2211yescharacteristic
47C5×#489C2211yescharacteristic
48C5×#485—21no—
49C5×#482—21no—
50C5×#479—21no—
51C5×#478—21no—
52C5×#470—21no—
53C5×#468—21no—
54C5×#467—21no—
55C5×#465—21no—
56C5×#441—21no—
57C5×#440—21no—
58C4×C5×Q16—21no—
59C4×C5×SD16—21no—
60C5×#432C2211yescharacteristic
61C4×C5×M16C2211yescharacteristic
62C2×C5×#97C2211yescharacteristic
63C5×#330C2211yescharacteristic
64C5×#330C2211yescharacteristic
65C5×#330C2211yescharacteristic
66C5×#330C2211yescharacteristic
67C5×#330C2211yescharacteristic
68C5×#330C2211yescharacteristic
69C5×#329C2211yescharacteristic
70C5×#329C2211yescharacteristic
71C5×#329C2211yescharacteristic
72C5×#329C2211yescharacteristic
73C5×#329C2211yescharacteristic
74C5×#329C2211yescharacteristic
75#19041C511yesmaximal, characteristic, direct product factor, Sylow
76C2×C5×Q16—21no—
77C2×C5×Q16—21no—
78C2×C5×SD16—21no—
79C2×C5×SD16—21no—
80C2×C5×M16—21no—
81C22×C5×C8—21no—
82C5×C4⋊Q8C2311yescharacteristic
83C5×C4⋊Q8C2311yescharacteristic
84C5×#127—21no—
85C5×#126—21no—
86C5×#126—21no—
87C5×#126—21no—
88C5×#126—21no—
89C5×#126—21no—
90C5×#126—21no—
91C5×#126—21no—
92C5×#125—21no—
93C5×#125—21no—
94C5×#125—21no—
95C5×#125—21no—
96C5×#125—21no—
97C5×#125—21no—
98C5×#125—21no—
99C5×#125—21no—
100C5×#125—21no—
101C5×#125—21no—
102C5×#125C2311yescharacteristic
103C5×#125C2311yescharacteristic
104C5×#125C2311yescharacteristic
105C5×#124C2311yescharacteristic
106C5×#124C2311yescharacteristic
107C5×#124C2311yescharacteristic
108C5×#123—21no—
109C5×#123—21no—
110C5×#123—21no—
111C5×#123—21no—
112C5×#123—21no—
113C5×#123—21no—
114C5×#123—21no—
115C5×#123—21no—
116C5×#123—21no—
117C5×#123—21no—
118C5×#123—21no—
119C5×#123—21no—
120C5×#123—21no—
121C5×#123—21no—
122C5×#123—21no—
123C5×C22⋊Q8—21no—
124C5×C22⋊Q8—21no—
125C5×C22⋊Q8—21no—
126C5×C22⋊Q8—21no—
127C5×C22⋊Q8—21no—
128C5×C22⋊Q8—21no—
129C5×C22⋊Q8—21no—
130C5×C22⋊Q8—21no—
131C5×C22⋊Q8D411yescharacteristic
132C5×C22⋊Q8D411yescharacteristic
133C5×C22⋊Q8D411yescharacteristic
134C5×#121—21no—
135C5×#121—21no—
136C5×#121—21no—
137C5×#121—21no—
138C5×#121—21no—
139C5×#121—21no—
140C5×#121—21no—
141C5×#121—21no—
142C5×#121—21no—
143C5×#121—21no—
144C5×#121—21no—
145C5×#121—21no—
146C5×#121D411yescharacteristic
147C5×#121D411yescharacteristic
148C5×#121D411yescharacteristic
149C4×C5×Q8—21no—
150C4×C5×Q8—21no—
151C4×C5×Q8D411yescharacteristic
152C4×C5×Q8D411yescharacteristic
153C4×C5×Q8D411yescharacteristic
154C4×C5×D4—21no—
155C4×C5×D4—21no—
156C4×C5×D4—21no—
157C4×C5×D4—21no—
158C4×C5×D4—21no—
159C4×C5×D4—21no—
160C4×C5×D4—21no—
161C4×C5×D4—21no—
162C4×C5×D4—21no—
163C4×C5×D4D411yescharacteristic
164C4×C5×D4D411yescharacteristic
165C4×C5×D4D411yescharacteristic
166C5×#117—21no—
167C5×#117—21no—
168C5×#117—21no—
169C5×#117—21no—
170C5×#117—21no—
171C5×#117—21no—
172C5×#117—21no—
173C2×C5×C4⋊C4—21no—
174C2×C5×C4⋊C4—21no—
175C2×C5×C4⋊C4—21no—
176C2×C42×C5C2311yescharacteristic
177C5×#107—21no—
178C5×#107—21no—
179C5×#107—21no—
180C5×#107—21no—
181C5×#106—21no—
182C5×#106—21no—
183C5×#106—21no—
184C5×#106—21no—
185C5×C4⋊C8—21no—
186C5×#103—21no—
187C5×#103—21no—
188C5×#103—21no—
189C5×#103—21no—
190C5×#103—21no—
191C5×#103—21no—
192C5×#103—21no—
193C5×#103—21no—
194C5×#102—21no—
195C5×#102—21no—
196C5×#102—21no—
197C5×#102—21no—
198C5×C22⋊C8—21no—
199C5×#97—21no—
200C5×#97C2311yescharacteristic
201C5×#97C2311yescharacteristic
202C5×#97C2311yescharacteristic
203C5×#97C2311yescharacteristic
204C5×#97C2311yescharacteristic
205C5×#97C2311yescharacteristic
206C4×C5×C8—21no—
207#3567C2×C511yescharacteristic
208#3240C2×C511yescharacteristic, complemented
209#3181C2×C511yescharacteristic, complemented
210#3172C2×C511yescharacteristic, complemented
211#1663C2×C511yescharacteristic, complemented
212#1663C2×C511yescharacteristic, complemented
213#1662C2×C511yescharacteristic, complemented
214#1662C2×C511yescharacteristic, complemented
215#1661C2×C511yescharacteristic, complemented
216#1661C2×C511yescharacteristic, complemented
217#1661C2×C511yescharacteristic, complemented
218#1661C2×C511yescharacteristic, complemented
219#1532C2×C511yescharacteristic, complemented
220#1529C2×C511yescharacteristic, complemented
221#1524C2×C511yescharacteristic, complemented
222C2×C5×Q8—21no—
223C2×C5×Q8—21no—
224C2×C5×Q8C2×D411yescharacteristic
225C2×C5×Q8C2×D411yescharacteristic
226C2×C5×Q8C2×D411yescharacteristic
227C2×C5×D4—21no—
228C2×C5×D4—21no—
229C2×C5×D4—21no—
230C2×C5×D4—21no—
231C2×C5×D4—21no—
232C2×C5×D4—21no—
233C2×C5×D4—21no—
234C2×C5×D4—21no—
235C2×C5×D4—21no—
236C2×C5×D4C2×D411yescharacteristic
237C2×C5×D4C2×D411yescharacteristic
238C2×C5×D4C2×D411yescharacteristic
239C22×C4×C5—21no—
240C22×C4×C5—21no—
241C22×C4×C5—21no—
242C22×C4×C5—21no—
243C22×C4×C5—21no—
244C22×C4×C5—21no—
245C22×C4×C5—21no—
246C22×C4×C5—21no—
247C22×C4×C5—21no—
248C22×C4×C5C2×D411yescharacteristic
249C22×C4×C5C2×D411yescharacteristic
250C22×C4×C5C2×D411yescharacteristic
251C5×Q16—42no—
252C5×Q16—42no—
253C5×SD16—42no—
254C5×SD16—42no—
255C5×M16—42no—
256C2×C5×C8—21no—
257C2×C5×C8—21no—
258C2×C5×C8—21no—
259C2×C5×C8—21no—
260C2×C5×C8—21no—
261C2×C5×C8—21no—
262C2×C5×C8—42no—
263C5×C4⋊C4—21no—
264C5×C4⋊C4—21no—
265C5×C4⋊C4—21no—
266C5×C4⋊C4—21no—
267C5×C4⋊C4—21no—
268C5×C4⋊C4—21no—
269C5×C4⋊C4—21no—
270C5×C4⋊C4—21no—
271C5×C4⋊C4—21no—
272C5×C4⋊C4—21no—
273C5×C4⋊C4—21no—
274C5×C4⋊C4—21no—
275C5×C4⋊C4—21no—
276C5×C4⋊C4—21no—
277C5×C4⋊C4—21no—
278C5×C4⋊C4—21no—
279C5×C4⋊C4—21no—
280C5×C4⋊C4—21no—
281C5×C4⋊C4—21no—
282C5×C4⋊C4—21no—
283C5×C4⋊C4—21no—
284C5×C4⋊C4—21no—
285C5×C4⋊C4—21no—
286C5×C4⋊C4—21no—
287C5×C4⋊C4—21no—
288C5×C4⋊C4—21no—
289C5×C4⋊C4—21no—
290C5×C4⋊C4—21no—
291C5×C4⋊C4—41no—
292C5×C4⋊C4—41no—
293C5×C4⋊C4C2×D411yescharacteristic
294C5×C4⋊C4C2×D411yescharacteristic
295C5×C4⋊C4C2×D411yescharacteristic
296C5×C4⋊C4C2×D411yescharacteristic
297C5×C4⋊C4C2×D411yescharacteristic
298C5×C4⋊C4C2×D411yescharacteristic
299C5×C22⋊C4—21no—
300C5×C22⋊C4—21no—
301C5×C22⋊C4—21no—
302C5×C22⋊C4—21no—
303C5×C22⋊C4—21no—
304C5×C22⋊C4—21no—
305C5×C22⋊C4—21no—
306C5×C22⋊C4—21no—
307C5×C22⋊C4—21no—
308C5×C22⋊C4—21no—
309C5×C22⋊C4—21no—
310C5×C22⋊C4—21no—
311C5×C22⋊C4—21no—
312C5×C22⋊C4—21no—
313C5×C22⋊C4—21no—
314C5×C22⋊C4—21no—
315C5×C22⋊C4—21no—
316C5×C22⋊C4—21no—
317C5×C22⋊C4—21no—
318C5×C22⋊C4—21no—
319C5×C22⋊C4—21no—
320C5×C22⋊C4—41no—
321C42×C5—21no—
322C42×C5—21no—
323C42×C5—21no—
324C42×C5—21no—
325C42×C5—21no—
326C42×C5—41no—
327C42×C5C2×D411yescharacteristic
328C42×C5C2×D411yescharacteristic
329C42×C5C2×D411yescharacteristic
330C42×C5C2411yescharacteristic
331#564C22×C511yescharacteristic
332#562C22×C511yescharacteristic
333#562C22×C511yescharacteristic
334#562C22×C511yescharacteristic
335#553—21no—
336#553—21no—
337#553—21no—
338#552—21no—
339#552—21no—
340#552—21no—
341#540—21no—
342#540—21no—
343#540—21no—
344#539—21no—
345#539—21no—
346#539—21no—
347#533C22×C511yescharacteristic
348#529C22×C511yescharacteristic
349#529C22×C511yescharacteristic
350#529C22×C511yescharacteristic
351#501C22×C511yescharacteristic
352#501C22×C511yescharacteristic
353#501C22×C511yescharacteristic
354#501C22×C511yescharacteristic
355#497C22×C511yescharacteristic
356#497C22×C511yescharacteristic
357#491C22×C511yescharacteristic
358#491C22×C511yescharacteristic
359#489C22×C511yescharacteristic
360#489C22×C511yescharacteristic
361#489C22×C511yescharacteristic
362#489C22×C511yescharacteristic
363#485—21no—
364#482—21no—
365#479—21no—
366#478—21no—
367#470—21no—
368#468—21no—
369#467—21no—
370#465—21no—
371#441—21no—
372#440—21no—
373C4×Q16—21no—
374C4×SD16—21no—
375#432C22×C511yescharacteristic
376C4×M16C22×C511yescharacteristic
377C2×#97C22×C511yescharacteristic
378#330C22×C511yescharacteristic
379#330C22×C511yescharacteristic
380#330C22×C511yescharacteristic
381#330C22×C511yescharacteristic
382#330C22×C511yescharacteristic
383#330C22×C511yescharacteristic
384#329C22×C511yescharacteristic
385#329C22×C511yescharacteristic
386#329C22×C511yescharacteristic
387#329C22×C511yescharacteristic
388#329C22×C511yescharacteristic
389#329C22×C511yescharacteristic
390C23×C5—21no—
391C23×C5—21no—
392C23×C5—21no—
393C23×C5#12011yescharacteristic
394C5×Q8—41no—
395C5×Q8—41no—
396C5×Q8—41no—
397C5×Q8—41no—
398C5×Q8—41no—
399C5×Q8—41no—
400C5×Q8—41no—
401C5×D4—41no—
402C5×D4—41no—
403C5×D4—41no—
404C5×D4—81no—
405C5×D4—81no—
406C5×D4—81no—
407C5×D4—81no—
408C5×D4—81no—
409C5×D4—81no—
410C5×D4—81no—
411C5×D4—81no—
412C5×D4—81no—
413C2×C4×C5—21no—
414C2×C4×C5—21no—
415C2×C4×C5—21no—
416C2×C4×C5—21no—
417C2×C4×C5—21no—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—41no—
423C2×C4×C5—41no—
424C2×C4×C5—41no—
425C2×C4×C5—41no—
426C2×C4×C5—41no—
427C2×C4×C5—81no—
428C2×C4×C5—81no—
429C2×C4×C5—81no—
430C2×C4×C5—81no—
431C2×C4×C5—81no—
432C2×C4×C5—81no—
433C2×C4×C5—81no—
434C2×C4×C5—81no—
435C2×C4×C5—81no—
436C2×C4×C5#12011yescharacteristic
437C2×C4×C5#12011yescharacteristic
438C2×C4×C5#12011yescharacteristic
439C2×C4×C5C22×D411yescharacteristic
440C2×C4×C5C22×D411yescharacteristic
441C2×C4×C5C22×D411yescharacteristic
442C5×C8—22no—
443C5×C8—22no—
444C5×C8—41no—
445C5×C8—41no—
446C5×C8—41no—
447C5×C8—41no—
448C2×Q16—21no—
449C2×Q16—21no—
450C2×SD16—21no—
451C2×SD16—21no—
452C2×M16—21no—
453C22×C8—21no—
454C4⋊Q8C23×C511yescharacteristic
455C4⋊Q8C23×C511yescharacteristic
456#127—21no—
457#126—21no—
458#126—21no—
459#126—21no—
460#126—21no—
461#126—21no—
462#126—21no—
463#126—21no—
464#125—21no—
465#125—21no—
466#125—21no—
467#125—21no—
468#125—21no—
469#125—21no—
470#125—21no—
471#125—21no—
472#125—21no—
473#125—21no—
474#125C23×C511yescharacteristic
475#125C23×C511yescharacteristic
476#125C23×C511yescharacteristic
477#124C23×C511yescharacteristic
478#124C23×C511yescharacteristic
479#124C23×C511yescharacteristic
480#123—21no—
481#123—21no—
482#123—21no—
483#123—21no—
484#123—21no—
485#123—21no—
486#123—21no—
487#123—21no—
488#123—21no—
489#123—21no—
490#123—21no—
491#123—21no—
492#123—21no—
493#123—21no—
494#123—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502C22⋊Q8—21no—
503C22⋊Q8C5×D411yescharacteristic
504C22⋊Q8C5×D411yescharacteristic
505C22⋊Q8C5×D411yescharacteristic
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121C5×D411yescharacteristic
519#121C5×D411yescharacteristic
520#121C5×D411yescharacteristic
521C4×Q8—21no—
522C4×Q8—21no—
523C4×Q8C5×D411yescharacteristic
524C4×Q8C5×D411yescharacteristic
525C4×Q8C5×D411yescharacteristic
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—21no—
533C4×D4—21no—
534C4×D4—21no—
535C4×D4C5×D411yescharacteristic
536C4×D4C5×D411yescharacteristic
537C4×D4C5×D411yescharacteristic
538#117—21no—
539#117—21no—
540#117—21no—
541#117—21no—
542#117—21no—
543#117—21no—
544#117—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C42C23×C511yescharacteristic
549#107—21no—
550#107—21no—
551#107—21no—
552#107—21no—
553#106—21no—
554#106—21no—
555#106—21no—
556#106—21no—
557C4⋊C8—21no—
558#103—21no—
559#103—21no—
560#103—21no—
561#103—21no—
562#103—21no—
563#103—21no—
564#103—21no—
565#103—21no—
566#102—21no—
567#102—21no—
568#102—21no—
569#102—21no—
570C22⋊C8—21no—
571#97—21no—
572#97C23×C511yescharacteristic
573#97C23×C511yescharacteristic
574#97C23×C511yescharacteristic
575#97C23×C511yescharacteristic
576#97C23×C511yescharacteristic
577#97C23×C511yescharacteristic
578C4×C8—21no—
579C22×C5—21no—
580C22×C5—21no—
581C22×C5—21no—
582C22×C5—41no—
583C22×C5—41no—
584C22×C5—41no—
585C22×C5—41no—
586C22×C5—41no—
587C22×C5—41no—
588C22×C5—41no—
589C22×C5—41no—
590C22×C5—41no—
591C22×C5C2×#12011yescharacteristic
592C4×C5—21no—
593C4×C5—21no—
594C4×C5—21no—
595C4×C5—21no—
596C4×C5—21no—
597C4×C5—21no—
598C4×C5—41no—
599C4×C5—41no—
600C4×C5—41no—
601C4×C5—41no—
602C4×C5—41no—
603C4×C5—41no—
604C4×C5—41no—
605C4×C5—41no—
606C4×C5—41no—
607C4×C5—81no—
608C4×C5—81no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8C2×C5×D411yescharacteristic
612C2×Q8C2×C5×D411yescharacteristic
613C2×Q8C2×C5×D411yescharacteristic
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4C2×C5×D411yescharacteristic
624C2×D4C2×C5×D411yescharacteristic
625C2×D4C2×C5×D411yescharacteristic
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4C2×C5×D411yescharacteristic
636C22×C4C2×C5×D411yescharacteristic
637C22×C4C2×C5×D411yescharacteristic
638Q16—42no—
639Q16—42no—
640SD16—42no—
641SD16—42no—
642M16—42no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—42no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—41no—
679C4⋊C4—41no—
680C4⋊C4C2×C5×D411yescharacteristic
681C4⋊C4C2×C5×D411yescharacteristic
682C4⋊C4C2×C5×D411yescharacteristic
683C4⋊C4C2×C5×D411yescharacteristic
684C4⋊C4C2×C5×D411yescharacteristic
685C4⋊C4C2×C5×D411yescharacteristic
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—21no—
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—21no—
700C22⋊C4—21no—
701C22⋊C4—21no—
702C22⋊C4—21no—
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—41no—
708C42—21no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—41no—
714C42C2×C5×D411yescharacteristic
715C42C2×C5×D411yescharacteristic
716C42C2×C5×D411yescharacteristic
717C42C24×C511yescharacteristic
718C2×C5—41no—
719C2×C5—81no—
720C2×C5—81no—
721C2×C5—81no—
722C2×C5#301811yescharacteristic
723C2×C5#301811yescharacteristic
724C2×C5#302211yescharacteristic
725C23—21no—
726C23—21no—
727C23—21no—
728C23C5×#12011yescharacteristic
729Q8—41no—
730Q8—41no—
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8—41no—
735Q8—41no—
736D4—41no—
737D4—41no—
738D4—41no—
739D4—81no—
740D4—81no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—81no—
746D4—81no—
747D4—81no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4C5×#12011yescharacteristic
772C2×C4C5×#12011yescharacteristic
773C2×C4C5×#12011yescharacteristic
774C2×C4C22×C5×D411yescharacteristic
775C2×C4C22×C5×D411yescharacteristic
776C2×C4C22×C5×D411yescharacteristic
777C8—22no—
778C8—22no—
779C8—41no—
780C8—41no—
781C8—41no—
782C8—41no—
783C5#1904111yescharacteristic, direct product factor, Sylow
784C22—21no—
785C22—21no—
786C22—21no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22C2×C5×#12011yescharacteristic
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—81no—
813C4—81no—
814C2—41no—
815C2—81no—
816C2—81no—
817C2—81no—
818C2C5×#301811yescharacteristic
819C2C5×#301811yescharacteristic
820C2C5×#302211yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3567C2
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×#3240C2semidirect
3. C5×#3181C2semidirect
4. C5×#3172C2semidirect
5. C5×#1663C2semidirect
6. C5×#1663C2semidirect
7. C5×#1662C2semidirect
8. C5×#1662C2semidirect
9. C5×#1661C2semidirect
10. C5×#1661C2semidirect
11. C5×#1661C2semidirect
12. C5×#1661C2semidirect
13. C5×#1532C2semidirect
14. C5×#1529C2semidirect
15. C5×#1524C2semidirect
75. #19041C5direct (N × H)
208. #3240C2×C5semidirect
209. #3181C2×C5semidirect
210. #3172C2×C5semidirect
211. #1663C2×C5semidirect
212. #1663C2×C5semidirect
213. #1662C2×C5semidirect
214. #1662C2×C5semidirect
215. #1661C2×C5semidirect
216. #1661C2×C5semidirect
217. #1661C2×C5semidirect
218. #1661C2×C5semidirect
219. #1532C2×C5semidirect
220. #1529C2×C5semidirect
221. #1524C2×C5semidirect
783. C5#19041direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35672
C5×#32402
C5×#31812
C5×#31722
C5×#16632
C5×#16622
C5×#16612
C5×#15322
C5×#15292
C5×#15242
#190415