Finite Group Databasebeta

← C5×#18281 #11941001

Subgroups — C5×#18281 #11941001

Order 1280.

946 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3560C211yesmaximal, characteristic
2C5×#3117C211yesmaximal, characteristic, complemented
3C5×#3103C211yesmaximal, characteristic, complemented
4C5×#2604C211yesmaximal, characteristic, complemented
5C5×#1618C211yesmaximal, characteristic, complemented
6C5×#1616C211yesmaximal, characteristic, complemented
7C5×#1615C211yesmaximal, characteristic, complemented
8C5×#1613C211yesmaximal, characteristic, complemented
9C5×#1606C211yesmaximal, characteristic, complemented
10C5×#1604C211yesmaximal, characteristic, complemented
11C5×#1603C211yesmaximal, characteristic, complemented
12C5×#1601C211yesmaximal, characteristic, complemented
13C5×#1505C211yesmaximal, characteristic, complemented
14C5×#1500C211yesmaximal, characteristic, complemented
15C5×#1473C211yesmaximal, characteristic, complemented
16C5×#563—21no—
17C5×#560—21no—
18C5×#553—21no—
19C5×#553—21no—
20C5×#551—21no—
21C5×#547—21no—
22C5×#546—21no—
23C5×#546—21no—
24C5×#542—21no—
25C5×#539—21no—
26C5×#539C2211yescharacteristic
27C5×#538—21no—
28C5×#538—21no—
29C5×#538C2211yescharacteristic
30C5×#537C2211yescharacteristic
31C5×#534C2211yescharacteristic
32C5×#532C2211yescharacteristic
33C5×#529C2211yescharacteristic
34C2×C5×#126C2211yescharacteristic
35C2×C4×C5×Q8C2211yescharacteristic, complemented
36C5×#484C2211yescharacteristic, complemented
37C5×#481C2211yescharacteristic
38C5×#481C2211yescharacteristic
39C5×#481C2211yescharacteristic, complemented
40C5×#479—21no—
41C5×#475—21no—
42C5×#464—21no—
43C5×#460—21no—
44C5×#451C2211yescharacteristic, complemented
45C5×#448C2211yescharacteristic
46C5×#448C2211yescharacteristic
47C5×#448C2211yescharacteristic, complemented
48C5×#441—21no—
49C5×#440—21no—
50C4×C5×SD16—21no—
51C4×C5×SD16—21no—
52C5×#432C2211yescharacteristic, complemented
53C5×#431C2211yescharacteristic, complemented
54C5×#400C2211yescharacteristic, complemented
55C5×#399C2211yescharacteristic
56C5×#395C2211yescharacteristic, complemented
57C5×#393C2211yescharacteristic
58C5×#389—21no—
59C5×#388—21no—
60C5×#388—21no—
61C5×#387—21no—
62C5×#376C2211yescharacteristic, complemented
63C5×#328C2211yescharacteristic, complemented
64C5×#328C2211yescharacteristic, complemented
65C5×#327C2211yescharacteristic
66C5×#327C2211yescharacteristic
67C5×#327C2211yescharacteristic
68C5×#327C2211yescharacteristic
69C5×#327C2211yescharacteristic, complemented
70C5×#327C2211yescharacteristic, complemented
71C5×#324C2211yescharacteristic, complemented
72C5×#324C2211yescharacteristic, complemented
73C5×#323C2211yescharacteristic
74C5×#323C2211yescharacteristic
75#18281C511yesmaximal, characteristic, direct product factor, Sylow
76C2×C5×#41—21no—
77C2×C5×#41—21no—
78C22×C5×Q8C2311yescharacteristic
79C22×C5×D4—21no—
80C2×C5×Q16—21no—
81C2×C5×SD16—21no—
82C2×C5×SD16—21no—
83C2×C5×SD16—21no—
84C5×C4⋊Q8—21no—
85C5×C4⋊Q8D411yescharacteristic
86C5×#127D411yescharacteristic
87C5×#126—21no—
88C5×#126—21no—
89C5×#126—21no—
90C5×#126—21no—
91C5×#126—21no—
92C5×#126—21no—
93C5×#126—21no—
94C5×#126—21no—
95C5×#126—21no—
96C5×#125—21no—
97C5×#125—21no—
98C5×#125D411yescharacteristic
99C5×#124—21no—
100C5×#124—21no—
101C5×#124—21no—
102C5×#124—21no—
103C5×#124D411yescharacteristic
104C5×#123—21no—
105C5×#123—21no—
106C5×#123—21no—
107C5×#123—21no—
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×C22⋊Q8—21no—
117C5×C22⋊Q8—21no—
118C5×C22⋊Q8—21no—
119C5×C22⋊Q8—21no—
120C5×C22⋊Q8—21no—
121C5×C22⋊Q8—21no—
122C5×C22⋊Q8—21no—
123C5×C22⋊Q8C2311yescharacteristic
124C5×#121—21no—
125C5×#121—21no—
126C5×#121—21no—
127C5×#121—21no—
128C5×#121—21no—
129C5×#121—21no—
130C5×#121—21no—
131C5×#121—21no—
132C5×#121—21no—
133C5×#121—21no—
134C5×#121—21no—
135C5×#121—21no—
136C5×#121C2311yescharacteristic
137C5×#121C2311yescharacteristic
138C5×#121C2311yescharacteristic
139C5×#120—21no—
140C5×#120—21no—
141C5×#120—21no—
142C5×#120—21no—
143C5×#120—21no—
144C4×C5×Q8—21no—
145C4×C5×Q8—21no—
146C4×C5×Q8—21no—
147C4×C5×Q8—21no—
148C4×C5×Q8D411yescharacteristic
149C4×C5×D4—21no—
150C4×C5×D4—21no—
151C4×C5×D4—21no—
152C4×C5×D4—21no—
153C4×C5×D4—21no—
154C4×C5×D4—21no—
155C4×C5×D4—21no—
156C4×C5×D4—21no—
157C4×C5×D4D411yescharacteristic
158C4×C5×D4D411yescharacteristic
159C4×C5×D4D411yescharacteristic
160C5×#117—21no—
161C5×#117—21no—
162C2×C5×C4⋊C4—21no—
163C2×C5×C4⋊C4—21no—
164C2×C5×C4⋊C4—21no—
165C2×C5×C4⋊C4—21no—
166C2×C5×C4⋊C4D411yescharacteristic
167C2×C5×C4⋊C4D411yescharacteristic
168C2×C5×C4⋊C4C2311yescharacteristic
169C2×C5×C4⋊C4C2311yescharacteristic
170C2×C5×C22⋊C4—21no—
171C2×C5×C22⋊C4—21no—
172C2×C5×C22⋊C4—21no—
173C2×C5×C22⋊C4—21no—
174C2×C5×C22⋊C4D411yescharacteristic
175C2×C5×C22⋊C4D411yescharacteristic
176C2×C5×C22⋊C4C2311yescharacteristic
177C2×C42×C5—21no—
178C2×C42×C5—21no—
179C2×C42×C5C2311yescharacteristic
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×#103—21no—
190C5×#103—21no—
191C5×#102—21no—
192C5×#102—21no—
193C5×#102—21no—
194C5×C22⋊C8C2311yescharacteristic
195C5×C22⋊C8C2311yescharacteristic
196C5×C22⋊C8C2311yescharacteristic
197C5×C22⋊C8C2311yescharacteristic
198C5×#97—21no—
199C4×C5×C8—21no—
200C5×#95—21no—
201C5×#95—21no—
202C5×#95—21no—
203C5×#95—21no—
204C5×#95—21no—
205C5×#95C2311yescharacteristic
206C5×#95C2311yescharacteristic
207#3560C2×C511yescharacteristic
208#3117C2×C511yescharacteristic, complemented
209#3103C2×C511yescharacteristic, complemented
210#2604C2×C511yescharacteristic, complemented
211#1618C2×C511yescharacteristic, complemented
212#1616C2×C511yescharacteristic, complemented
213#1615C2×C511yescharacteristic, complemented
214#1613C2×C511yescharacteristic, complemented
215#1606C2×C511yescharacteristic, complemented
216#1604C2×C511yescharacteristic, complemented
217#1603C2×C511yescharacteristic, complemented
218#1601C2×C511yescharacteristic, complemented
219#1505C2×C511yescharacteristic, complemented
220#1500C2×C511yescharacteristic, complemented
221#1473C2×C511yescharacteristic, complemented
222C24×C5—21no—
223C24×C5C2×D411yescharacteristic
224C5×#41—81no—
225C5×#41—81no—
226C5×#41—81no—
227C5×#41—81no—
228C2×C5×Q8—21no—
229C2×C5×Q8—21no—
230C2×C5×Q8—21no—
231C2×C5×Q8—21no—
232C2×C5×Q8—42no—
233C2×C5×Q8C2×D411yescharacteristic
234C2×C5×D4—21no—
235C2×C5×D4—21no—
236C2×C5×D4—21no—
237C2×C5×D4—21no—
238C2×C5×D4—21no—
239C2×C5×D4—21no—
240C2×C5×D4—21no—
241C2×C5×D4—21no—
242C2×C5×D4—21no—
243C2×C5×D4—21no—
244C2×C5×D4—21no—
245C2×C5×D4—21no—
246C2×C5×D4—81no—
247C2×C5×D4—81no—
248C2×C5×D4C2×D411yescharacteristic
249C2×C5×D4C2×D411yescharacteristic
250C2×C5×D4C2×D411yescharacteristic
251C22×C4×C5—21no—
252C22×C4×C5—21no—
253C22×C4×C5—21no—
254C22×C4×C5—21no—
255C22×C4×C5—21no—
256C22×C4×C5—21no—
257C22×C4×C5—21no—
258C22×C4×C5—21no—
259C22×C4×C5—21no—
260C22×C4×C5—21no—
261C22×C4×C5—21no—
262C22×C4×C5—21no—
263C22×C4×C5C2×D411yescharacteristic
264C22×C4×C5C2×D411yescharacteristic
265C22×C4×C5C2×D411yescharacteristic
266C22×C4×C5C2×D411yescharacteristic
267C22×C4×C5C2×D411yescharacteristic
268C22×C4×C5C2411yescharacteristic
269C5×Q16—42no—
270C5×SD16—42no—
271C5×SD16—42no—
272C5×SD16—42no—
273C2×C5×C8—21no—
274C2×C5×C8—21no—
275C2×C5×C8—21no—
276C2×C5×C8—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⋊C4—21no—
293C5×C4⋊C4—21no—
294C5×C4⋊C4—21no—
295C5×C4⋊C4—21no—
296C5×C4⋊C4—42no—
297C5×C4⋊C4—42no—
298C5×C4⋊C4—41no—
299C5×C4⋊C4—41no—
300C5×C4⋊C4C2×D411yescharacteristic
301C5×C4⋊C4C2×D411yescharacteristic
302C5×C4⋊C4C2×D411yescharacteristic
303C5×C4⋊C4C2×D411yescharacteristic
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—21no—
321C5×C22⋊C4—21no—
322C5×C22⋊C4—21no—
323C5×C22⋊C4—21no—
324C5×C22⋊C4—21no—
325C5×C22⋊C4—21no—
326C5×C22⋊C4—21no—
327C5×C22⋊C4—21no—
328C5×C22⋊C4—21no—
329C5×C22⋊C4—42no—
330C5×C22⋊C4—42no—
331C42×C5—21no—
332C42×C5—21no—
333C42×C5—21no—
334C42×C5—42no—
335C42×C5—41no—
336C42×C5—41no—
337C42×C5C2×D411yescharacteristic
338C42×C5C2×D411yescharacteristic
339C42×C5C2×D411yescharacteristic
340C42×C5C2×D411yescharacteristic
341#563—21no—
342#560—21no—
343#553—21no—
344#553—21no—
345#551—21no—
346#547—21no—
347#546—21no—
348#546—21no—
349#542—21no—
350#539—21no—
351#539C22×C511yescharacteristic
352#538—21no—
353#538—21no—
354#538C22×C511yescharacteristic
355#537C22×C511yescharacteristic
356#534C22×C511yescharacteristic
357#532C22×C511yescharacteristic
358#529C22×C511yescharacteristic
359C2×#126C22×C511yescharacteristic
360C2×C4×Q8C22×C511yescharacteristic, complemented
361#484C22×C511yescharacteristic, complemented
362#481C22×C511yescharacteristic
363#481C22×C511yescharacteristic
364#481C22×C511yescharacteristic, complemented
365#479—21no—
366#475—21no—
367#464—21no—
368#460—21no—
369#451C22×C511yescharacteristic, complemented
370#448C22×C511yescharacteristic
371#448C22×C511yescharacteristic
372#448C22×C511yescharacteristic, complemented
373#441—21no—
374#440—21no—
375C4×SD16—21no—
376C4×SD16—21no—
377#432C22×C511yescharacteristic, complemented
378#431C22×C511yescharacteristic, complemented
379#400C22×C511yescharacteristic, complemented
380#399C22×C511yescharacteristic
381#395C22×C511yescharacteristic, complemented
382#393C22×C511yescharacteristic
383#389—21no—
384#388—21no—
385#388—21no—
386#387—21no—
387#376C22×C511yescharacteristic, complemented
388#328C22×C511yescharacteristic, complemented
389#328C22×C511yescharacteristic, complemented
390#327C22×C511yescharacteristic
391#327C22×C511yescharacteristic
392#327C22×C511yescharacteristic
393#327C22×C511yescharacteristic
394#327C22×C511yescharacteristic, complemented
395#327C22×C511yescharacteristic, complemented
396#324C22×C511yescharacteristic, complemented
397#324C22×C511yescharacteristic, complemented
398#323C22×C511yescharacteristic
399#323C22×C511yescharacteristic
400C23×C5—21no—
401C23×C5—21no—
402C23×C5—21no—
403C23×C5—21no—
404C23×C5—21no—
405C23×C5—21no—
406C23×C5—41no—
407C23×C5—41no—
408C23×C5—81no—
409C23×C5—81no—
410C23×C5—81no—
411C23×C5C22×D411yescharacteristic
412C5×Q8—22no—
413C5×Q8—22no—
414C5×Q8—41no—
415C5×Q8—41no—
416C5×Q8—41no—
417C5×Q8—81no—
418C5×Q8—81no—
419C5×D4—41no—
420C5×D4—41no—
421C5×D4—41no—
422C5×D4—41no—
423C5×D4—41no—
424C5×D4—41no—
425C5×D4—41no—
426C5×D4—41no—
427C5×D4—41no—
428C5×D4—81no—
429C5×D4—81no—
430C5×D4—81no—
431C5×D4—81no—
432C5×D4—81no—
433C5×D4—81no—
434C5×D4—81no—
435C5×D4—81no—
436C5×D4—81no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—22no—
440C2×C4×C5—22no—
441C2×C4×C5—21no—
442C2×C4×C5—21no—
443C2×C4×C5—21no—
444C2×C4×C5—21no—
445C2×C4×C5—21no—
446C2×C4×C5—21no—
447C2×C4×C5—21no—
448C2×C4×C5—21no—
449C2×C4×C5—21no—
450C2×C4×C5—21no—
451C2×C4×C5—41no—
452C2×C4×C5—41no—
453C2×C4×C5—41no—
454C2×C4×C5—41no—
455C2×C4×C5—41no—
456C2×C4×C5—41no—
457C2×C4×C5—41no—
458C2×C4×C5—41no—
459C2×C4×C5—41no—
460C2×C4×C5—41no—
461C2×C4×C5—41no—
462C2×C4×C5—41no—
463C2×C4×C5—41no—
464C2×C4×C5—41no—
465C2×C4×C5—81no—
466C2×C4×C5—81no—
467C2×C4×C5—81no—
468C2×C4×C5—81no—
469C2×C4×C5—81no—
470C2×C4×C5—81no—
471C2×C4×C5—81no—
472C2×C4×C5—81no—
473C2×C4×C5#12011yescharacteristic
474C2×C4×C5#12011yescharacteristic
475C2×C4×C5#12011yescharacteristic
476C2×C4×C5#12011yescharacteristic
477C2×C4×C5C22×D411yescharacteristic
478C2×C4×C5C22×D411yescharacteristic
479C5×C8—41no—
480C5×C8—41no—
481C5×C8—41no—
482C5×C8—41no—
483C2×#41—21no—
484C2×#41—21no—
485C22×Q8C23×C511yescharacteristic
486C22×D4—21no—
487C2×Q16—21no—
488C2×SD16—21no—
489C2×SD16—21no—
490C2×SD16—21no—
491C4⋊Q8—21no—
492C4⋊Q8C5×D411yescharacteristic
493#127C5×D411yescharacteristic
494#126—21no—
495#126—21no—
496#126—21no—
497#126—21no—
498#126—21no—
499#126—21no—
500#126—21no—
501#126—21no—
502#126—21no—
503#125—21no—
504#125—21no—
505#125C5×D411yescharacteristic
506#124—21no—
507#124—21no—
508#124—21no—
509#124—21no—
510#124C5×D411yescharacteristic
511#123—21no—
512#123—21no—
513#123—21no—
514#123—21no—
515#123—21no—
516#123—21no—
517#123—21no—
518#123—21no—
519#123—21no—
520#123—21no—
521#123—21no—
522#123—21no—
523C22⋊Q8—21no—
524C22⋊Q8—21no—
525C22⋊Q8—21no—
526C22⋊Q8—21no—
527C22⋊Q8—21no—
528C22⋊Q8—21no—
529C22⋊Q8—21no—
530C22⋊Q8C23×C511yescharacteristic
531#121—21no—
532#121—21no—
533#121—21no—
534#121—21no—
535#121—21no—
536#121—21no—
537#121—21no—
538#121—21no—
539#121—21no—
540#121—21no—
541#121—21no—
542#121—21no—
543#121C23×C511yescharacteristic
544#121C23×C511yescharacteristic
545#121C23×C511yescharacteristic
546#120—21no—
547#120—21no—
548#120—21no—
549#120—21no—
550#120—21no—
551C4×Q8—21no—
552C4×Q8—21no—
553C4×Q8—21no—
554C4×Q8—21no—
555C4×Q8C5×D411yescharacteristic
556C4×D4—21no—
557C4×D4—21no—
558C4×D4—21no—
559C4×D4—21no—
560C4×D4—21no—
561C4×D4—21no—
562C4×D4—21no—
563C4×D4—21no—
564C4×D4C5×D411yescharacteristic
565C4×D4C5×D411yescharacteristic
566C4×D4C5×D411yescharacteristic
567#117—21no—
568#117—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4C5×D411yescharacteristic
574C2×C4⋊C4C5×D411yescharacteristic
575C2×C4⋊C4C23×C511yescharacteristic
576C2×C4⋊C4C23×C511yescharacteristic
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4C5×D411yescharacteristic
582C2×C22⋊C4C5×D411yescharacteristic
583C2×C22⋊C4C23×C511yescharacteristic
584C2×C42—21no—
585C2×C42—21no—
586C2×C42C23×C511yescharacteristic
587#107—21no—
588#106—21no—
589#106—21no—
590#106—21no—
591C4⋊C8—21no—
592C4⋊C8—21no—
593#103—21no—
594#103—21no—
595#103—21no—
596#103—21no—
597#103—21no—
598#102—21no—
599#102—21no—
600#102—21no—
601C22⋊C8C23×C511yescharacteristic
602C22⋊C8C23×C511yescharacteristic
603C22⋊C8C23×C511yescharacteristic
604C22⋊C8C23×C511yescharacteristic
605#97—21no—
606C4×C8—21no—
607#95—21no—
608#95—21no—
609#95—21no—
610#95—21no—
611#95—21no—
612#95C23×C511yescharacteristic
613#95C23×C511yescharacteristic
614C22×C5—21no—
615C22×C5—21no—
616C22×C5—41no—
617C22×C5—41no—
618C22×C5—41no—
619C22×C5—41no—
620C22×C5—41no—
621C22×C5—41no—
622C22×C5—41no—
623C22×C5—41no—
624C22×C5—41no—
625C22×C5—41no—
626C22×C5—41no—
627C22×C5—41no—
628C22×C5—81no—
629C22×C5—81no—
630C22×C5—162no—
631C22×C5C2×#12011yescharacteristic
632C22×C5#57711yescharacteristic
633C22×C5#57711yescharacteristic
634C4×C5—21no—
635C4×C5—21no—
636C4×C5—21no—
637C4×C5—21no—
638C4×C5—21no—
639C4×C5—21no—
640C4×C5—42no—
641C4×C5—41no—
642C4×C5—41no—
643C4×C5—41no—
644C4×C5—41no—
645C4×C5—41no—
646C4×C5—41no—
647C4×C5—42no—
648C4×C5—41no—
649C4×C5—41no—
650C4×C5—81no—
651C4×C5—81no—
652C24—21no—
653C24C2×C5×D411yescharacteristic
654#41—81no—
655#41—81no—
656#41—81no—
657#41—81no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—42no—
663C2×Q8C2×C5×D411yescharacteristic
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—81no—
677C2×D4—81no—
678C2×D4C2×C5×D411yescharacteristic
679C2×D4C2×C5×D411yescharacteristic
680C2×D4C2×C5×D411yescharacteristic
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—21no—
692C22×C4—21no—
693C22×C4C2×C5×D411yescharacteristic
694C22×C4C2×C5×D411yescharacteristic
695C22×C4C2×C5×D411yescharacteristic
696C22×C4C2×C5×D411yescharacteristic
697C22×C4C2×C5×D411yescharacteristic
698C22×C4C24×C511yescharacteristic
699Q16—42no—
700SD16—42no—
701SD16—42no—
702SD16—42no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—41no—
729C4⋊C4—41no—
730C4⋊C4C2×C5×D411yescharacteristic
731C4⋊C4C2×C5×D411yescharacteristic
732C4⋊C4C2×C5×D411yescharacteristic
733C4⋊C4C2×C5×D411yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—42no—
760C22⋊C4—42no—
761C42—21no—
762C42—21no—
763C42—21no—
764C42—42no—
765C42—41no—
766C42—41no—
767C42C2×C5×D411yescharacteristic
768C42C2×C5×D411yescharacteristic
769C42C2×C5×D411yescharacteristic
770C42C2×C5×D411yescharacteristic
771C2×C5—21no—
772C2×C5—21no—
773C2×C5—81no—
774C2×C5—81no—
775C2×C5—81no—
776C2×C5—81no—
777C2×C5#300911yescharacteristic
778C2×C5#301811yescharacteristic
779C2×C5#302511yescharacteristic
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—41no—
787C23—41no—
788C23—81no—
789C23—81no—
790C23—81no—
791C23C22×C5×D411yescharacteristic
792Q8—22no—
793Q8—22no—
794Q8—41no—
795Q8—41no—
796Q8—41no—
797Q8—81no—
798Q8—81no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—41no—
803D4—41no—
804D4—41no—
805D4—41no—
806D4—41no—
807D4—41no—
808D4—81no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—81no—
813D4—81no—
814D4—81no—
815D4—81no—
816D4—81no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—81no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4—81no—
851C2×C4—81no—
852C2×C4—81no—
853C2×C4C5×#12011yescharacteristic
854C2×C4C5×#12011yescharacteristic
855C2×C4C5×#12011yescharacteristic
856C2×C4C5×#12011yescharacteristic
857C2×C4C22×C5×D411yescharacteristic
858C2×C4C22×C5×D411yescharacteristic
859C8—41no—
860C8—41no—
861C8—41no—
862C8—41no—
863C5#1828111yescharacteristic, direct product factor, Sylow
864C22—21no—
865C22—21no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—81no—
879C22—81no—
880C22—162no—
881C22C2×C5×#12011yescharacteristic
882C22C5×#57711yescharacteristic
883C22C5×#57711yescharacteristic
884C4—21no—
885C4—21no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—21no—
890C4—42no—
891C4—41no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—41no—
897C4—42no—
898C4—41no—
899C4—41no—
900C4—81no—
901C4—81no—
902C2—21no—
903C2—21no—
904C2—81no—
905C2—81no—
906C2—81no—
907C2—81no—
908C2C5×#300911yescharacteristic
909C2C5×#301811yescharacteristic
910C2C5×#302511yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3560C2
LCSG ▷ C22×C4 ▷ 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×#3117C2semidirect
3. C5×#3103C2semidirect
4. C5×#2604C2semidirect
5. C5×#1618C2semidirect
6. C5×#1616C2semidirect
7. C5×#1615C2semidirect
8. C5×#1613C2semidirect
9. C5×#1606C2semidirect
10. C5×#1604C2semidirect
11. C5×#1603C2semidirect
12. C5×#1601C2semidirect
13. C5×#1505C2semidirect
14. C5×#1500C2semidirect
15. C5×#1473C2semidirect
35. C2×C4×C5×Q8C22semidirect
36. C5×#484C22semidirect
39. C5×#481C22semidirect
44. C5×#451C22semidirect
47. C5×#448C22semidirect
52. C5×#432C22semidirect
53. C5×#431C22semidirect
54. C5×#400C22semidirect
56. C5×#395C22semidirect
62. C5×#376C22semidirect
63. C5×#328C22semidirect
64. C5×#328C22semidirect
69. C5×#327C22semidirect
70. C5×#327C22semidirect
71. C5×#324C22semidirect
72. C5×#324C22semidirect
75. #18281C5direct (N × H)
208. #3117C2×C5semidirect
209. #3103C2×C5semidirect
210. #2604C2×C5semidirect
211. #1618C2×C5semidirect
212. #1616C2×C5semidirect
213. #1615C2×C5semidirect
214. #1613C2×C5semidirect
215. #1606C2×C5semidirect
216. #1604C2×C5semidirect
217. #1603C2×C5semidirect
218. #1601C2×C5semidirect
219. #1505C2×C5semidirect
220. #1500C2×C5semidirect
221. #1473C2×C5semidirect
360. C2×C4×Q8C22×C5semidirect
361. #484C22×C5semidirect
364. #481C22×C5semidirect
369. #451C22×C5semidirect
372. #448C22×C5semidirect
377. #432C22×C5semidirect
378. #431C22×C5semidirect
379. #400C22×C5semidirect
381. #395C22×C5semidirect
387. #376C22×C5semidirect
388. #328C22×C5semidirect
389. #328C22×C5semidirect
394. #327C22×C5semidirect
395. #327C22×C5semidirect
396. #324C22×C5semidirect
397. #324C22×C5semidirect
863. C5#18281direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35602
C5×#31172
C5×#31032
C5×#26042
C5×#16182
C5×#16162
C5×#16152
C5×#16132
C5×#16062
C5×#16042
C5×#16032
C5×#16012
C5×#15052
C5×#15002
C5×#14732
#182815