Finite Group Databasebeta

← C5×#19071 #11941791

Subgroups — C5×#19071 #11941791

Order 1280.

810 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3553C211yesmaximal, characteristic
2C5×#3240C211yesmaximal, characteristic, complemented
3C5×#3236C211yesmaximal, characteristic, complemented
4C5×#3172C211yesmaximal, characteristic, complemented
5C5×#1664C211yesmaximal, characteristic, complemented
6C5×#1664C211yesmaximal, characteristic, complemented
7C5×#1664C211yesmaximal, characteristic, complemented
8C5×#1663C211yesmaximal, characteristic, complemented
9C5×#1663C211yesmaximal, characteristic, complemented
10C5×#1662C211yesmaximal, characteristic, complemented
11C5×#1661C211yesmaximal, characteristic, complemented
12C5×#1660C211yesmaximal, characteristic, complemented
13C5×#1535C211yesmaximal, characteristic, complemented
14C5×#1529C211yesmaximal, characteristic, complemented
15C5×#1528C211yesmaximal, characteristic, complemented
16C5×#564C2211yescharacteristic
17C5×#563C2211yescharacteristic
18C5×#563C2211yescharacteristic
19C5×#562C2211yescharacteristic
20C5×#554—21no—
21C5×#554—21no—
22C5×#553—21no—
23C5×#553—21no—
24C5×#552—21no—
25C5×#552—21no—
26C5×#541—21no—
27C5×#541—21no—
28C5×#539—21no—
29C5×#539—21no—
30C5×#539—21no—
31C5×#539—21no—
32C5×#533C2211yescharacteristic
33C5×#529C2211yescharacteristic
34C5×#529C2211yescharacteristic
35C2×C5×#125C2211yescharacteristic
36C5×#501C2211yescharacteristic
37C5×#501C2211yescharacteristic
38C5×#501C2211yescharacteristic
39C5×#501C2211yescharacteristic
40C5×#501C2211yescharacteristic
41C5×#497C2211yescharacteristic
42C5×#491C2211yescharacteristic
43C5×#491C2211yescharacteristic
44C5×#491C2211yescharacteristic
45C5×#489C2211yescharacteristic
46C5×#489C2211yescharacteristic
47C5×#489C2211yescharacteristic
48C5×#485—21no—
49C5×#484—21no—
50C5×#483—21no—
51C5×#482—21no—
52C5×#479—21no—
53C5×#479—21no—
54C5×#479—21no—
55C5×#478—21no—
56C5×#470—21no—
57C5×#468—21no—
58C4×C5×Q16—21no—
59C4×C5×SD16—21no—
60C5×#432C2211yescharacteristic
61C5×#432C2211yescharacteristic
62C4×C5×M16C2211yescharacteristic
63C5×#330C2211yescharacteristic
64C5×#330C2211yescharacteristic
65C5×#330C2211yescharacteristic
66C5×#330C2211yescharacteristic
67C5×#330C2211yescharacteristic
68C5×#330C2211yescharacteristic
69C5×#330C2211yescharacteristic
70C5×#330C2211yescharacteristic
71C5×#329C2211yescharacteristic
72C5×#329C2211yescharacteristic
73C5×#329C2211yescharacteristic
74C5×#329C2211yescharacteristic
75#19071C511yesmaximal, characteristic, direct product factor, Sylow
76C2×C5×Q16—21no—
77C2×C5×SD16—21no—
78C2×C5×M16—21no—
79C5×C4⋊Q8—21no—
80C5×C4⋊Q8—21no—
81C5×C4⋊Q8C2311yescharacteristic
82C5×C4⋊Q8C2311yescharacteristic
83C5×#126—21no—
84C5×#126—21no—
85C5×#126—21no—
86C5×#126—21no—
87C5×#126—21no—
88C5×#126—21no—
89C5×#126—21no—
90C5×#126—21no—
91C5×#126—21no—
92C5×#126—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×#125—21no—
103C5×#125—21no—
104C5×#125—21no—
105C5×#125—21no—
106C5×#125D411yescharacteristic
107C5×#125D411yescharacteristic
108C5×#125C2311yescharacteristic
109C5×#125C2311yescharacteristic
110C5×#125C2311yescharacteristic
111C5×#125C2311yescharacteristic
112C5×#124C2311yescharacteristic
113C5×#124C2311yescharacteristic
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×#123—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⋊Q8—21no—
132C5×C22⋊Q8—21no—
133C5×C22⋊Q8—21no—
134C5×C22⋊Q8—21no—
135C5×C22⋊Q8—21no—
136C5×C22⋊Q8—21no—
137C5×C22⋊Q8—21no—
138C5×C22⋊Q8D411yescharacteristic
139C5×C22⋊Q8D411yescharacteristic
140C5×#121—21no—
141C5×#121—21no—
142C5×#121—21no—
143C5×#121—21no—
144C5×#121D411yescharacteristic
145C5×#121D411yescharacteristic
146C4×C5×Q8—21no—
147C4×C5×Q8—21no—
148C4×C5×Q8—21no—
149C4×C5×Q8—21no—
150C4×C5×Q8D411yescharacteristic
151C4×C5×Q8D411yescharacteristic
152C4×C5×D4—21no—
153C4×C5×D4—21no—
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×D4D411yescharacteristic
161C4×C5×D4D411yescharacteristic
162C5×#117—21no—
163C5×#117—21no—
164C5×#117—21no—
165C5×#117—21no—
166C5×#117—21no—
167C2×C5×C4⋊C4—21no—
168C2×C5×C4⋊C4—21no—
169C2×C5×C4⋊C4—21no—
170C2×C5×C4⋊C4—21no—
171C2×C5×C4⋊C4D411yescharacteristic
172C2×C5×C4⋊C4D411yescharacteristic
173C2×C42×C5C2311yescharacteristic
174C5×#107—21no—
175C5×#107—21no—
176C5×#107—21no—
177C5×#107—21no—
178C5×#107—21no—
179C5×#106—21no—
180C5×#106—21no—
181C5×#106—21no—
182C5×#106—21no—
183C5×#106—21no—
184C5×C4⋊C8—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×#103—21no—
195C5×#102—21no—
196C5×#102—21no—
197C5×#102—21no—
198C5×C22⋊C8—21no—
199C5×C22⋊C8—21no—
200C5×#97C2311yescharacteristic
201C5×#97C2311yescharacteristic
202C5×#97C2311yescharacteristic
203C5×#97C2311yescharacteristic
204C5×#97C2311yescharacteristic
205C5×#97C2311yescharacteristic
206C4×C5×C8—21no—
207#3553C2×C511yescharacteristic
208#3240C2×C511yescharacteristic, complemented
209#3236C2×C511yescharacteristic, complemented
210#3172C2×C511yescharacteristic, complemented
211#1664C2×C511yescharacteristic, complemented
212#1664C2×C511yescharacteristic, complemented
213#1664C2×C511yescharacteristic, complemented
214#1663C2×C511yescharacteristic, complemented
215#1663C2×C511yescharacteristic, complemented
216#1662C2×C511yescharacteristic, complemented
217#1661C2×C511yescharacteristic, complemented
218#1660C2×C511yescharacteristic, complemented
219#1535C2×C511yescharacteristic, complemented
220#1529C2×C511yescharacteristic, complemented
221#1528C2×C511yescharacteristic, complemented
222C2×C5×Q8—21no—
223C2×C5×Q8—21no—
224C2×C5×Q8—21no—
225C2×C5×Q8—21no—
226C2×C5×Q8C2×D411yescharacteristic
227C2×C5×Q8C2×D411yescharacteristic
228C2×C5×D4—21no—
229C2×C5×D4—21no—
230C2×C5×D4—21no—
231C2×C5×D4—21no—
232C2×C5×D4C2×D411yescharacteristic
233C2×C5×D4C2×D411yescharacteristic
234C22×C4×C5—21no—
235C22×C4×C5—21no—
236C22×C4×C5—21no—
237C22×C4×C5—21no—
238C22×C4×C5—21no—
239C22×C4×C5—21no—
240C22×C4×C5—21no—
241C22×C4×C5—21no—
242C22×C4×C5C2×D411yescharacteristic
243C22×C4×C5C2×D411yescharacteristic
244C22×C4×C5C2×D411yescharacteristic
245C5×Q16—42no—
246C5×SD16—42no—
247C5×M16—42no—
248C2×C5×C8—21no—
249C2×C5×C8—21no—
250C2×C5×C8—21no—
251C2×C5×C8—21no—
252C2×C5×C8—21no—
253C2×C5×C8—21no—
254C5×C4⋊C4—21no—
255C5×C4⋊C4—21no—
256C5×C4⋊C4—21no—
257C5×C4⋊C4—21no—
258C5×C4⋊C4—21no—
259C5×C4⋊C4—21no—
260C5×C4⋊C4—21no—
261C5×C4⋊C4—21no—
262C5×C4⋊C4—21no—
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—41no—
289C5×C4⋊C4—41no—
290C5×C4⋊C4C2×D411yescharacteristic
291C5×C4⋊C4C2×D411yescharacteristic
292C5×C4⋊C4C2×D411yescharacteristic
293C5×C4⋊C4C2×D411yescharacteristic
294C5×C4⋊C4C2×D411yescharacteristic
295C5×C4⋊C4C2×D411yescharacteristic
296C5×C4⋊C4C2×D411yescharacteristic
297C5×C4⋊C4C2×D411yescharacteristic
298C5×C22⋊C4—21no—
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—41no—
317C42×C5—21no—
318C42×C5—21no—
319C42×C5—21no—
320C42×C5—21no—
321C42×C5—21no—
322C42×C5—21no—
323C42×C5—41no—
324C42×C5C2×D411yescharacteristic
325C42×C5C2×D411yescharacteristic
326C42×C5C2×D411yescharacteristic
327C42×C5C2411yescharacteristic
328#564C22×C511yescharacteristic
329#563C22×C511yescharacteristic
330#563C22×C511yescharacteristic
331#562C22×C511yescharacteristic
332#554—21no—
333#554—21no—
334#553—21no—
335#553—21no—
336#552—21no—
337#552—21no—
338#541—21no—
339#541—21no—
340#539—21no—
341#539—21no—
342#539—21no—
343#539—21no—
344#533C22×C511yescharacteristic
345#529C22×C511yescharacteristic
346#529C22×C511yescharacteristic
347C2×#125C22×C511yescharacteristic
348#501C22×C511yescharacteristic
349#501C22×C511yescharacteristic
350#501C22×C511yescharacteristic
351#501C22×C511yescharacteristic
352#501C22×C511yescharacteristic
353#497C22×C511yescharacteristic
354#491C22×C511yescharacteristic
355#491C22×C511yescharacteristic
356#491C22×C511yescharacteristic
357#489C22×C511yescharacteristic
358#489C22×C511yescharacteristic
359#489C22×C511yescharacteristic
360#485—21no—
361#484—21no—
362#483—21no—
363#482—21no—
364#479—21no—
365#479—21no—
366#479—21no—
367#478—21no—
368#470—21no—
369#468—21no—
370C4×Q16—21no—
371C4×SD16—21no—
372#432C22×C511yescharacteristic
373#432C22×C511yescharacteristic
374C4×M16C22×C511yescharacteristic
375#330C22×C511yescharacteristic
376#330C22×C511yescharacteristic
377#330C22×C511yescharacteristic
378#330C22×C511yescharacteristic
379#330C22×C511yescharacteristic
380#330C22×C511yescharacteristic
381#330C22×C511yescharacteristic
382#330C22×C511yescharacteristic
383#329C22×C511yescharacteristic
384#329C22×C511yescharacteristic
385#329C22×C511yescharacteristic
386#329C22×C511yescharacteristic
387C23×C5—21no—
388C23×C5—21no—
389C23×C5#12011yescharacteristic
390C5×Q8—41no—
391C5×Q8—41no—
392C5×Q8—41no—
393C5×Q8—41no—
394C5×Q8—42no—
395C5×Q8—81no—
396C5×Q8—81no—
397C5×D4—41no—
398C5×D4—41no—
399C5×D4—42no—
400C5×D4—42no—
401C5×D4—81no—
402C5×D4—81no—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—21no—
406C2×C4×C5—21no—
407C2×C4×C5—21no—
408C2×C4×C5—21no—
409C2×C4×C5—21no—
410C2×C4×C5—21no—
411C2×C4×C5—21no—
412C2×C4×C5—21no—
413C2×C4×C5—41no—
414C2×C4×C5—41no—
415C2×C4×C5—41no—
416C2×C4×C5—41no—
417C2×C4×C5—41no—
418C2×C4×C5—81no—
419C2×C4×C5—81no—
420C2×C4×C5—81no—
421C2×C4×C5—81no—
422C2×C4×C5—81no—
423C2×C4×C5—81no—
424C2×C4×C5—81no—
425C2×C4×C5—81no—
426C2×C4×C5#12011yescharacteristic
427C2×C4×C5#12011yescharacteristic
428C2×C4×C5#12011yescharacteristic
429C2×C4×C5C22×D411yescharacteristic
430C2×C4×C5C22×D411yescharacteristic
431C2×C4×C5C22×D411yescharacteristic
432C5×C8—22no—
433C5×C8—41no—
434C5×C8—41no—
435C5×C8—41no—
436C5×C8—41no—
437C5×C8—41no—
438C2×Q16—21no—
439C2×SD16—21no—
440C2×M16—21no—
441C4⋊Q8—21no—
442C4⋊Q8—21no—
443C4⋊Q8C23×C511yescharacteristic
444C4⋊Q8C23×C511yescharacteristic
445#126—21no—
446#126—21no—
447#126—21no—
448#126—21no—
449#126—21no—
450#126—21no—
451#126—21no—
452#126—21no—
453#126—21no—
454#126—21no—
455#125—21no—
456#125—21no—
457#125—21no—
458#125—21no—
459#125—21no—
460#125—21no—
461#125—21no—
462#125—21no—
463#125—21no—
464#125—21no—
465#125—21no—
466#125—21no—
467#125—21no—
468#125C5×D411yescharacteristic
469#125C5×D411yescharacteristic
470#125C23×C511yescharacteristic
471#125C23×C511yescharacteristic
472#125C23×C511yescharacteristic
473#125C23×C511yescharacteristic
474#124C23×C511yescharacteristic
475#124C23×C511yescharacteristic
476#123—21no—
477#123—21no—
478#123—21no—
479#123—21no—
480#123—21no—
481#123—21no—
482#123—21no—
483#123—21no—
484#123—21no—
485#123—21no—
486C22⋊Q8—21no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8C5×D411yescharacteristic
501C22⋊Q8C5×D411yescharacteristic
502#121—21no—
503#121—21no—
504#121—21no—
505#121—21no—
506#121C5×D411yescharacteristic
507#121C5×D411yescharacteristic
508C4×Q8—21no—
509C4×Q8—21no—
510C4×Q8—21no—
511C4×Q8—21no—
512C4×Q8C5×D411yescharacteristic
513C4×Q8C5×D411yescharacteristic
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4C5×D411yescharacteristic
523C4×D4C5×D411yescharacteristic
524#117—21no—
525#117—21no—
526#117—21no—
527#117—21no—
528#117—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4C5×D411yescharacteristic
534C2×C4⋊C4C5×D411yescharacteristic
535C2×C42C23×C511yescharacteristic
536#107—21no—
537#107—21no—
538#107—21no—
539#107—21no—
540#107—21no—
541#106—21no—
542#106—21no—
543#106—21no—
544#106—21no—
545#106—21no—
546C4⋊C8—21no—
547C4⋊C8—21no—
548#103—21no—
549#103—21no—
550#103—21no—
551#103—21no—
552#103—21no—
553#103—21no—
554#103—21no—
555#103—21no—
556#103—21no—
557#102—21no—
558#102—21no—
559#102—21no—
560C22⋊C8—21no—
561C22⋊C8—21no—
562#97C23×C511yescharacteristic
563#97C23×C511yescharacteristic
564#97C23×C511yescharacteristic
565#97C23×C511yescharacteristic
566#97C23×C511yescharacteristic
567#97C23×C511yescharacteristic
568C4×C8—21no—
569C22×C5—21no—
570C22×C5—21no—
571C22×C5—21no—
572C22×C5—41no—
573C22×C5—41no—
574C22×C5—41no—
575C22×C5—41no—
576C22×C5—41no—
577C22×C5—41no—
578C22×C5C2×#12011yescharacteristic
579C4×C5—21no—
580C4×C5—21no—
581C4×C5—21no—
582C4×C5—21no—
583C4×C5—21no—
584C4×C5—21no—
585C4×C5—41no—
586C4×C5—41no—
587C4×C5—41no—
588C4×C5—41no—
589C4×C5—41no—
590C4×C5—41no—
591C4×C5—41no—
592C4×C5—41no—
593C4×C5—41no—
594C4×C5—41no—
595C4×C5—81no—
596C4×C5—81no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C2×C5×D411yescharacteristic
602C2×Q8C2×C5×D411yescharacteristic
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4C2×C5×D411yescharacteristic
608C2×D4C2×C5×D411yescharacteristic
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4C2×C5×D411yescharacteristic
618C22×C4C2×C5×D411yescharacteristic
619C22×C4C2×C5×D411yescharacteristic
620Q16—42no—
621SD16—42no—
622M16—42no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
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—41no—
664C4⋊C4—41no—
665C4⋊C4C2×C5×D411yescharacteristic
666C4⋊C4C2×C5×D411yescharacteristic
667C4⋊C4C2×C5×D411yescharacteristic
668C4⋊C4C2×C5×D411yescharacteristic
669C4⋊C4C2×C5×D411yescharacteristic
670C4⋊C4C2×C5×D411yescharacteristic
671C4⋊C4C2×C5×D411yescharacteristic
672C4⋊C4C2×C5×D411yescharacteristic
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—21no—
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—41no—
692C42—21no—
693C42—21no—
694C42—21no—
695C42—21no—
696C42—21no—
697C42—21no—
698C42—41no—
699C42C2×C5×D411yescharacteristic
700C42C2×C5×D411yescharacteristic
701C42C2×C5×D411yescharacteristic
702C42C24×C511yescharacteristic
703C2×C5—41no—
704C2×C5—81no—
705C2×C5—81no—
706C2×C5#301811yescharacteristic
707C2×C5#302011yescharacteristic
708C2×C5#302211yescharacteristic
709C23—21no—
710C23—21no—
711C23C5×#12011yescharacteristic
712Q8—41no—
713Q8—41no—
714Q8—41no—
715Q8—41no—
716Q8—42no—
717Q8—81no—
718Q8—81no—
719D4—41no—
720D4—41no—
721D4—42no—
722D4—42no—
723D4—81no—
724D4—81no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4C5×#12011yescharacteristic
749C2×C4C5×#12011yescharacteristic
750C2×C4C5×#12011yescharacteristic
751C2×C4C22×C5×D411yescharacteristic
752C2×C4C22×C5×D411yescharacteristic
753C2×C4C22×C5×D411yescharacteristic
754C8—22no—
755C8—41no—
756C8—41no—
757C8—41no—
758C8—41no—
759C8—41no—
760C5#1907111yescharacteristic, direct product factor, Sylow
761C22—21no—
762C22—21no—
763C22—21no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22C2×C5×#12011yescharacteristic
771C4—21no—
772C4—21no—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—81no—
788C4—81no—
789C2—41no—
790C2—81no—
791C2—81no—
792C2C5×#301811yescharacteristic
793C2C5×#302011yescharacteristic
794C2C5×#302211yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3553C2
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×#3236C2semidirect
4. C5×#3172C2semidirect
5. C5×#1664C2semidirect
6. C5×#1664C2semidirect
7. C5×#1664C2semidirect
8. C5×#1663C2semidirect
9. C5×#1663C2semidirect
10. C5×#1662C2semidirect
11. C5×#1661C2semidirect
12. C5×#1660C2semidirect
13. C5×#1535C2semidirect
14. C5×#1529C2semidirect
15. C5×#1528C2semidirect
75. #19071C5direct (N × H)
208. #3240C2×C5semidirect
209. #3236C2×C5semidirect
210. #3172C2×C5semidirect
211. #1664C2×C5semidirect
212. #1664C2×C5semidirect
213. #1664C2×C5semidirect
214. #1663C2×C5semidirect
215. #1663C2×C5semidirect
216. #1662C2×C5semidirect
217. #1661C2×C5semidirect
218. #1660C2×C5semidirect
219. #1535C2×C5semidirect
220. #1529C2×C5semidirect
221. #1528C2×C5semidirect
760. C5#19071direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35532
C5×#32402
C5×#32362
C5×#31722
C5×#16642
C5×#16632
C5×#16622
C5×#16612
C5×#16602
C5×#15352
C5×#15292
C5×#15282
#190715