Finite Group Databasebeta

← C5×#19012 #11941732

Subgroups — C5×#19012 #11941732

Order 1280.

844 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3531C211yesmaximal, characteristic, complemented
2C5×#3235C211yesmaximal, characteristic, complemented
3C5×#3219C211yesmaximal, characteristic, complemented
4C5×#3180C211yesmaximal, characteristic, complemented
5C5×#1664C211yesmaximal, characteristic, complemented
6C5×#1663C211yesmaximal, characteristic, complemented
7C5×#1661C211yesmaximal, characteristic, complemented
8C5×#1660C211yesmaximal, characteristic, complemented
9C5×#1658C211yesmaximal, characteristic, complemented
10C5×#1657C211yesmaximal, characteristic, complemented
11C5×#1657C211yesmaximal, characteristic, complemented
12C5×#1656C211yesmaximal, characteristic, complemented
13C5×#1535C211yesmaximal, characteristic, complemented
14C5×#1532C211yesmaximal, characteristic, complemented
15C5×#1531C211yesmaximal, characteristic, complemented
16C5×#564C2211yescharacteristic
17C5×#563—21no—
18C5×#563—21no—
19C5×#563—21no—
20C5×#563—21no—
21C5×#563C2211yescharacteristic
22C5×#563C2211yescharacteristic
23C5×#562—21no—
24C5×#562—21no—
25C5×#562C2211yescharacteristic
26C5×#533—21no—
27C5×#533—21no—
28C5×#533C2211yescharacteristic
29C5×#532C2211yescharacteristic
30C5×#529—21no—
31C5×#529—21no—
32C5×#529—21no—
33C5×#529—21no—
34C5×#529C2211yescharacteristic
35C5×#529C2211yescharacteristic
36C5×#501C2211yescharacteristic
37C5×#501C2211yescharacteristic
38C5×#501C2211yescharacteristic
39C5×#497C2211yescharacteristic
40C5×#496C2211yescharacteristic
41C5×#496C2211yescharacteristic
42C5×#491C2211yescharacteristic
43C5×#490C2211yescharacteristic
44C5×#490C2211yescharacteristic
45C5×#490C2211yescharacteristic
46C5×#490C2211yescharacteristic
47C5×#489C2211yescharacteristic
48C5×#482—21no—
49C5×#482—21no—
50C5×#476—21no—
51C5×#474—21no—
52C5×#466—21no—
53C5×#465—21no—
54C5×#464—21no—
55C5×#463—21no—
56C5×#452—21no—
57C5×#449—21no—
58C5×#442—21no—
59C5×#440—21no—
60C5×#432C2211yescharacteristic
61C5×#432C2211yescharacteristic
62C2×C5×#97C2211yescharacteristic
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#19012C511yesmaximal, characteristic, direct product factor, Sylow
76C2×C5×#41—21no—
77C2×C5×Q16—21no—
78C2×C5×SD16—21no—
79C2×C5×SD16—21no—
80C2×C5×SD16—21no—
81C2×C5×D8—21no—
82C2×C5×D8—21no—
83C22×C5×C8—21no—
84C5×C4⋊Q8—21no—
85C5×C4⋊Q8—21no—
86C5×C4⋊Q8—21no—
87C5×C4⋊Q8—21no—
88C5×C4⋊Q8D411yescharacteristic
89C5×C4⋊Q8D411yescharacteristic
90C5×C4⋊Q8C2311yescharacteristic
91C5×#127C2311yescharacteristic
92C5×#126—21no—
93C5×#126—21no—
94C5×#126—21no—
95C5×#126—21no—
96C5×#126—21no—
97C5×#126—21no—
98C5×#126—21no—
99C5×#126—21no—
100C5×#126—21no—
101C5×#126—21no—
102C5×#125—21no—
103C5×#125—21no—
104C5×#125—21no—
105C5×#125—21no—
106C5×#125—21no—
107C5×#125—21no—
108C5×#125—21no—
109C5×#125—21no—
110C5×#125C2311yescharacteristic
111C5×#125C2311yescharacteristic
112C5×#125C2311yescharacteristic
113C5×#125C2311yescharacteristic
114C5×#124—21no—
115C5×#124—21no—
116C5×#124—21no—
117C5×#124—21no—
118C5×#124—21no—
119C5×#124C2311yescharacteristic
120C5×#124C2311yescharacteristic
121C5×#123—21no—
122C5×#123—21no—
123C5×#123—21no—
124C5×#123—21no—
125C5×#123—21no—
126C5×#123—21no—
127C5×#123—21no—
128C5×#123—21no—
129C5×#123—21no—
130C5×#123—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⋊Q8—21no—
139C5×C22⋊Q8—21no—
140C5×C22⋊Q8—21no—
141C5×C22⋊Q8—21no—
142C5×C22⋊Q8—21no—
143C5×C22⋊Q8—21no—
144C5×C22⋊Q8—21no—
145C5×C22⋊Q8D411yescharacteristic
146C5×C22⋊Q8D411yescharacteristic
147C5×#121—21no—
148C5×#121—21no—
149C5×#121—21no—
150C5×#121—21no—
151C5×#121—21no—
152C5×#121—21no—
153C5×#121D411yescharacteristic
154C5×#121D411yescharacteristic
155C4×C5×Q8—21no—
156C4×C5×Q8—21no—
157C4×C5×Q8—21no—
158C4×C5×Q8—21no—
159C4×C5×Q8D411yescharacteristic
160C4×C5×Q8D411yescharacteristic
161C4×C5×D4—21no—
162C4×C5×D4—21no—
163C4×C5×D4—21no—
164C4×C5×D4—21no—
165C4×C5×D4—21no—
166C4×C5×D4—21no—
167C4×C5×D4D411yescharacteristic
168C4×C5×D4D411yescharacteristic
169C5×#117—21no—
170C5×#117—21no—
171C5×#117—21no—
172C5×#117—21no—
173C5×#117D411yescharacteristic
174C5×#117D411yescharacteristic
175C2×C42×C5—21no—
176C2×C42×C5—21no—
177C2×C42×C5C2311yescharacteristic
178C5×#107—21no—
179C5×#107—21no—
180C5×#107—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×#102—21no—
190C5×#102—21no—
191C5×#102—21no—
192C5×#102—21no—
193C5×#102—21no—
194C5×#102—21no—
195C5×#102—21no—
196C5×#102—21no—
197C5×#102—21no—
198C5×C22⋊C8—21no—
199C5×C22⋊C8—21no—
200C5×#97—21no—
201C5×#97C2311yescharacteristic
202C5×#97C2311yescharacteristic
203C5×#97C2311yescharacteristic
204C5×#97C2311yescharacteristic
205C5×#97C2311yescharacteristic
206C5×#97C2311yescharacteristic
207#3531C2×C511yescharacteristic, complemented
208#3235C2×C511yescharacteristic, complemented
209#3219C2×C511yescharacteristic, complemented
210#3180C2×C511yescharacteristic, complemented
211#1664C2×C511yescharacteristic, complemented
212#1663C2×C511yescharacteristic, complemented
213#1661C2×C511yescharacteristic, complemented
214#1660C2×C511yescharacteristic, complemented
215#1658C2×C511yescharacteristic, complemented
216#1657C2×C511yescharacteristic, complemented
217#1657C2×C511yescharacteristic, complemented
218#1656C2×C511yescharacteristic, complemented
219#1535C2×C511yescharacteristic, complemented
220#1532C2×C511yescharacteristic, complemented
221#1531C2×C511yescharacteristic, complemented
222C5×#41—81no—
223C5×#41—81no—
224C2×C5×Q8—21no—
225C2×C5×Q8—21no—
226C2×C5×Q8—21no—
227C2×C5×Q8—21no—
228C2×C5×Q8—21no—
229C2×C5×Q8C2×D411yescharacteristic
230C2×C5×Q8C2×D411yescharacteristic
231C2×C5×D4—21no—
232C2×C5×D4—21no—
233C2×C5×D4—21no—
234C2×C5×D4—21no—
235C2×C5×D4—21no—
236C2×C5×D4—21no—
237C2×C5×D4—21no—
238C2×C5×D4—41no—
239C2×C5×D4C2×D411yescharacteristic
240C2×C5×D4C2×D411yescharacteristic
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—41no—
248C22×C4×C5C2×D411yescharacteristic
249C22×C4×C5C2×D411yescharacteristic
250C22×C4×C5C2×D411yescharacteristic
251C5×Q16—81no—
252C5×SD16—42no—
253C5×SD16—81no—
254C5×SD16—81no—
255C5×D8—42no—
256C5×D8—81no—
257C2×C5×C8—21no—
258C2×C5×C8—21no—
259C2×C5×C8—21no—
260C2×C5×C8—21no—
261C2×C5×C8—21no—
262C2×C5×C8—21no—
263C2×C5×C8—42no—
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—21no—
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×C4⋊C4C2×D411yescharacteristic
299C5×C4⋊C4C2×D411yescharacteristic
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—
321C5×C22⋊C4—41no—
322C42×C5—21no—
323C42×C5—21no—
324C42×C5—21no—
325C42×C5—21no—
326C42×C5—21no—
327C42×C5—21no—
328C42×C5—21no—
329C42×C5—21no—
330C42×C5C2×D411yescharacteristic
331C42×C5C2×D411yescharacteristic
332C42×C5C2×D411yescharacteristic
333C42×C5C2411yescharacteristic
334#564C22×C511yescharacteristic
335#563—21no—
336#563—21no—
337#563—21no—
338#563—21no—
339#563C22×C511yescharacteristic
340#563C22×C511yescharacteristic
341#562—21no—
342#562—21no—
343#562C22×C511yescharacteristic
344#533—21no—
345#533—21no—
346#533C22×C511yescharacteristic
347#532C22×C511yescharacteristic
348#529—21no—
349#529—21no—
350#529—21no—
351#529—21no—
352#529C22×C511yescharacteristic
353#529C22×C511yescharacteristic
354#501C22×C511yescharacteristic
355#501C22×C511yescharacteristic
356#501C22×C511yescharacteristic
357#497C22×C511yescharacteristic
358#496C22×C511yescharacteristic
359#496C22×C511yescharacteristic
360#491C22×C511yescharacteristic
361#490C22×C511yescharacteristic
362#490C22×C511yescharacteristic
363#490C22×C511yescharacteristic
364#490C22×C511yescharacteristic
365#489C22×C511yescharacteristic
366#482—21no—
367#482—21no—
368#476—21no—
369#474—21no—
370#466—21no—
371#465—21no—
372#464—21no—
373#463—21no—
374#452—21no—
375#449—21no—
376#442—21no—
377#440—21no—
378#432C22×C511yescharacteristic
379#432C22×C511yescharacteristic
380C2×#97C22×C511yescharacteristic
381#330C22×C511yescharacteristic
382#330C22×C511yescharacteristic
383#330C22×C511yescharacteristic
384#330C22×C511yescharacteristic
385#330C22×C511yescharacteristic
386#330C22×C511yescharacteristic
387#330C22×C511yescharacteristic
388#330C22×C511yescharacteristic
389#329C22×C511yescharacteristic
390#329C22×C511yescharacteristic
391#329C22×C511yescharacteristic
392#329C22×C511yescharacteristic
393C23×C5—21no—
394C23×C5—21no—
395C23×C5—41no—
396C23×C5#12011yescharacteristic
397C5×Q8—41no—
398C5×Q8—41no—
399C5×Q8—41no—
400C5×Q8—41no—
401C5×Q8—81no—
402C5×Q8—81no—
403C5×Q8—81no—
404C5×Q8—81no—
405C5×D4—41no—
406C5×D4—41no—
407C5×D4—41no—
408C5×D4—41no—
409C5×D4—41no—
410C5×D4—41no—
411C5×D4—42no—
412C5×D4—81no—
413C5×D4—81no—
414C5×D4—81no—
415C5×D4—81no—
416C5×D4—82no—
417C2×C4×C5—21no—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5—21no—
425C2×C4×C5—21no—
426C2×C4×C5—21no—
427C2×C4×C5—41no—
428C2×C4×C5—41no—
429C2×C4×C5—41no—
430C2×C4×C5—42no—
431C2×C4×C5—42no—
432C2×C4×C5—41no—
433C2×C4×C5—82no—
434C2×C4×C5—81no—
435C2×C4×C5—81no—
436C2×C4×C5—81no—
437C2×C4×C5—81no—
438C2×C4×C5#12011yescharacteristic
439C2×C4×C5#12011yescharacteristic
440C2×C4×C5#12011yescharacteristic
441C2×C4×C5C22×D411yescharacteristic
442C2×C4×C5C22×D411yescharacteristic
443C2×C4×C5C22×D411yescharacteristic
444C5×C8—22no—
445C5×C8—41no—
446C5×C8—41no—
447C5×C8—41no—
448C5×C8—41no—
449C5×C8—41no—
450C2×#41—21no—
451C2×Q16—21no—
452C2×SD16—21no—
453C2×SD16—21no—
454C2×SD16—21no—
455C2×D8—21no—
456C2×D8—21no—
457C22×C8—21no—
458C4⋊Q8—21no—
459C4⋊Q8—21no—
460C4⋊Q8—21no—
461C4⋊Q8—21no—
462C4⋊Q8C5×D411yescharacteristic
463C4⋊Q8C5×D411yescharacteristic
464C4⋊Q8C23×C511yescharacteristic
465#127C23×C511yescharacteristic
466#126—21no—
467#126—21no—
468#126—21no—
469#126—21no—
470#126—21no—
471#126—21no—
472#126—21no—
473#126—21no—
474#126—21no—
475#126—21no—
476#125—21no—
477#125—21no—
478#125—21no—
479#125—21no—
480#125—21no—
481#125—21no—
482#125—21no—
483#125—21no—
484#125C23×C511yescharacteristic
485#125C23×C511yescharacteristic
486#125C23×C511yescharacteristic
487#125C23×C511yescharacteristic
488#124—21no—
489#124—21no—
490#124—21no—
491#124—21no—
492#124—21no—
493#124C23×C511yescharacteristic
494#124C23×C511yescharacteristic
495#123—21no—
496#123—21no—
497#123—21no—
498#123—21no—
499#123—21no—
500#123—21no—
501#123—21no—
502#123—21no—
503#123—21no—
504#123—21no—
505C22⋊Q8—21no—
506C22⋊Q8—21no—
507C22⋊Q8—21no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—21no—
512C22⋊Q8—21no—
513C22⋊Q8—21no—
514C22⋊Q8—21no—
515C22⋊Q8—21no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8C5×D411yescharacteristic
520C22⋊Q8C5×D411yescharacteristic
521#121—21no—
522#121—21no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121C5×D411yescharacteristic
528#121C5×D411yescharacteristic
529C4×Q8—21no—
530C4×Q8—21no—
531C4×Q8—21no—
532C4×Q8—21no—
533C4×Q8C5×D411yescharacteristic
534C4×Q8C5×D411yescharacteristic
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4C5×D411yescharacteristic
542C4×D4C5×D411yescharacteristic
543#117—21no—
544#117—21no—
545#117—21no—
546#117—21no—
547#117C5×D411yescharacteristic
548#117C5×D411yescharacteristic
549C2×C42—21no—
550C2×C42—21no—
551C2×C42C23×C511yescharacteristic
552#107—21no—
553#107—21no—
554#107—21no—
555#106—21no—
556#106—21no—
557#106—21no—
558C4⋊C8—21no—
559C4⋊C8—21no—
560#103—21no—
561#103—21no—
562#103—21no—
563#102—21no—
564#102—21no—
565#102—21no—
566#102—21no—
567#102—21no—
568#102—21no—
569#102—21no—
570#102—21no—
571#102—21no—
572C22⋊C8—21no—
573C22⋊C8—21no—
574#97—21no—
575#97C23×C511yescharacteristic
576#97C23×C511yescharacteristic
577#97C23×C511yescharacteristic
578#97C23×C511yescharacteristic
579#97C23×C511yescharacteristic
580#97C23×C511yescharacteristic
581C22×C5—21no—
582C22×C5—21no—
583C22×C5—21no—
584C22×C5—41no—
585C22×C5—41no—
586C22×C5—41no—
587C22×C5—41no—
588C22×C5—41no—
589C22×C5—41no—
590C22×C5—81no—
591C22×C5—81no—
592C22×C5—81no—
593C22×C5C2×#12011yescharacteristic
594C4×C5—21no—
595C4×C5—21no—
596C4×C5—21no—
597C4×C5—21no—
598C4×C5—21no—
599C4×C5—21no—
600C4×C5—41no—
601C4×C5—41no—
602C4×C5—41no—
603C4×C5—41no—
604C4×C5—41no—
605C4×C5—41no—
606C4×C5—41no—
607C4×C5—41no—
608C4×C5—41no—
609C4×C5—41no—
610C4×C5—81no—
611#41—81no—
612#41—81no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8C2×C5×D411yescharacteristic
619C2×Q8C2×C5×D411yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—41no—
628C2×D4C2×C5×D411yescharacteristic
629C2×D4C2×C5×D411yescharacteristic
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—41no—
637C22×C4C2×C5×D411yescharacteristic
638C22×C4C2×C5×D411yescharacteristic
639C22×C4C2×C5×D411yescharacteristic
640Q16—81no—
641SD16—42no—
642SD16—81no—
643SD16—81no—
644D8—42no—
645D8—81no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—42no—
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—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4C2×C5×D411yescharacteristic
682C4⋊C4C2×C5×D411yescharacteristic
683C4⋊C4C2×C5×D411yescharacteristic
684C4⋊C4C2×C5×D411yescharacteristic
685C4⋊C4C2×C5×D411yescharacteristic
686C4⋊C4C2×C5×D411yescharacteristic
687C4⋊C4C2×C5×D411yescharacteristic
688C4⋊C4C2×C5×D411yescharacteristic
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—21no—
708C22⋊C4—21no—
709C22⋊C4—41no—
710C22⋊C4—41no—
711C42—21no—
712C42—21no—
713C42—21no—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42C2×C5×D411yescharacteristic
720C42C2×C5×D411yescharacteristic
721C42C2×C5×D411yescharacteristic
722C42C24×C511yescharacteristic
723C2×C5—41no—
724C2×C5—81no—
725C2×C5—81no—
726C2×C5—161no—
727C2×C5#301811yescharacteristic
728C2×C5#302011yescharacteristic
729C2×C5#302111yescharacteristic
730C23—21no—
731C23—21no—
732C23—41no—
733C23C5×#12011yescharacteristic
734Q8—41no—
735Q8—41no—
736Q8—41no—
737Q8—41no—
738Q8—81no—
739Q8—81no—
740Q8—81no—
741Q8—81no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—42no—
749D4—81no—
750D4—81no—
751D4—81no—
752D4—81no—
753D4—82no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—82no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4C5×#12011yescharacteristic
776C2×C4C5×#12011yescharacteristic
777C2×C4C5×#12011yescharacteristic
778C2×C4C22×C5×D411yescharacteristic
779C2×C4C22×C5×D411yescharacteristic
780C2×C4C22×C5×D411yescharacteristic
781C8—22no—
782C8—41no—
783C8—41no—
784C8—41no—
785C8—41no—
786C8—41no—
787C5#1901211yescharacteristic, direct product factor, Sylow
788C22—21no—
789C22—21no—
790C22—21no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22C2×C5×#12011yescharacteristic
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—21no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—81no—
818C2—41no—
819C2—81no—
820C2—81no—
821C2—161no—
822C2C5×#301811yescharacteristic
823C2C5×#302011yescharacteristic
824C2C5×#302111yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
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
1. C5×#3531C2semidirect
2. C5×#3235C2semidirect
3. C5×#3219C2semidirect
4. C5×#3180C2semidirect
5. C5×#1664C2semidirect
6. C5×#1663C2semidirect
7. C5×#1661C2semidirect
8. C5×#1660C2semidirect
9. C5×#1658C2semidirect
10. C5×#1657C2semidirect
11. C5×#1657C2semidirect
12. C5×#1656C2semidirect
13. C5×#1535C2semidirect
14. C5×#1532C2semidirect
15. C5×#1531C2semidirect
75. #19012C5direct (N × H)
207. #3531C2×C5semidirect
208. #3235C2×C5semidirect
209. #3219C2×C5semidirect
210. #3180C2×C5semidirect
211. #1664C2×C5semidirect
212. #1663C2×C5semidirect
213. #1661C2×C5semidirect
214. #1660C2×C5semidirect
215. #1658C2×C5semidirect
216. #1657C2×C5semidirect
217. #1657C2×C5semidirect
218. #1656C2×C5semidirect
219. #1535C2×C5semidirect
220. #1532C2×C5semidirect
221. #1531C2×C5semidirect
787. C5#19012direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35312
C5×#32352
C5×#32192
C5×#31802
C5×#16642
C5×#16632
C5×#16612
C5×#16602
C5×#16582
C5×#16572
C5×#16562
C5×#15352
C5×#15322
C5×#15312
#190125