Finite Group Databasebeta

← C5×#18253 #11940973

Subgroups — C5×#18253 #11940973

Order 1280.

1196 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3535C211yesmaximal, characteristic, complemented
2C5×#3007C211yesmaximal, characteristic, complemented
3C5×#3002C211yesmaximal, characteristic, complemented
4C5×#2430C211yesmaximal, characteristic, complemented
5C5×#1606C211yesmaximal, characteristic, complemented
6C5×#1605C211yesmaximal, characteristic, complemented
7C5×#1603C211yesmaximal, characteristic, complemented
8C5×#1602C211yesmaximal, characteristic, complemented
9C5×#1600C211yesmaximal, characteristic, complemented
10C5×#1599C211yesmaximal, characteristic, complemented
11C5×#1597C211yesmaximal, characteristic, complemented
12C5×#1596C211yesmaximal, characteristic, complemented
13C5×#1504C211yesmaximal, characteristic, complemented
14C2×C5×#328C211yesmaximal, characteristic, complemented
15C5×#1468C211yesmaximal, characteristic, complemented
16C22×C5×#41C2211yescharacteristic
17C2×C5×#137—21no—
18C2×C5×#135—21no—
19C5×#563—21no—
20C5×#562—21no—
21C5×#554—21no—
22C5×#552—21no—
23C5×#551—21no—
24C5×#551—21no—
25C5×#547—21no—
26C5×#546—21no—
27C5×#544C2211yescharacteristic
28C5×#543C2211yescharacteristic
29C5×#542—21no—
30C5×#539—21no—
31C5×#539—21no—
32C5×#539C2211yescharacteristic
33C5×#538C2211yescharacteristic
34C5×#536—21no—
35C5×#525C2211yescharacteristic
36C2×C5×#123C2211yescharacteristic
37C2×C5×C22⋊Q8C2211yescharacteristic
38C2×C5×#121—21no—
39C5×#452—21no—
40C5×#452—21no—
41C5×#452—21no—
42C5×#451C2211yescharacteristic
43C5×#451C2211yescharacteristic
44C5×#451C2211yescharacteristic
45C5×#450C2211yescharacteristic
46C5×#450C2211yescharacteristic
47C5×#450C2211yescharacteristic
48C5×#449—21no—
49C5×#448C2211yescharacteristic
50C5×#447C2211yescharacteristic
51C5×#417—21no—
52C5×#416—21no—
53C5×#407C2211yescharacteristic
54C2×C5×C22⋊C8C2211yescharacteristic
55C5×#395C2211yescharacteristic
56C5×#394C2211yescharacteristic
57C5×#393C2211yescharacteristic
58C5×#392C2211yescharacteristic
59C5×#386—21no—
60C5×#386—21no—
61C5×#385—21no—
62C2×C5×#95C2211yescharacteristic
63C5×#328C2211yescharacteristic
64C5×#328C2211yescharacteristic
65C5×#328C2211yescharacteristic
66C5×#328C2211yescharacteristic
67C5×#328C2211yescharacteristic
68C5×#328C2211yescharacteristic
69C5×#327C2211yescharacteristic
70C5×#327C2211yescharacteristic
71C5×#324C2211yescharacteristic
72C5×#324C2211yescharacteristic
73C5×#323C2211yescharacteristic
74C5×#323C2211yescharacteristic
75#18253C511yesmaximal, characteristic, direct product factor, Sylow
76C2×C5×#41—21no—
77C2×C5×#41—21no—
78C2×C5×#41—21no—
79C2×C5×#41—21no—
80C2×C5×#41—21no—
81C2×C5×#41—44no—
82C2×C5×#41D411yescharacteristic, complemented
83C22×C5×Q8D411yescharacteristic, complemented
84C22×C5×Q8C2311yescharacteristic
85C22×C5×D4—21no—
86C22×C5×D4—21no—
87C22×C5×D4D411yescharacteristic
88C22×C5×D4C2311yescharacteristic
89C23×C4×C5—21no—
90C23×C4×C5—21no—
91C23×C4×C5C2311yescharacteristic
92C5×#137—44no—
93C5×#135—44no—
94C2×C5×Q16—21no—
95C2×C5×Q16—21no—
96C2×C5×Q16—21no—
97C2×C5×SD16—21no—
98C2×C5×SD16—21no—
99C2×C5×SD16—21no—
100C2×C5×SD16—21no—
101C2×C5×D8—21no—
102C2×C5×M16—21no—
103C22×C5×C8—21no—
104C5×C4⋊Q8—21no—
105C5×C4⋊Q8—21no—
106C5×C4⋊Q8—21no—
107C5×#126—21no—
108C5×#126—21no—
109C5×#126—21no—
110C5×#126—21no—
111C5×#126—21no—
112C5×#126—21no—
113C5×#125—21no—
114C5×#125—21no—
115C5×#125—21no—
116C5×#125—21no—
117C5×#125—21no—
118C5×#124—21no—
119C5×#124—21no—
120C5×#124—21no—
121C5×#124—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×#123—21no—
132C5×#123—21no—
133C5×#123—21no—
134C5×#123—21no—
135C5×#123—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⋊Q8—21no—
146C5×C22⋊Q8—21no—
147C5×C22⋊Q8—21no—
148C5×C22⋊Q8—21no—
149C5×C22⋊Q8—21no—
150C5×C22⋊Q8D411yescharacteristic, complemented
151C5×C22⋊Q8D411yescharacteristic, complemented
152C5×C22⋊Q8D411yescharacteristic, complemented
153C5×C22⋊Q8C2311yescharacteristic
154C5×C22⋊Q8C2311yescharacteristic
155C5×C22⋊Q8C2311yescharacteristic
156C5×#121—21no—
157C5×#121—21no—
158C5×#121—21no—
159C5×#121—21no—
160C5×#121—44no—
161C5×#121D411yescharacteristic, complemented
162C5×#121C2311yescharacteristic
163C5×#120—21no—
164C5×#120—21no—
165C4×C5×Q8—21no—
166C4×C5×D4—21no—
167C4×C5×D4—21no—
168C4×C5×D4—21no—
169C4×C5×D4—21no—
170C4×C5×D4—21no—
171C4×C5×D4—21no—
172C4×C5×D4—21no—
173C5×#117—21no—
174C5×#117—21no—
175C5×#117—21no—
176C5×#117D411yescharacteristic, complemented
177C2×C5×C4⋊C4—21no—
178C2×C5×C4⋊C4—21no—
179C2×C5×C4⋊C4—21no—
180C2×C5×C4⋊C4D411yescharacteristic
181C2×C5×C4⋊C4D411yescharacteristic, complemented
182C2×C5×C4⋊C4C2311yescharacteristic
183C2×C5×C22⋊C4—21no—
184C2×C5×C22⋊C4—21no—
185C2×C5×C22⋊C4—21no—
186C2×C5×C22⋊C4—21no—
187C2×C5×C22⋊C4—21no—
188C2×C5×C22⋊C4—21no—
189C2×C5×C22⋊C4D411yescharacteristic
190C2×C5×C22⋊C4D411yescharacteristic
191C2×C5×C22⋊C4C2311yescharacteristic
192C5×#103—21no—
193C5×#103—21no—
194C5×#103—21no—
195C5×#103—21no—
196C5×#102—21no—
197C5×#102—21no—
198C5×#102—21no—
199C5×#102—21no—
200C5×C22⋊C8—21no—
201C5×C22⋊C8—21no—
202C5×C22⋊C8C2311yescharacteristic
203C5×C22⋊C8C2311yescharacteristic
204C5×C22⋊C8C2311yescharacteristic
205C5×C22⋊C8C2311yescharacteristic
206C5×#95—21no—
207C5×#95—21no—
208C5×#95—21no—
209C5×#95C2311yescharacteristic
210C5×#95C2311yescharacteristic
211#3535C2×C511yescharacteristic, complemented
212#3007C2×C511yescharacteristic, complemented
213#3002C2×C511yescharacteristic, complemented
214#2430C2×C511yescharacteristic, complemented
215#1606C2×C511yescharacteristic, complemented
216#1605C2×C511yescharacteristic, complemented
217#1603C2×C511yescharacteristic, complemented
218#1602C2×C511yescharacteristic, complemented
219#1600C2×C511yescharacteristic, complemented
220#1599C2×C511yescharacteristic, complemented
221#1597C2×C511yescharacteristic, complemented
222#1596C2×C511yescharacteristic, complemented
223#1504C2×C511yescharacteristic, complemented
224C2×#328C2×C511yescharacteristic, complemented
225#1468C2×C511yescharacteristic, complemented
226C24×C5—21no—
227C24×C5C2×D411yescharacteristic
228C24×C5C2×D411yescharacteristic
229C5×#41—24no—
230C5×#41—24no—
231C5×#41—42no—
232C5×#41—42no—
233C5×#41—42no—
234C5×#41—42no—
235C5×#41—42no—
236C5×#41—42no—
237C5×#41—42no—
238C5×#41—82no—
239C2×C5×Q8—21no—
240C2×C5×Q8—21no—
241C2×C5×Q8—21no—
242C2×C5×Q8—21no—
243C2×C5×Q8—21no—
244C2×C5×Q8—42no—
245C2×C5×Q8—42no—
246C2×C5×Q8C2×D411yescharacteristic
247C2×C5×Q8C2×D411yescharacteristic
248C2×C5×Q8C2×D411yescharacteristic
249C2×C5×D4—24no—
250C2×C5×D4—21no—
251C2×C5×D4—21no—
252C2×C5×D4—21no—
253C2×C5×D4—21no—
254C2×C5×D4—21no—
255C2×C5×D4—21no—
256C2×C5×D4—21no—
257C2×C5×D4—21no—
258C2×C5×D4—21no—
259C2×C5×D4—42no—
260C2×C5×D4—42no—
261C2×C5×D4—42no—
262C2×C5×D4—41no—
263C2×C5×D4—41no—
264C2×C5×D4—42no—
265C2×C5×D4—42no—
266C2×C5×D4—81no—
267C2×C5×D4C2×D411yescharacteristic
268C22×C4×C5—21no—
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—42no—
279C22×C4×C5—42no—
280C22×C4×C5—42no—
281C22×C4×C5—42no—
282C22×C4×C5—41no—
283C22×C4×C5—41no—
284C22×C4×C5—42no—
285C22×C4×C5—81no—
286C22×C4×C5C2×D411yescharacteristic
287C22×C4×C5C2×D411yescharacteristic
288C22×C4×C5C2×D411yescharacteristic
289C22×C4×C5C2×D411yescharacteristic
290C22×C4×C5C2×D411yescharacteristic
291C22×C4×C5C2×D411yescharacteristic
292C22×C4×C5C2×D411yescharacteristic
293C22×C4×C5C2×D411yescharacteristic
294C22×C4×C5C2411yescharacteristic
295C5×Q16—42no—
296C5×Q16—42no—
297C5×Q16—42no—
298C5×SD16—42no—
299C5×SD16—42no—
300C5×SD16—42no—
301C5×SD16—42no—
302C5×D8—42no—
303C5×M16—42no—
304C2×C5×C8—21no—
305C2×C5×C8—21no—
306C2×C5×C8—21no—
307C2×C5×C8—21no—
308C2×C5×C8—42no—
309C5×C4⋊C4—21no—
310C5×C4⋊C4—21no—
311C5×C4⋊C4—21no—
312C5×C4⋊C4—21no—
313C5×C4⋊C4—21no—
314C5×C4⋊C4—21no—
315C5×C4⋊C4—21no—
316C5×C4⋊C4—21no—
317C5×C4⋊C4—21no—
318C5×C4⋊C4—21no—
319C5×C4⋊C4—21no—
320C5×C4⋊C4—21no—
321C5×C4⋊C4—21no—
322C5×C4⋊C4—21no—
323C5×C4⋊C4—21no—
324C5×C4⋊C4—21no—
325C5×C4⋊C4—21no—
326C5×C4⋊C4—21no—
327C5×C4⋊C4—21no—
328C5×C4⋊C4—21no—
329C5×C4⋊C4—21no—
330C5×C4⋊C4—21no—
331C5×C4⋊C4—21no—
332C5×C4⋊C4—42no—
333C5×C4⋊C4C2×D411yescharacteristic
334C5×C4⋊C4C2×D411yescharacteristic
335C5×C4⋊C4C2×D411yescharacteristic
336C5×C4⋊C4C2×D411yescharacteristic
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—21no—
345C5×C22⋊C4—21no—
346C5×C22⋊C4—21no—
347C5×C22⋊C4—21no—
348C5×C22⋊C4—21no—
349C5×C22⋊C4—21no—
350C5×C22⋊C4—21no—
351C5×C22⋊C4—21no—
352C5×C22⋊C4—21no—
353C5×C22⋊C4—21no—
354C5×C22⋊C4—21no—
355C5×C22⋊C4—21no—
356C5×C22⋊C4—21no—
357C5×C22⋊C4—21no—
358C5×C22⋊C4—21no—
359C5×C22⋊C4—21no—
360C5×C22⋊C4—42no—
361C5×C22⋊C4—42no—
362C5×C22⋊C4—42no—
363C5×C22⋊C4—81no—
364C42×C5—21no—
365C42×C5—21no—
366C42×C5—21no—
367C42×C5—21no—
368C42×C5—21no—
369C22×#41C22×C511yescharacteristic
370C2×#137—21no—
371C2×#135—21no—
372#563—21no—
373#562—21no—
374#554—21no—
375#552—21no—
376#551—21no—
377#551—21no—
378#547—21no—
379#546—21no—
380#544C22×C511yescharacteristic
381#543C22×C511yescharacteristic
382#542—21no—
383#539—21no—
384#539—21no—
385#539C22×C511yescharacteristic
386#538C22×C511yescharacteristic
387#536—21no—
388#525C22×C511yescharacteristic
389C2×#123C22×C511yescharacteristic
390C2×C22⋊Q8C22×C511yescharacteristic
391C2×#121—21no—
392#452—21no—
393#452—21no—
394#452—21no—
395#451C22×C511yescharacteristic
396#451C22×C511yescharacteristic
397#451C22×C511yescharacteristic
398#450C22×C511yescharacteristic
399#450C22×C511yescharacteristic
400#450C22×C511yescharacteristic
401#449—21no—
402#448C22×C511yescharacteristic
403#447C22×C511yescharacteristic
404#417—21no—
405#416—21no—
406#407C22×C511yescharacteristic
407C2×C22⋊C8C22×C511yescharacteristic
408#395C22×C511yescharacteristic
409#394C22×C511yescharacteristic
410#393C22×C511yescharacteristic
411#392C22×C511yescharacteristic
412#386—21no—
413#386—21no—
414#385—21no—
415C2×#95C22×C511yescharacteristic
416#328C22×C511yescharacteristic
417#328C22×C511yescharacteristic
418#328C22×C511yescharacteristic
419#328C22×C511yescharacteristic
420#328C22×C511yescharacteristic
421#328C22×C511yescharacteristic
422#327C22×C511yescharacteristic
423#327C22×C511yescharacteristic
424#324C22×C511yescharacteristic
425#324C22×C511yescharacteristic
426#323C22×C511yescharacteristic
427#323C22×C511yescharacteristic
428C23×C5—21no—
429C23×C5—21no—
430C23×C5—22no—
431C23×C5—22no—
432C23×C5—21no—
433C23×C5—21no—
434C23×C5—21no—
435C23×C5—21no—
436C23×C5—41no—
437C23×C5—41no—
438C23×C5—41no—
439C23×C5—41no—
440C23×C5—41no—
441C23×C5—41no—
442C23×C5—41no—
443C23×C5—41no—
444C23×C5—41no—
445C23×C5#12011yescharacteristic
446C23×C5#12011yescharacteristic
447C23×C5C22×D411yescharacteristic
448C5×Q8—22no—
449C5×Q8—22no—
450C5×Q8—41no—
451C5×Q8—41no—
452C5×Q8—41no—
453C5×Q8—41no—
454C5×Q8—41no—
455C5×Q8—81no—
456C5×Q8—81no—
457C5×Q8—81no—
458C5×D4—22no—
459C5×D4—22no—
460C5×D4—41no—
461C5×D4—41no—
462C5×D4—41no—
463C5×D4—44no—
464C5×D4—41no—
465C5×D4—41no—
466C5×D4—44no—
467C5×D4—42no—
468C5×D4—42no—
469C5×D4—81no—
470C5×D4—81no—
471C5×D4—81no—
472C5×D4—81no—
473C5×D4—84no—
474C2×C4×C5—22no—
475C2×C4×C5—22no—
476C2×C4×C5—22no—
477C2×C4×C5—22no—
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—21no—
486C2×C4×C5—21no—
487C2×C4×C5—21no—
488C2×C4×C5—21no—
489C2×C4×C5—21no—
490C2×C4×C5—41no—
491C2×C4×C5—41no—
492C2×C4×C5—41no—
493C2×C4×C5—41no—
494C2×C4×C5—44no—
495C2×C4×C5—44no—
496C2×C4×C5—41no—
497C2×C4×C5—41no—
498C2×C4×C5—41no—
499C2×C4×C5—41no—
500C2×C4×C5—42no—
501C2×C4×C5—41no—
502C2×C4×C5—41no—
503C2×C4×C5—41no—
504C2×C4×C5—41no—
505C2×C4×C5—41no—
506C2×C4×C5—81no—
507C2×C4×C5—81no—
508C2×C4×C5—81no—
509C2×C4×C5—81no—
510C2×C4×C5—81no—
511C2×C4×C5—81no—
512C2×C4×C5—84no—
513C2×C4×C5#12011yescharacteristic
514C2×C4×C5#12011yescharacteristic
515C2×C4×C5C22×D411yescharacteristic
516C2×C4×C5C22×D411yescharacteristic
517C5×C8—41no—
518C5×C8—41no—
519C5×C8—41no—
520C5×C8—41no—
521C2×#41—21no—
522C2×#41—21no—
523C2×#41—21no—
524C2×#41—21no—
525C2×#41—21no—
526C2×#41—44no—
527C2×#41C5×D411yescharacteristic, complemented
528C22×Q8C5×D411yescharacteristic, complemented
529C22×Q8C23×C511yescharacteristic
530C22×D4—21no—
531C22×D4—21no—
532C22×D4C5×D411yescharacteristic
533C22×D4C23×C511yescharacteristic
534C23×C4—21no—
535C23×C4—21no—
536C23×C4C23×C511yescharacteristic
537#137—44no—
538#135—44no—
539C2×Q16—21no—
540C2×Q16—21no—
541C2×Q16—21no—
542C2×SD16—21no—
543C2×SD16—21no—
544C2×SD16—21no—
545C2×SD16—21no—
546C2×D8—21no—
547C2×M16—21no—
548C22×C8—21no—
549C4⋊Q8—21no—
550C4⋊Q8—21no—
551C4⋊Q8—21no—
552#126—21no—
553#126—21no—
554#126—21no—
555#126—21no—
556#126—21no—
557#126—21no—
558#125—21no—
559#125—21no—
560#125—21no—
561#125—21no—
562#125—21no—
563#124—21no—
564#124—21no—
565#124—21no—
566#124—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572#123—21no—
573#123—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8—21no—
585C22⋊Q8—21no—
586C22⋊Q8—21no—
587C22⋊Q8—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8—21no—
594C22⋊Q8—21no—
595C22⋊Q8C5×D411yescharacteristic, complemented
596C22⋊Q8C5×D411yescharacteristic, complemented
597C22⋊Q8C5×D411yescharacteristic, complemented
598C22⋊Q8C23×C511yescharacteristic
599C22⋊Q8C23×C511yescharacteristic
600C22⋊Q8C23×C511yescharacteristic
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—44no—
606#121C5×D411yescharacteristic, complemented
607#121C23×C511yescharacteristic
608#120—21no—
609#120—21no—
610C4×Q8—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618#117—21no—
619#117—21no—
620#117—21no—
621#117C5×D411yescharacteristic, complemented
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4C5×D411yescharacteristic
626C2×C4⋊C4C5×D411yescharacteristic, complemented
627C2×C4⋊C4C23×C511yescharacteristic
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4C5×D411yescharacteristic
635C2×C22⋊C4C5×D411yescharacteristic
636C2×C22⋊C4C23×C511yescharacteristic
637#103—21no—
638#103—21no—
639#103—21no—
640#103—21no—
641#102—21no—
642#102—21no—
643#102—21no—
644#102—21no—
645C22⋊C8—21no—
646C22⋊C8—21no—
647C22⋊C8C23×C511yescharacteristic
648C22⋊C8C23×C511yescharacteristic
649C22⋊C8C23×C511yescharacteristic
650C22⋊C8C23×C511yescharacteristic
651#95—21no—
652#95—21no—
653#95—21no—
654#95C23×C511yescharacteristic
655#95C23×C511yescharacteristic
656C22×C5—21no—
657C22×C5—21no—
658C22×C5—21no—
659C22×C5—21no—
660C22×C5—21no—
661C22×C5—21no—
662C22×C5—21no—
663C22×C5—42no—
664C22×C5—42no—
665C22×C5—42no—
666C22×C5—42no—
667C22×C5—41no—
668C22×C5—41no—
669C22×C5—41no—
670C22×C5—41no—
671C22×C5—42no—
672C22×C5—41no—
673C22×C5—41no—
674C22×C5—81no—
675C22×C5—81no—
676C22×C5—81no—
677C22×C5—81no—
678C22×C5—81no—
679C22×C5—81no—
680C22×C5B(4,𝔽2)12yes—
681C22×C5C2×#12011yescharacteristic
682C22×C5#57711yescharacteristic
683C22×C5#57811yescharacteristic
684C4×C5—21no—
685C4×C5—21no—
686C4×C5—21no—
687C4×C5—21no—
688C4×C5—42no—
689C4×C5—41no—
690C4×C5—41no—
691C4×C5—41no—
692C4×C5—41no—
693C4×C5—41no—
694C4×C5—41no—
695C4×C5—42no—
696C4×C5—41no—
697C4×C5—41no—
698C4×C5—41no—
699C4×C5—41no—
700C4×C5—81no—
701C24—21no—
702C24C2×C5×D411yescharacteristic
703C24C2×C5×D411yescharacteristic
704#41—24no—
705#41—24no—
706#41—42no—
707#41—42no—
708#41—42no—
709#41—42no—
710#41—42no—
711#41—42no—
712#41—42no—
713#41—82no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8—21no—
719C2×Q8—42no—
720C2×Q8—42no—
721C2×Q8C2×C5×D411yescharacteristic
722C2×Q8C2×C5×D411yescharacteristic
723C2×Q8C2×C5×D411yescharacteristic
724C2×D4—24no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—41no—
738C2×D4—41no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—81no—
742C2×D4C2×C5×D411yescharacteristic
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—42no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—41no—
758C22×C4—41no—
759C22×C4—42no—
760C22×C4—81no—
761C22×C4C2×C5×D411yescharacteristic
762C22×C4C2×C5×D411yescharacteristic
763C22×C4C2×C5×D411yescharacteristic
764C22×C4C2×C5×D411yescharacteristic
765C22×C4C2×C5×D411yescharacteristic
766C22×C4C2×C5×D411yescharacteristic
767C22×C4C2×C5×D411yescharacteristic
768C22×C4C2×C5×D411yescharacteristic
769C22×C4C24×C511yescharacteristic
770Q16—42no—
771Q16—42no—
772Q16—42no—
773SD16—42no—
774SD16—42no—
775SD16—42no—
776SD16—42no—
777D8—42no—
778M16—42no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—42no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—42no—
808C4⋊C4C2×C5×D411yescharacteristic
809C4⋊C4C2×C5×D411yescharacteristic
810C4⋊C4C2×C5×D411yescharacteristic
811C4⋊C4C2×C5×D411yescharacteristic
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—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—21no—
835C22⋊C4—42no—
836C22⋊C4—42no—
837C22⋊C4—42no—
838C22⋊C4—81no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—21no—
844C2×C5—21no—
845C2×C5—21no—
846C2×C5—22no—
847C2×C5—41no—
848C2×C5—81no—
849C2×C5—81no—
850C2×C5—82no—
851C2×C5#301311yescharacteristic
852C2×C5#301811yescharacteristic
853C2×C5C2×B(4,𝔽2)11yescharacteristic
854C23—22no—
855C23—21no—
856C23—21no—
857C23—22no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23C5×#12011yescharacteristic
872C23C5×#12011yescharacteristic
873C23C22×C5×D411yescharacteristic
874Q8—22no—
875Q8—22no—
876Q8—41no—
877Q8—41no—
878Q8—41no—
879Q8—41no—
880Q8—41no—
881Q8—81no—
882Q8—81no—
883Q8—81no—
884D4—22no—
885D4—22no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—44no—
890D4—44no—
891D4—42no—
892D4—42no—
893D4—41no—
894D4—41no—
895D4—81no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—84no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
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—21no—
915C2×C4—21no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—44no—
921C2×C4—44no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4—84no—
939C2×C4C5×#12011yescharacteristic
940C2×C4C5×#12011yescharacteristic
941C2×C4C22×C5×D411yescharacteristic
942C2×C4C22×C5×D411yescharacteristic
943C8—41no—
944C8—41no—
945C8—41no—
946C8—41no—
947C5#1825311yescharacteristic, direct product factor, Sylow
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22C5×B(4,𝔽2)12yes—
973C22C2×C5×#12011yescharacteristic
974C22C5×#57711yescharacteristic
975C22C5×#57811yescharacteristic
976C4—21no—
977C4—21no—
978C4—21no—
979C4—21no—
980C4—42no—
981C4—41no—
982C4—41no—
983C4—41no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—42no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—81no—
993C2—21no—
994C2—21no—
995C2—22no—
996C2—41no—
997C2—82no—
998C2—81no—
999C2—81no—
1000C2C5×#301311yescharacteristic
1001C2C5×#301811yescharacteristic
1002C2C2×C5×B(4,𝔽2)11yescharacteristic
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×#3535C2semidirect
2. C5×#3007C2semidirect
3. C5×#3002C2semidirect
4. C5×#2430C2semidirect
5. C5×#1606C2semidirect
6. C5×#1605C2semidirect
7. C5×#1603C2semidirect
8. C5×#1602C2semidirect
9. C5×#1600C2semidirect
10. C5×#1599C2semidirect
11. C5×#1597C2semidirect
12. C5×#1596C2semidirect
13. C5×#1504C2semidirect
14. C2×C5×#328C2semidirect
15. C5×#1468C2semidirect
75. #18253C5direct (N × H)
82. C2×C5×#41D4semidirect
83. C22×C5×Q8D4semidirect
150. C5×C22⋊Q8D4semidirect
151. C5×C22⋊Q8D4semidirect
152. C5×C22⋊Q8D4semidirect
161. C5×#121D4semidirect
176. C5×#117D4semidirect
181. C2×C5×C4⋊C4D4semidirect
211. #3535C2×C5semidirect
212. #3007C2×C5semidirect
213. #3002C2×C5semidirect
214. #2430C2×C5semidirect
215. #1606C2×C5semidirect
216. #1605C2×C5semidirect
217. #1603C2×C5semidirect
218. #1602C2×C5semidirect
219. #1600C2×C5semidirect
220. #1599C2×C5semidirect
221. #1597C2×C5semidirect
222. #1596C2×C5semidirect
223. #1504C2×C5semidirect
224. C2×#328C2×C5semidirect
225. #1468C2×C5semidirect
527. C2×#41C5×D4semidirect
528. C22×Q8C5×D4semidirect
595. C22⋊Q8C5×D4semidirect
596. C22⋊Q8C5×D4semidirect
597. C22⋊Q8C5×D4semidirect
606. #121C5×D4semidirect
621. #117C5×D4semidirect
626. C2×C4⋊C4C5×D4semidirect
947. C5#18253direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35352
C5×#30072
C5×#30022
C5×#24302
C5×#16062
C5×#16052
C5×#16032
C5×#16022
C5×#16002
C5×#15992
C5×#15972
C5×#15962
C5×#15042
C2×C5×#3282
C5×#14682
#182535