Finite Group Databasebeta

← C5×#18282 #11941002

Subgroups — C5×#18282 #11941002

Order 1280.

942 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3564C211yesmaximal, characteristic, complemented
2C5×#3114C211yesmaximal, characteristic, complemented
3C5×#3101C211yesmaximal, characteristic, complemented
4C5×#2603C211yesmaximal, characteristic, complemented
5C5×#1612C211yesmaximal, characteristic, complemented
6C5×#1611C211yesmaximal, characteristic, complemented
7C5×#1609C211yesmaximal, characteristic, complemented
8C5×#1608C211yesmaximal, characteristic, complemented
9C5×#1600C211yesmaximal, characteristic
10C5×#1599C211yesmaximal, characteristic, complemented
11C5×#1597C211yesmaximal, characteristic, complemented
12C5×#1596C211yesmaximal, characteristic, complemented
13C5×#1506C211yesmaximal, characteristic, complemented
14C5×#1500C211yesmaximal, characteristic, complemented
15C5×#1473C211yesmaximal, characteristic, complemented
16C5×#563—21no—
17C5×#563—21no—
18C5×#556—21no—
19C5×#554—21no—
20C5×#552—21no—
21C5×#552—21no—
22C5×#551—21no—
23C5×#551—21no—
24C5×#544C2211yescharacteristic
25C5×#543C2211yescharacteristic
26C5×#542—21no—
27C5×#541—21no—
28C5×#541—21no—
29C5×#539—21no—
30C5×#539C2211yescharacteristic
31C5×#538C2211yescharacteristic
32C5×#533C2211yescharacteristic
33C5×#529C2211yescharacteristic
34C2×C5×#126C2211yescharacteristic
35C2×C4×C5×D4C2211yescharacteristic
36C5×#483C2211yescharacteristic
37C5×#483C2211yescharacteristic
38C5×#483C2211yescharacteristic
39C5×#480C2211yescharacteristic
40C5×#478—21no—
41C5×#476—21no—
42C5×#463—21no—
43C5×#461—21no—
44C5×#450C2211yescharacteristic
45C5×#450C2211yescharacteristic
46C5×#450C2211yescharacteristic
47C5×#447C2211yescharacteristic
48C5×#442—21no—
49C5×#440—21no—
50C4×C5×SD16—21no—
51C4×C5×SD16—21no—
52C5×#432C2211yescharacteristic
53C5×#431C2211yescharacteristic
54C5×#398C2211yescharacteristic
55C5×#397C2211yescharacteristic
56C5×#394C2211yescharacteristic
57C5×#392C2211yescharacteristic
58C5×#390—21no—
59C5×#388—21no—
60C5×#386—21no—
61C5×#385—21no—
62C5×#376C2211yescharacteristic
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#18282C511yesmaximal, characteristic, direct product factor, Sylow
76C22×C5×D4—21no—
77C22×C5×D4C2311yescharacteristic
78C23×C4×C5—21no—
79C2×C5×SD16—21no—
80C2×C5×SD16—21no—
81C2×C5×SD16—21no—
82C2×C5×D8—21no—
83C5×C4⋊Q8—21no—
84C5×C4⋊Q8—21no—
85C5×C4⋊Q8—21no—
86C5×C4⋊Q8D411yescharacteristic, complemented
87C5×C4⋊Q8D411yescharacteristic, complemented
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×#126—21no—
97C5×#126—21no—
98C5×#126—21no—
99C5×#126—21no—
100C5×#126—21no—
101C5×#125—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×#125D411yescharacteristic, complemented
111C5×#124—21no—
112C5×#124—21no—
113C5×#124—21no—
114C5×#124D411yescharacteristic, complemented
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×C22⋊Q8—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⋊Q8C2311yescharacteristic
138C5×C22⋊Q8C2311yescharacteristic
139C5×C22⋊Q8C2311yescharacteristic
140C5×#121—21no—
141C5×#121C2311yescharacteristic
142C5×#120—21no—
143C4×C5×Q8—21no—
144C4×C5×Q8—21no—
145C4×C5×Q8—21no—
146C4×C5×Q8D411yescharacteristic, complemented
147C4×C5×Q8D411yescharacteristic, complemented
148C4×C5×Q8D411yescharacteristic, complemented
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×D4—21no—
158C4×C5×D4D411yescharacteristic, complemented
159C5×#117—21no—
160C5×#117—21no—
161C5×#117—21no—
162C5×#117—21no—
163C5×#117—21no—
164C5×#117—21no—
165C2×C5×C4⋊C4—21no—
166C2×C5×C4⋊C4—21no—
167C2×C5×C4⋊C4D411yescharacteristic
168C2×C5×C4⋊C4D411yescharacteristic
169C2×C5×C4⋊C4C2311yescharacteristic
170C2×C5×C4⋊C4C2311yescharacteristic
171C2×C5×C22⋊C4—21no—
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⋊C4D411yescharacteristic
178C2×C5×C22⋊C4D411yescharacteristic
179C2×C5×C22⋊C4C2311yescharacteristic
180C2×C42×C5—21no—
181C2×C42×C5C2311yescharacteristic
182C5×#107—21no—
183C5×#106—21no—
184C5×#106—21no—
185C5×#106—21no—
186C5×C4⋊C8—21no—
187C5×C4⋊C8—21no—
188C5×#103—21no—
189C5×#103—21no—
190C5×#103—21no—
191C5×#102—21no—
192C5×#102—21no—
193C5×#102—21no—
194C5×#102—21no—
195C5×#102—21no—
196C5×C22⋊C8C2311yescharacteristic
197C5×C22⋊C8C2311yescharacteristic
198C5×C22⋊C8C2311yescharacteristic
199C5×C22⋊C8C2311yescharacteristic
200C5×#97—21no—
201C4×C5×C8—21no—
202C5×#95—21no—
203C5×#95—21no—
204C5×#95—21no—
205C5×#95C2311yescharacteristic
206C5×#95C2311yescharacteristic
207#3564C2×C511yescharacteristic, complemented
208#3114C2×C511yescharacteristic, complemented
209#3101C2×C511yescharacteristic, complemented
210#2603C2×C511yescharacteristic, complemented
211#1612C2×C511yescharacteristic, complemented
212#1611C2×C511yescharacteristic, complemented
213#1609C2×C511yescharacteristic, complemented
214#1608C2×C511yescharacteristic, complemented
215#1600C2×C511yescharacteristic
216#1599C2×C511yescharacteristic, complemented
217#1597C2×C511yescharacteristic, complemented
218#1596C2×C511yescharacteristic, complemented
219#1506C2×C511yescharacteristic, complemented
220#1500C2×C511yescharacteristic, complemented
221#1473C2×C511yescharacteristic, complemented
222C24×C5—21no—
223C24×C5C2×D411yescharacteristic
224C2×C5×Q8—21no—
225C2×C5×Q8—21no—
226C2×C5×Q8—21no—
227C2×C5×Q8C2×D411yescharacteristic
228C2×C5×Q8C2×D411yescharacteristic
229C2×C5×Q8C2×D411yescharacteristic
230C2×C5×D4—21no—
231C2×C5×D4—21no—
232C2×C5×D4—21no—
233C2×C5×D4—21no—
234C2×C5×D4—21no—
235C2×C5×D4—42no—
236C2×C5×D4—42no—
237C2×C5×D4—42no—
238C2×C5×D4—81no—
239C2×C5×D4C2×D411yescharacteristic
240C22×C4×C5—21no—
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—21no—
248C22×C4×C5—41no—
249C22×C4×C5—41no—
250C22×C4×C5—81no—
251C22×C4×C5—81no—
252C22×C4×C5C2×D411yescharacteristic
253C22×C4×C5C2×D411yescharacteristic
254C22×C4×C5C2×D411yescharacteristic
255C22×C4×C5C2×D411yescharacteristic
256C22×C4×C5C2×D411yescharacteristic
257C22×C4×C5C2411yescharacteristic
258C5×SD16—42no—
259C5×SD16—42no—
260C5×SD16—42no—
261C5×D8—42no—
262C2×C5×C8—21no—
263C2×C5×C8—21no—
264C2×C5×C8—21no—
265C2×C5×C8—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⋊C4—21no—
293C5×C4⋊C4—21no—
294C5×C4⋊C4—21no—
295C5×C4⋊C4—21no—
296C5×C4⋊C4—21no—
297C5×C4⋊C4—81no—
298C5×C4⋊C4C2×D411yescharacteristic
299C5×C4⋊C4C2×D411yescharacteristic
300C5×C4⋊C4C2×D411yescharacteristic
301C5×C4⋊C4C2×D411yescharacteristic
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—21no—
321C5×C22⋊C4—21no—
322C5×C22⋊C4—21no—
323C5×C22⋊C4—42no—
324C5×C22⋊C4—42no—
325C5×C22⋊C4—41no—
326C5×C22⋊C4—41no—
327C5×C22⋊C4—81no—
328C5×C22⋊C4—81no—
329C42×C5—21no—
330C42×C5—21no—
331C42×C5—21no—
332C42×C5—21no—
333C42×C5—21no—
334C42×C5—21no—
335C42×C5—21no—
336C42×C5—42no—
337C42×C5C2×D411yescharacteristic
338C42×C5C2×D411yescharacteristic
339C42×C5C2×D411yescharacteristic
340C42×C5C2×D411yescharacteristic
341#563—21no—
342#563—21no—
343#556—21no—
344#554—21no—
345#552—21no—
346#552—21no—
347#551—21no—
348#551—21no—
349#544C22×C511yescharacteristic
350#543C22×C511yescharacteristic
351#542—21no—
352#541—21no—
353#541—21no—
354#539—21no—
355#539C22×C511yescharacteristic
356#538C22×C511yescharacteristic
357#533C22×C511yescharacteristic
358#529C22×C511yescharacteristic
359C2×#126C22×C511yescharacteristic
360C2×C4×D4C22×C511yescharacteristic
361#483C22×C511yescharacteristic
362#483C22×C511yescharacteristic
363#483C22×C511yescharacteristic
364#480C22×C511yescharacteristic
365#478—21no—
366#476—21no—
367#463—21no—
368#461—21no—
369#450C22×C511yescharacteristic
370#450C22×C511yescharacteristic
371#450C22×C511yescharacteristic
372#447C22×C511yescharacteristic
373#442—21no—
374#440—21no—
375C4×SD16—21no—
376C4×SD16—21no—
377#432C22×C511yescharacteristic
378#431C22×C511yescharacteristic
379#398C22×C511yescharacteristic
380#397C22×C511yescharacteristic
381#394C22×C511yescharacteristic
382#392C22×C511yescharacteristic
383#390—21no—
384#388—21no—
385#386—21no—
386#385—21no—
387#376C22×C511yescharacteristic
388#328C22×C511yescharacteristic
389#328C22×C511yescharacteristic
390#328C22×C511yescharacteristic
391#328C22×C511yescharacteristic
392#328C22×C511yescharacteristic
393#328C22×C511yescharacteristic
394#327C22×C511yescharacteristic
395#327C22×C511yescharacteristic
396#324C22×C511yescharacteristic
397#324C22×C511yescharacteristic
398#323C22×C511yescharacteristic
399#323C22×C511yescharacteristic
400C23×C5—22no—
401C23×C5—21no—
402C23×C5—21no—
403C23×C5—21no—
404C23×C5—21no—
405C23×C5—41no—
406C23×C5—41no—
407C23×C5—41no—
408C23×C5—41no—
409C23×C5—41no—
410C23×C5—41no—
411C23×C5—41no—
412C23×C5—41no—
413C23×C5C22×D411yescharacteristic
414C5×Q8—41no—
415C5×Q8—41no—
416C5×Q8—41no—
417C5×Q8—81no—
418C5×Q8—81no—
419C5×Q8—81no—
420C5×D4—22no—
421C5×D4—22no—
422C5×D4—41no—
423C5×D4—41no—
424C5×D4—41no—
425C5×D4—41no—
426C5×D4—41no—
427C5×D4—81no—
428C5×D4—81no—
429C5×D4—84no—
430C2×C4×C5—21no—
431C2×C4×C5—21no—
432C2×C4×C5—22no—
433C2×C4×C5—21no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—21no—
442C2×C4×C5—21no—
443C2×C4×C5—21no—
444C2×C4×C5—21no—
445C2×C4×C5—41no—
446C2×C4×C5—41no—
447C2×C4×C5—41no—
448C2×C4×C5—41no—
449C2×C4×C5—41no—
450C2×C4×C5—41no—
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—81no—
458C2×C4×C5—82no—
459C2×C4×C5—82no—
460C2×C4×C5—81no—
461C2×C4×C5—81no—
462C2×C4×C5—81no—
463C2×C4×C5—81no—
464C2×C4×C5#12011yescharacteristic
465C2×C4×C5#12011yescharacteristic
466C2×C4×C5#12011yescharacteristic
467C2×C4×C5#12011yescharacteristic
468C2×C4×C5C22×D411yescharacteristic
469C2×C4×C5C22×D411yescharacteristic
470C5×C8—41no—
471C5×C8—41no—
472C5×C8—41no—
473C5×C8—41no—
474C22×D4—21no—
475C22×D4C23×C511yescharacteristic
476C23×C4—21no—
477C2×SD16—21no—
478C2×SD16—21no—
479C2×SD16—21no—
480C2×D8—21no—
481C4⋊Q8—21no—
482C4⋊Q8—21no—
483C4⋊Q8—21no—
484C4⋊Q8C5×D411yescharacteristic, complemented
485C4⋊Q8C5×D411yescharacteristic, complemented
486#126—21no—
487#126—21no—
488#126—21no—
489#126—21no—
490#126—21no—
491#126—21no—
492#126—21no—
493#126—21no—
494#126—21no—
495#126—21no—
496#126—21no—
497#126—21no—
498#126—21no—
499#125—21no—
500#125—21no—
501#125—21no—
502#125—21no—
503#125—21no—
504#125—21no—
505#125—21no—
506#125—21no—
507#125—21no—
508#125C5×D411yescharacteristic, complemented
509#124—21no—
510#124—21no—
511#124—21no—
512#124C5×D411yescharacteristic, complemented
513#123—21no—
514#123—21no—
515#123—21no—
516#123—21no—
517#123—21no—
518#123—21no—
519#123—21no—
520#123—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524C22⋊Q8—21no—
525C22⋊Q8—21no—
526C22⋊Q8—21no—
527C22⋊Q8—21no—
528C22⋊Q8—21no—
529C22⋊Q8—21no—
530C22⋊Q8—21no—
531C22⋊Q8—21no—
532C22⋊Q8—21no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8C23×C511yescharacteristic
536C22⋊Q8C23×C511yescharacteristic
537C22⋊Q8C23×C511yescharacteristic
538#121—21no—
539#121C23×C511yescharacteristic
540#120—21no—
541C4×Q8—21no—
542C4×Q8—21no—
543C4×Q8—21no—
544C4×Q8C5×D411yescharacteristic, complemented
545C4×Q8C5×D411yescharacteristic, complemented
546C4×Q8C5×D411yescharacteristic, complemented
547C4×D4—21no—
548C4×D4—21no—
549C4×D4—21no—
550C4×D4—21no—
551C4×D4—21no—
552C4×D4—21no—
553C4×D4—21no—
554C4×D4—21no—
555C4×D4—21no—
556C4×D4C5×D411yescharacteristic, complemented
557#117—21no—
558#117—21no—
559#117—21no—
560#117—21no—
561#117—21no—
562#117—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4C5×D411yescharacteristic
566C2×C4⋊C4C5×D411yescharacteristic
567C2×C4⋊C4C23×C511yescharacteristic
568C2×C4⋊C4C23×C511yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4C5×D411yescharacteristic
576C2×C22⋊C4C5×D411yescharacteristic
577C2×C22⋊C4C23×C511yescharacteristic
578C2×C42—21no—
579C2×C42C23×C511yescharacteristic
580#107—21no—
581#106—21no—
582#106—21no—
583#106—21no—
584C4⋊C8—21no—
585C4⋊C8—21no—
586#103—21no—
587#103—21no—
588#103—21no—
589#102—21no—
590#102—21no—
591#102—21no—
592#102—21no—
593#102—21no—
594C22⋊C8C23×C511yescharacteristic
595C22⋊C8C23×C511yescharacteristic
596C22⋊C8C23×C511yescharacteristic
597C22⋊C8C23×C511yescharacteristic
598#97—21no—
599C4×C8—21no—
600#95—21no—
601#95—21no—
602#95—21no—
603#95C23×C511yescharacteristic
604#95C23×C511yescharacteristic
605C22×C5—21no—
606C22×C5—21no—
607C22×C5—42no—
608C22×C5—42no—
609C22×C5—41no—
610C22×C5—41no—
611C22×C5—41no—
612C22×C5—41no—
613C22×C5—41no—
614C22×C5—41no—
615C22×C5—42no—
616C22×C5—81no—
617C22×C5—81no—
618C22×C5—81no—
619C22×C5—81no—
620C22×C5—81no—
621C22×C5—81no—
622C22×C5C2×#12011yescharacteristic
623C22×C5#57711yescharacteristic
624C22×C5#57711yescharacteristic
625C4×C5—21no—
626C4×C5—21no—
627C4×C5—21no—
628C4×C5—21no—
629C4×C5—21no—
630C4×C5—21no—
631C4×C5—42no—
632C4×C5—41no—
633C4×C5—41no—
634C4×C5—41no—
635C4×C5—41no—
636C4×C5—41no—
637C4×C5—41no—
638C4×C5—41no—
639C4×C5—41no—
640C4×C5—41no—
641C4×C5—41no—
642C4×C5—81no—
643C4×C5—81no—
644C24—21no—
645C24C2×C5×D411yescharacteristic
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8C2×C5×D411yescharacteristic
650C2×Q8C2×C5×D411yescharacteristic
651C2×Q8C2×C5×D411yescharacteristic
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—81no—
661C2×D4C2×C5×D411yescharacteristic
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—41no—
671C22×C4—41no—
672C22×C4—81no—
673C22×C4—81no—
674C22×C4C2×C5×D411yescharacteristic
675C22×C4C2×C5×D411yescharacteristic
676C22×C4C2×C5×D411yescharacteristic
677C22×C4C2×C5×D411yescharacteristic
678C22×C4C2×C5×D411yescharacteristic
679C22×C4C24×C511yescharacteristic
680SD16—42no—
681SD16—42no—
682SD16—42no—
683D8—42no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—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—81no—
720C4⋊C4C2×C5×D411yescharacteristic
721C4⋊C4C2×C5×D411yescharacteristic
722C4⋊C4C2×C5×D411yescharacteristic
723C4⋊C4C2×C5×D411yescharacteristic
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
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—42no—
746C22⋊C4—42no—
747C22⋊C4—41no—
748C22⋊C4—41no—
749C22⋊C4—81no—
750C22⋊C4—81no—
751C42—21no—
752C42—21no—
753C42—21no—
754C42—21no—
755C42—21no—
756C42—21no—
757C42—21no—
758C42—42no—
759C42C2×C5×D411yescharacteristic
760C42C2×C5×D411yescharacteristic
761C42C2×C5×D411yescharacteristic
762C42C2×C5×D411yescharacteristic
763C2×C5—21no—
764C2×C5—21no—
765C2×C5—81no—
766C2×C5—81no—
767C2×C5—82no—
768C2×C5#301011yescharacteristic
769C2×C5#301811yescharacteristic
770C2×C5#302511yescharacteristic
771C23—22no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23C22×C5×D411yescharacteristic
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—81no—
789Q8—81no—
790Q8—81no—
791D4—22no—
792D4—22no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—81no—
799D4—81no—
800D4—84no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—81no—
829C2×C4—82no—
830C2×C4—82no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4C5×#12011yescharacteristic
836C2×C4C5×#12011yescharacteristic
837C2×C4C5×#12011yescharacteristic
838C2×C4C5×#12011yescharacteristic
839C2×C4C22×C5×D411yescharacteristic
840C2×C4C22×C5×D411yescharacteristic
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C5#1828211yescharacteristic, direct product factor, Sylow
846C22—21no—
847C22—21no—
848C22—42no—
849C22—42no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—42no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22C2×C5×#12011yescharacteristic
864C22C5×#57711yescharacteristic
865C22C5×#57711yescharacteristic
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—42no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—81no—
884C4—81no—
885C2—21no—
886C2—21no—
887C2—82no—
888C2—81no—
889C2—81no—
890C2C5×#301011yescharacteristic
891C2C5×#301811yescharacteristic
892C2C5×#302511yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#1600C2
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
1. C5×#3564C2semidirect
2. C5×#3114C2semidirect
3. C5×#3101C2semidirect
4. C5×#2603C2semidirect
5. C5×#1612C2semidirect
6. C5×#1611C2semidirect
7. C5×#1609C2semidirect
8. C5×#1608C2semidirect
10. C5×#1599C2semidirect
11. C5×#1597C2semidirect
12. C5×#1596C2semidirect
13. C5×#1506C2semidirect
14. C5×#1500C2semidirect
15. C5×#1473C2semidirect
75. #18282C5direct (N × H)
86. C5×C4⋊Q8D4semidirect
87. C5×C4⋊Q8D4semidirect
110. C5×#125D4semidirect
114. C5×#124D4semidirect
146. C4×C5×Q8D4semidirect
147. C4×C5×Q8D4semidirect
148. C4×C5×Q8D4semidirect
158. C4×C5×D4D4semidirect
207. #3564C2×C5semidirect
208. #3114C2×C5semidirect
209. #3101C2×C5semidirect
210. #2603C2×C5semidirect
211. #1612C2×C5semidirect
212. #1611C2×C5semidirect
213. #1609C2×C5semidirect
214. #1608C2×C5semidirect
216. #1599C2×C5semidirect
217. #1597C2×C5semidirect
218. #1596C2×C5semidirect
219. #1506C2×C5semidirect
220. #1500C2×C5semidirect
221. #1473C2×C5semidirect
484. C4⋊Q8C5×D4semidirect
485. C4⋊Q8C5×D4semidirect
508. #125C5×D4semidirect
512. #124C5×D4semidirect
544. C4×Q8C5×D4semidirect
545. C4×Q8C5×D4semidirect
546. C4×Q8C5×D4semidirect
556. C4×D4C5×D4semidirect
845. C5#18282direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35642
C5×#31142
C5×#31012
C5×#26032
C5×#16122
C5×#16112
C5×#16092
C5×#16082
C5×#16002
C5×#15992
C5×#15972
C5×#15962
C5×#15062
C5×#15002
C5×#14732
#182825