Finite Group Databasebeta

← C5×#18414 #11941134

Subgroups — C5×#18414 #11941134

Order 1280.

1042 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3534C211yesmaximal, characteristic, complemented
2C5×#3194C211yesmaximal, characteristic, complemented
3C5×#3186C211yesmaximal, characteristic, complemented
4C5×#2661C211yesmaximal, characteristic, complemented
5C5×#1612C211yesmaximal, characteristic, complemented
6C5×#1610C211yesmaximal, characteristic, complemented
7C5×#1609C211yesmaximal, characteristic, complemented
8C5×#1607C211yesmaximal, characteristic, complemented
9C5×#1600C211yesmaximal, characteristic, complemented
10C5×#1598C211yesmaximal, characteristic, complemented
11C5×#1597C211yesmaximal, characteristic, complemented
12C5×#1595C211yesmaximal, characteristic, complemented
13C5×#1507C211yesmaximal, characteristic, complemented
14C5×#1501C211yesmaximal, characteristic, complemented
15C5×#1468C211yesmaximal, characteristic, complemented
16C5×#562—21no—
17C5×#560—21no—
18C5×#553—21no—
19C5×#551—21no—
20C5×#546—21no—
21C5×#546—21no—
22C5×#546—21no—
23C5×D42—21no—
24C5×#540—21no—
25C5×#539—21no—
26C5×#539C2211yescharacteristic
27C5×#538—21no—
28C5×#538C2211yescharacteristic
29C5×#537C2211yescharacteristic
30C5×#534—21no—
31C5×#534C2211yescharacteristic
32C5×#525C2211yescharacteristic
33C2×C5×#123C2211yescharacteristic
34C2×C5×#121C2211yescharacteristic
35C2×C5×#121C2211yescharacteristic, complemented
36C5×#483C2211yescharacteristic, complemented
37C5×#482—21no—
38C5×#480—21no—
39C5×#480C2211yescharacteristic
40C5×#480C2211yescharacteristic, complemented
41C5×#480C2211yescharacteristic, complemented
42C5×#469—21no—
43C5×#468—21no—
44C5×#466—21no—
45C5×#466—21no—
46C5×#450C2211yescharacteristic, complemented
47C5×#449—21no—
48C5×#447—21no—
49C5×#447C2211yescharacteristic
50C5×#447C2211yescharacteristic, complemented
51C5×#447C2211yescharacteristic, complemented
52C5×#407C2211yescharacteristic, complemented
53C2×C5×C22⋊C8C2211yescharacteristic, complemented
54C5×#398C2211yescharacteristic, complemented
55C5×#397C2211yescharacteristic, complemented
56C5×#394—21no—
57C5×#394C2211yescharacteristic, complemented
58C5×#392—21no—
59C5×#392C2211yescharacteristic, complemented
60C5×#390—21no—
61C5×#388—21no—
62C4×C5×C22⋊C4C2211yescharacteristic, complemented
63C5×#328C2211yescharacteristic, complemented
64C5×#328C2211yescharacteristic, complemented
65C5×#327C2211yescharacteristic
66C5×#327C2211yescharacteristic
67C5×#327C2211yescharacteristic, complemented
68C5×#327C2211yescharacteristic, complemented
69C5×#327C2211yescharacteristic, complemented
70C5×#327C2211yescharacteristic, complemented
71C5×#324C2211yescharacteristic, complemented
72C5×#324C2211yescharacteristic, complemented
73C5×#323C2211yescharacteristic, complemented
74C5×#323C2211yescharacteristic, complemented
75#18414C511yesmaximal, characteristic, direct product factor, Sylow
76C2×C5×#41—21no—
77C2×C5×#41D411yescharacteristic, complemented
78C22×C5×D4—21no—
79C22×C5×D4—21no—
80C22×C5×D4—21no—
81C22×C5×D4—21no—
82C22×C5×D4—21no—
83C22×C5×D4D411yescharacteristic
84C22×C5×D4D411yescharacteristic, complemented
85C22×C5×D4C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C2×C5×SD16—21no—
88C2×C5×D8—21no—
89C2×C5×D8—21no—
90C2×C5×D8—21no—
91C2×C5×M16—21no—
92C22×C5×C8—21no—
93C5×#127—21no—
94C5×#126—21no—
95C5×#126—21no—
96C5×#126—21no—
97C5×#126—21no—
98C5×#125—21no—
99C5×#125—21no—
100C5×#124—21no—
101C5×#124—21no—
102C5×#124—21no—
103C5×#123—21no—
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×#123—21no—
117C5×C22⋊Q8—21no—
118C5×C22⋊Q8—21no—
119C5×C22⋊Q8—21no—
120C5×C22⋊Q8—21no—
121C5×C22⋊Q8—21no—
122C5×C22⋊Q8D411yescharacteristic, complemented
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×#121—21no—
137C5×#121—21no—
138C5×#121—21no—
139C5×#121—21no—
140C5×#121—21no—
141C5×#121—21no—
142C5×#121—21no—
143C5×#121D411yescharacteristic, complemented
144C5×#121D411yescharacteristic, complemented
145C5×#121D411yescharacteristic, complemented
146C5×#121C2311yescharacteristic
147C5×#121C2311yescharacteristic
148C5×#121C2311yescharacteristic
149C5×#120—21no—
150C5×#120—21no—
151C5×#120—21no—
152C5×#120—21no—
153C5×#120—21no—
154C5×#120—21no—
155C5×#120—21no—
156C5×#120—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×D4—21no—
164C4×C5×D4—21no—
165C5×#117—21no—
166C5×#117D411yescharacteristic, complemented
167C2×C5×C4⋊C4—21no—
168C2×C5×C4⋊C4D411yescharacteristic
169C2×C5×C4⋊C4D411yescharacteristic, complemented
170C2×C5×C4⋊C4C2311yescharacteristic
171C2×C5×C4⋊C4C2311yescharacteristic
172C2×C5×C22⋊C4—21no—
173C2×C5×C22⋊C4—21no—
174C2×C5×C22⋊C4—21no—
175C2×C5×C22⋊C4—21no—
176C2×C5×C22⋊C4—21no—
177C2×C5×C22⋊C4—21no—
178C2×C5×C22⋊C4—21no—
179C2×C5×C22⋊C4—21no—
180C2×C5×C22⋊C4—21no—
181C2×C5×C22⋊C4D411yescharacteristic
182C2×C5×C22⋊C4D411yescharacteristic
183C2×C5×C22⋊C4C2311yescharacteristic
184C2×C42×C5—21no—
185C5×#107—21no—
186C5×#107—21no—
187C5×#107—21no—
188C5×#106—21no—
189C5×#103—21no—
190C5×#102—21no—
191C5×#102—21no—
192C5×#102—21no—
193C5×#102—21no—
194C5×#102—21no—
195C5×#102—21no—
196C5×#102—21no—
197C5×C22⋊C8—21no—
198C5×C22⋊C8—21no—
199C5×C22⋊C8C2311yescharacteristic
200C5×C22⋊C8C2311yescharacteristic
201C5×C22⋊C8C2311yescharacteristic
202C5×C22⋊C8C2311yescharacteristic
203C5×#95—21no—
204C5×#95—21no—
205C5×#95C2311yescharacteristic
206C5×#95C2311yescharacteristic
207#3534C2×C511yescharacteristic, complemented
208#3194C2×C511yescharacteristic, complemented
209#3186C2×C511yescharacteristic, complemented
210#2661C2×C511yescharacteristic, complemented
211#1612C2×C511yescharacteristic, complemented
212#1610C2×C511yescharacteristic, complemented
213#1609C2×C511yescharacteristic, complemented
214#1607C2×C511yescharacteristic, complemented
215#1600C2×C511yescharacteristic, complemented
216#1598C2×C511yescharacteristic, complemented
217#1597C2×C511yescharacteristic, complemented
218#1595C2×C511yescharacteristic, complemented
219#1507C2×C511yescharacteristic, complemented
220#1501C2×C511yescharacteristic, complemented
221#1468C2×C511yescharacteristic, complemented
222C24×C5—21no—
223C24×C5—21no—
224C24×C5—21no—
225C24×C5C2×D411yescharacteristic
226C24×C5C2×D411yescharacteristic
227C5×#41—81no—
228C5×#41—81no—
229C5×#41—81no—
230C2×C5×Q8—21no—
231C2×C5×Q8C2×D411yescharacteristic
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—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—21no—
247C2×C5×D4—21no—
248C2×C5×D4—21no—
249C2×C5×D4—21no—
250C2×C5×D4—21no—
251C2×C5×D4—42no—
252C2×C5×D4—41no—
253C2×C5×D4—41no—
254C2×C5×D4—81no—
255C2×C5×D4—81no—
256C2×C5×D4—81no—
257C2×C5×D4—81no—
258C2×C5×D4—81no—
259C2×C5×D4—81no—
260C2×C5×D4—81no—
261C2×C5×D4—81no—
262C2×C5×D4—81no—
263C2×C5×D4—81no—
264C2×C5×D4—81no—
265C2×C5×D4—82no—
266C2×C5×D4C2×D411yescharacteristic
267C2×C5×D4C2×D411yescharacteristic
268C2×C5×D4C2×D411yescharacteristic
269C22×C4×C5—21no—
270C22×C4×C5—21no—
271C22×C4×C5—21no—
272C22×C4×C5—21no—
273C22×C4×C5—21no—
274C22×C4×C5—21no—
275C22×C4×C5—21no—
276C22×C4×C5—21no—
277C22×C4×C5—21no—
278C22×C4×C5—21no—
279C22×C4×C5—81no—
280C22×C4×C5C2×D411yescharacteristic
281C22×C4×C5C2×D411yescharacteristic
282C22×C4×C5C2×D411yescharacteristic
283C22×C4×C5C2×D411yescharacteristic
284C22×C4×C5C2×D411yescharacteristic
285C22×C4×C5C2×D411yescharacteristic
286C22×C4×C5C2×D411yescharacteristic
287C22×C4×C5C2×D411yescharacteristic
288C22×C4×C5C2411yescharacteristic
289C5×SD16—81no—
290C5×D8—81no—
291C5×D8—81no—
292C5×D8—81no—
293C5×M16—81no—
294C2×C5×C8—21no—
295C2×C5×C8—21no—
296C2×C5×C8—21no—
297C2×C5×C8—21no—
298C2×C5×C8—81no—
299C5×C4⋊C4—21no—
300C5×C4⋊C4—21no—
301C5×C4⋊C4—21no—
302C5×C4⋊C4—21no—
303C5×C4⋊C4—21no—
304C5×C4⋊C4—21no—
305C5×C4⋊C4—21no—
306C5×C4⋊C4—21no—
307C5×C4⋊C4—21no—
308C5×C4⋊C4—21no—
309C5×C4⋊C4—21no—
310C5×C4⋊C4—21no—
311C5×C4⋊C4—21no—
312C5×C4⋊C4—21no—
313C5×C4⋊C4—21no—
314C5×C4⋊C4—81no—
315C5×C4⋊C4C2×D411yescharacteristic
316C5×C4⋊C4C2×D411yescharacteristic
317C5×C4⋊C4C2×D411yescharacteristic
318C5×C4⋊C4C2×D411yescharacteristic
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—21no—
330C5×C22⋊C4—21no—
331C5×C22⋊C4—21no—
332C5×C22⋊C4—21no—
333C5×C22⋊C4—21no—
334C5×C22⋊C4—21no—
335C5×C22⋊C4—21no—
336C5×C22⋊C4—21no—
337C5×C22⋊C4—21no—
338C5×C22⋊C4—21no—
339C5×C22⋊C4—21no—
340C5×C22⋊C4—21no—
341C5×C22⋊C4—21no—
342C5×C22⋊C4—21no—
343C5×C22⋊C4—21no—
344C5×C22⋊C4—42no—
345C5×C22⋊C4—42no—
346C5×C22⋊C4—41no—
347C5×C22⋊C4—41no—
348C5×C22⋊C4—81no—
349C5×C22⋊C4—81no—
350C5×C22⋊C4—81no—
351C42×C5—21no—
352C42×C5—21no—
353C42×C5—21no—
354C42×C5—81no—
355#562—21no—
356#560—21no—
357#553—21no—
358#551—21no—
359#546—21no—
360#546—21no—
361#546—21no—
362D42—21no—
363#540—21no—
364#539—21no—
365#539C22×C511yescharacteristic
366#538—21no—
367#538C22×C511yescharacteristic
368#537C22×C511yescharacteristic
369#534—21no—
370#534C22×C511yescharacteristic
371#525C22×C511yescharacteristic
372C2×#123C22×C511yescharacteristic
373C2×#121C22×C511yescharacteristic
374C2×#121C22×C511yescharacteristic, complemented
375#483C22×C511yescharacteristic, complemented
376#482—21no—
377#480—21no—
378#480C22×C511yescharacteristic
379#480C22×C511yescharacteristic, complemented
380#480C22×C511yescharacteristic, complemented
381#469—21no—
382#468—21no—
383#466—21no—
384#466—21no—
385#450C22×C511yescharacteristic, complemented
386#449—21no—
387#447—21no—
388#447C22×C511yescharacteristic
389#447C22×C511yescharacteristic, complemented
390#447C22×C511yescharacteristic, complemented
391#407C22×C511yescharacteristic, complemented
392C2×C22⋊C8C22×C511yescharacteristic, complemented
393#398C22×C511yescharacteristic, complemented
394#397C22×C511yescharacteristic, complemented
395#394—21no—
396#394C22×C511yescharacteristic, complemented
397#392—21no—
398#392C22×C511yescharacteristic, complemented
399#390—21no—
400#388—21no—
401C4×C22⋊C4C22×C511yescharacteristic, complemented
402#328C22×C511yescharacteristic, complemented
403#328C22×C511yescharacteristic, complemented
404#327C22×C511yescharacteristic
405#327C22×C511yescharacteristic
406#327C22×C511yescharacteristic, complemented
407#327C22×C511yescharacteristic, complemented
408#327C22×C511yescharacteristic, complemented
409#327C22×C511yescharacteristic, complemented
410#324C22×C511yescharacteristic, complemented
411#324C22×C511yescharacteristic, complemented
412#323C22×C511yescharacteristic, complemented
413#323C22×C511yescharacteristic, complemented
414C23×C5—21no—
415C23×C5—21no—
416C23×C5—21no—
417C23×C5—21no—
418C23×C5—21no—
419C23×C5—21no—
420C23×C5—21no—
421C23×C5—21no—
422C23×C5—41no—
423C23×C5—41no—
424C23×C5—42no—
425C23×C5—41no—
426C23×C5—41no—
427C23×C5—41no—
428C23×C5—41no—
429C23×C5—41no—
430C23×C5—41no—
431C23×C5—41no—
432C23×C5—41no—
433C23×C5—41no—
434C23×C5—81no—
435C23×C5—81no—
436C23×C5—81no—
437C23×C5—81no—
438C23×C5—81no—
439C23×C5#12011yescharacteristic
440C23×C5#12011yescharacteristic
441C23×C5C22×D411yescharacteristic
442C5×Q8—41no—
443C5×Q8—81no—
444C5×D4—41no—
445C5×D4—41no—
446C5×D4—41no—
447C5×D4—41no—
448C5×D4—41no—
449C5×D4—41no—
450C5×D4—41no—
451C5×D4—42no—
452C5×D4—42no—
453C5×D4—41no—
454C5×D4—41no—
455C5×D4—41no—
456C5×D4—41no—
457C5×D4—41no—
458C5×D4—41no—
459C5×D4—81no—
460C5×D4—81no—
461C5×D4—81no—
462C5×D4—81no—
463C5×D4—81no—
464C5×D4—81no—
465C5×D4—81no—
466C5×D4—81no—
467C5×D4—81no—
468C5×D4—81no—
469C5×D4—81no—
470C5×D4—81no—
471C5×D4—84no—
472C5×D4—82no—
473C5×D4—82no—
474C2×C4×C5—22no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5—21no—
482C2×C4×C5—21no—
483C2×C4×C5—21no—
484C2×C4×C5—21no—
485C2×C4×C5—41no—
486C2×C4×C5—41no—
487C2×C4×C5—41no—
488C2×C4×C5—41no—
489C2×C4×C5—41no—
490C2×C4×C5—41no—
491C2×C4×C5—41no—
492C2×C4×C5—41no—
493C2×C4×C5—41no—
494C2×C4×C5—41no—
495C2×C4×C5—41no—
496C2×C4×C5—41no—
497C2×C4×C5—41no—
498C2×C4×C5—41no—
499C2×C4×C5—41no—
500C2×C4×C5—41no—
501C2×C4×C5—81no—
502C2×C4×C5—81no—
503C2×C4×C5—81no—
504C2×C4×C5—81no—
505C2×C4×C5—81no—
506C2×C4×C5—81no—
507C2×C4×C5—81no—
508C2×C4×C5#12011yescharacteristic
509C2×C4×C5#12011yescharacteristic
510C2×C4×C5C22×D411yescharacteristic
511C2×C4×C5C22×D411yescharacteristic
512C5×C8—41no—
513C5×C8—41no—
514C5×C8—41no—
515C5×C8—41no—
516C2×#41—21no—
517C2×#41C5×D411yescharacteristic, complemented
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4C5×D411yescharacteristic
524C22×D4C5×D411yescharacteristic, complemented
525C22×D4C23×C511yescharacteristic
526C23×C4C23×C511yescharacteristic
527C2×SD16—21no—
528C2×D8—21no—
529C2×D8—21no—
530C2×D8—21no—
531C2×M16—21no—
532C22×C8—21no—
533#127—21no—
534#126—21no—
535#126—21no—
536#126—21no—
537#126—21no—
538#125—21no—
539#125—21no—
540#124—21no—
541#124—21no—
542#124—21no—
543#123—21no—
544#123—21no—
545#123—21no—
546#123—21no—
547#123—21no—
548#123—21no—
549#123—21no—
550#123—21no—
551#123—21no—
552#123—21no—
553#123—21no—
554#123—21no—
555#123—21no—
556#123—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—21no—
562C22⋊Q8C5×D411yescharacteristic, complemented
563C22⋊Q8C23×C511yescharacteristic
564#121—21no—
565#121—21no—
566#121—21no—
567#121—21no—
568#121—21no—
569#121—21no—
570#121—21no—
571#121—21no—
572#121—21no—
573#121—21no—
574#121—21no—
575#121—21no—
576#121—21no—
577#121—21no—
578#121—21no—
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121C5×D411yescharacteristic, complemented
584#121C5×D411yescharacteristic, complemented
585#121C5×D411yescharacteristic, complemented
586#121C23×C511yescharacteristic
587#121C23×C511yescharacteristic
588#121C23×C511yescharacteristic
589#120—21no—
590#120—21no—
591#120—21no—
592#120—21no—
593#120—21no—
594#120—21no—
595#120—21no—
596#120—21no—
597C4×D4—21no—
598C4×D4—21no—
599C4×D4—21no—
600C4×D4—21no—
601C4×D4—21no—
602C4×D4—21no—
603C4×D4—21no—
604C4×D4—21no—
605#117—21no—
606#117C5×D411yescharacteristic, complemented
607C2×C4⋊C4—21no—
608C2×C4⋊C4C5×D411yescharacteristic
609C2×C4⋊C4C5×D411yescharacteristic, complemented
610C2×C4⋊C4C23×C511yescharacteristic
611C2×C4⋊C4C23×C511yescharacteristic
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4C5×D411yescharacteristic
622C2×C22⋊C4C5×D411yescharacteristic
623C2×C22⋊C4C23×C511yescharacteristic
624C2×C42—21no—
625#107—21no—
626#107—21no—
627#107—21no—
628#106—21no—
629#103—21no—
630#102—21no—
631#102—21no—
632#102—21no—
633#102—21no—
634#102—21no—
635#102—21no—
636#102—21no—
637C22⋊C8—21no—
638C22⋊C8—21no—
639C22⋊C8C23×C511yescharacteristic
640C22⋊C8C23×C511yescharacteristic
641C22⋊C8C23×C511yescharacteristic
642C22⋊C8C23×C511yescharacteristic
643#95—21no—
644#95—21no—
645#95C23×C511yescharacteristic
646#95C23×C511yescharacteristic
647C22×C5—21no—
648C22×C5—21no—
649C22×C5—21no—
650C22×C5—21no—
651C22×C5—21no—
652C22×C5—21no—
653C22×C5—21no—
654C22×C5—21no—
655C22×C5—41no—
656C22×C5—41no—
657C22×C5—41no—
658C22×C5—41no—
659C22×C5—41no—
660C22×C5—41no—
661C22×C5—41no—
662C22×C5—41no—
663C22×C5—41no—
664C22×C5—41no—
665C22×C5—41no—
666C22×C5—41no—
667C22×C5—81no—
668C22×C5—81no—
669C22×C5—81no—
670C22×C5—81no—
671C22×C5—81no—
672C22×C5—81no—
673C22×C5—81no—
674C22×C5—81no—
675C22×C5—81no—
676C22×C5—81no—
677C22×C5—81no—
678C22×C5—162no—
679C22×C5—162no—
680C22×C5C2×#12011yescharacteristic
681C22×C5#57611yescharacteristic
682C22×C5#57611yescharacteristic
683C4×C5—21no—
684C4×C5—21no—
685C4×C5—21no—
686C4×C5—21no—
687C4×C5—42no—
688C4×C5—41no—
689C4×C5—41no—
690C4×C5—41no—
691C4×C5—41no—
692C4×C5—41no—
693C4×C5—41no—
694C4×C5—41no—
695C4×C5—41no—
696C4×C5—81no—
697C4×C5—81no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24C2×C5×D411yescharacteristic
702C24C2×C5×D411yescharacteristic
703#41—81no—
704#41—81no—
705#41—81no—
706C2×Q8—21no—
707C2×Q8C2×C5×D411yescharacteristic
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—42no—
728C2×D4—41no—
729C2×D4—41no—
730C2×D4—81no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4—81no—
734C2×D4—81no—
735C2×D4—81no—
736C2×D4—81no—
737C2×D4—81no—
738C2×D4—81no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4—82no—
742C2×D4C2×C5×D411yescharacteristic
743C2×D4C2×C5×D411yescharacteristic
744C2×D4C2×C5×D411yescharacteristic
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—81no—
756C22×C4C2×C5×D411yescharacteristic
757C22×C4C2×C5×D411yescharacteristic
758C22×C4C2×C5×D411yescharacteristic
759C22×C4C2×C5×D411yescharacteristic
760C22×C4C2×C5×D411yescharacteristic
761C22×C4C2×C5×D411yescharacteristic
762C22×C4C2×C5×D411yescharacteristic
763C22×C4C2×C5×D411yescharacteristic
764C22×C4C24×C511yescharacteristic
765SD16—81no—
766D8—81no—
767D8—81no—
768D8—81no—
769M16—81no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—81no—
775C4⋊C4—21no—
776C4⋊C4—21no—
777C4⋊C4—21no—
778C4⋊C4—21no—
779C4⋊C4—21no—
780C4⋊C4—21no—
781C4⋊C4—21no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—81no—
791C4⋊C4C2×C5×D411yescharacteristic
792C4⋊C4C2×C5×D411yescharacteristic
793C4⋊C4C2×C5×D411yescharacteristic
794C4⋊C4C2×C5×D411yescharacteristic
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—41no—
823C22⋊C4—41no—
824C22⋊C4—81no—
825C22⋊C4—81no—
826C22⋊C4—81no—
827C42—21no—
828C42—21no—
829C42—21no—
830C42—81no—
831C2×C5—21no—
832C2×C5—21no—
833C2×C5—41no—
834C2×C5—41no—
835C2×C5—81no—
836C2×C5—81no—
837C2×C5—81no—
838C2×C5—81no—
839C2×C5—161no—
840C2×C5#300811yescharacteristic
841C2×C5#301811yescharacteristic
842C2×C5#302611yescharacteristic
843C23—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—41no—
852C23—41no—
853C23—42no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—81no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23C5×#12011yescharacteristic
869C23C5×#12011yescharacteristic
870C23C22×C5×D411yescharacteristic
871Q8—41no—
872Q8—81no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—42no—
881D4—42no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—81no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—84no—
901D4—82no—
902D4—82no—
903C2×C4—22no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—81no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4C5×#12011yescharacteristic
938C2×C4C5×#12011yescharacteristic
939C2×C4C22×C5×D411yescharacteristic
940C2×C4C22×C5×D411yescharacteristic
941C8—41no—
942C8—41no—
943C8—41no—
944C8—41no—
945C5#1841411yescharacteristic, direct product factor, Sylow
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22—162no—
978C22—162no—
979C22C2×C5×#12011yescharacteristic
980C22C5×#57611yescharacteristic
981C22C5×#57611yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—42no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—161no—
1006C2C5×#300811yescharacteristic
1007C2C5×#301811yescharacteristic
1008C2C5×#302611yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3534C2semidirect
2. C5×#3194C2semidirect
3. C5×#3186C2semidirect
4. C5×#2661C2semidirect
5. C5×#1612C2semidirect
6. C5×#1610C2semidirect
7. C5×#1609C2semidirect
8. C5×#1607C2semidirect
9. C5×#1600C2semidirect
10. C5×#1598C2semidirect
11. C5×#1597C2semidirect
12. C5×#1595C2semidirect
13. C5×#1507C2semidirect
14. C5×#1501C2semidirect
15. C5×#1468C2semidirect
35. C2×C5×#121C22semidirect
36. C5×#483C22semidirect
40. C5×#480C22semidirect
41. C5×#480C22semidirect
46. C5×#450C22semidirect
50. C5×#447C22semidirect
51. C5×#447C22semidirect
52. C5×#407C22semidirect
53. C2×C5×C22⋊C8C22semidirect
54. C5×#398C22semidirect
55. C5×#397C22semidirect
57. C5×#394C22semidirect
59. C5×#392C22semidirect
62. C4×C5×C22⋊C4C22semidirect
63. C5×#328C22semidirect
64. C5×#328C22semidirect
67. C5×#327C22semidirect
68. C5×#327C22semidirect
69. C5×#327C22semidirect
70. C5×#327C22semidirect
71. C5×#324C22semidirect
72. C5×#324C22semidirect
73. C5×#323C22semidirect
74. C5×#323C22semidirect
75. #18414C5direct (N × H)
77. C2×C5×#41D4semidirect
84. C22×C5×D4D4semidirect
122. C5×C22⋊Q8D4semidirect
143. C5×#121D4semidirect
144. C5×#121D4semidirect
145. C5×#121D4semidirect
166. C5×#117D4semidirect
169. C2×C5×C4⋊C4D4semidirect
207. #3534C2×C5semidirect
208. #3194C2×C5semidirect
209. #3186C2×C5semidirect
210. #2661C2×C5semidirect
211. #1612C2×C5semidirect
212. #1610C2×C5semidirect
213. #1609C2×C5semidirect
214. #1607C2×C5semidirect
215. #1600C2×C5semidirect
216. #1598C2×C5semidirect
217. #1597C2×C5semidirect
218. #1595C2×C5semidirect
219. #1507C2×C5semidirect
220. #1501C2×C5semidirect
221. #1468C2×C5semidirect
374. C2×#121C22×C5semidirect
375. #483C22×C5semidirect
379. #480C22×C5semidirect
380. #480C22×C5semidirect
385. #450C22×C5semidirect
389. #447C22×C5semidirect
390. #447C22×C5semidirect
391. #407C22×C5semidirect
392. C2×C22⋊C8C22×C5semidirect
393. #398C22×C5semidirect
394. #397C22×C5semidirect
396. #394C22×C5semidirect
398. #392C22×C5semidirect
401. C4×C22⋊C4C22×C5semidirect
402. #328C22×C5semidirect
403. #328C22×C5semidirect
406. #327C22×C5semidirect
407. #327C22×C5semidirect
408. #327C22×C5semidirect
409. #327C22×C5semidirect
410. #324C22×C5semidirect
411. #324C22×C5semidirect
412. #323C22×C5semidirect
413. #323C22×C5semidirect
517. C2×#41C5×D4semidirect
524. C22×D4C5×D4semidirect
562. C22⋊Q8C5×D4semidirect
583. #121C5×D4semidirect
584. #121C5×D4semidirect
585. #121C5×D4semidirect
606. #117C5×D4semidirect
609. C2×C4⋊C4C5×D4semidirect
945. C5#18414direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35342
C5×#31942
C5×#31862
C5×#26612
C5×#16122
C5×#16102
C5×#16092
C5×#16072
C5×#16002
C5×#15982
C5×#15972
C5×#15952
C5×#15072
C5×#15012
C5×#14682
#184145