Finite Group Databasebeta

← C5×#19069 #11941789

Subgroups — C5×#19069 #11941789

Order 1280.

886 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3545C211yesmaximal, characteristic
2C5×#3240C211yesmaximal, characteristic, complemented
3C5×#3215C211yesmaximal, characteristic, complemented
4C5×#3172C211yesmaximal, characteristic, complemented
5C5×#1664C211yesmaximal, characteristic, complemented
6C5×#1662C211yesmaximal, characteristic, complemented
7C5×#1661C211yesmaximal, characteristic, complemented
8C5×#1661C211yesmaximal, characteristic, complemented
9C5×#1661C211yesmaximal, characteristic, complemented
10C5×#1660C211yesmaximal, characteristic, complemented
11C5×#1659C211yesmaximal, characteristic, complemented
12C5×#1659C211yesmaximal, characteristic, complemented
13C5×#1535C211yesmaximal, characteristic, complemented
14C5×#1529C211yesmaximal, characteristic, complemented
15C5×#1527C211yesmaximal, characteristic, complemented
16C5×#563C2211yescharacteristic
17C5×#562C2211yescharacteristic
18C5×#562C2211yescharacteristic
19C5×H(3,𝔽4)C2211yescharacteristic
20C5×#555—21no—
21C5×#551—21no—
22C5×#551—21no—
23C5×#551—21no—
24C5×#546—21no—
25C5×#546—21no—
26C5×#542—21no—
27C5×#542—21no—
28C5×#538—21no—
29C5×#538—21no—
30C5×#536—21no—
31C5×#534—21no—
32C5×#533C2211yescharacteristic, complemented
33C5×#529C2211yescharacteristic
34C5×#529C2211yescharacteristic
35C2×C5×#124C2211yescharacteristic
36C5×#501C2211yescharacteristic, complemented
37C5×#501C2211yescharacteristic, complemented
38C5×#501C2211yescharacteristic, complemented
39C5×#497C2211yescharacteristic
40C5×#497C2211yescharacteristic, complemented
41C5×#497C2211yescharacteristic, complemented
42C5×#491C2211yescharacteristic, complemented
43C5×#489C2211yescharacteristic
44C5×#489C2211yescharacteristic, complemented
45C5×#489C2211yescharacteristic, complemented
46C5×#489C2211yescharacteristic, complemented
47C5×#489C2211yescharacteristic, complemented
48C5×#485—21no—
49C5×#482—21no—
50C5×#479—21no—
51C5×#478—21no—
52C5×#470—21no—
53C5×#468—21no—
54C5×#464—21no—
55C5×#464—21no—
56C5×#451—21no—
57C5×#450—21no—
58C4×C5×Q16—21no—
59C4×C5×SD16—21no—
60C5×#432C2211yescharacteristic, complemented
61C5×#432C2211yescharacteristic, complemented
62C4×C5×M16C2211yescharacteristic, complemented
63C5×#330C2211yescharacteristic, complemented
64C5×#330C2211yescharacteristic, complemented
65C5×#330C2211yescharacteristic, complemented
66C5×#330C2211yescharacteristic, complemented
67C5×#329C2211yescharacteristic
68C5×#329C2211yescharacteristic
69C5×#329C2211yescharacteristic, complemented
70C5×#329C2211yescharacteristic, complemented
71C5×#329C2211yescharacteristic, complemented
72C5×#329C2211yescharacteristic, complemented
73C5×#329C2211yescharacteristic, complemented
74C5×#329C2211yescharacteristic, complemented
75#19069C511yesmaximal, characteristic, direct product factor, Sylow
76C2×C5×#41—21no—
77C22×C5×Q8D411yescharacteristic
78C22×C5×D4—21no—
79C22×C5×D4D411yescharacteristic
80C2×C5×Q16—21no—
81C2×C5×Q16—21no—
82C2×C5×Q16—21no—
83C2×C5×SD16—21no—
84C2×C5×SD16—21no—
85C2×C5×SD16—21no—
86C2×C5×M16—21no—
87C5×C4⋊Q8—21no—
88C5×C4⋊Q8—21no—
89C5×C4⋊Q8C2311yescharacteristic
90C5×C4⋊Q8C2311yescharacteristic
91C5×#126—21no—
92C5×#126—21no—
93C5×#126—21no—
94C5×#126—21no—
95C5×#126—21no—
96C5×#126—21no—
97C5×#125—21no—
98C5×#125C2311yescharacteristic
99C5×#125C2311yescharacteristic
100C5×#124—21no—
101C5×#124—21no—
102C5×#124—21no—
103C5×#124—21no—
104C5×#124—21no—
105C5×#124—21no—
106C5×#124—21no—
107C5×#124—21no—
108C5×#124D411yescharacteristic
109C5×#124D411yescharacteristic
110C5×#124C2311yescharacteristic
111C5×#124C2311yescharacteristic
112C5×#124C2311yescharacteristic
113C5×#124C2311yescharacteristic
114C5×#123—21no—
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×#123—21no—
124C5×#123—21no—
125C5×#123—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⋊Q8D411yescharacteristic
137C5×C22⋊Q8D411yescharacteristic
138C5×#121—21no—
139C5×#121—21no—
140C5×#121—21no—
141C5×#121—21no—
142C5×#121—21no—
143C5×#121—21no—
144C5×#121—21no—
145C5×#121—21no—
146C5×#121D411yescharacteristic
147C5×#121D411yescharacteristic
148C5×#120—21no—
149C5×#120—21no—
150C5×#120—21no—
151C5×#120—21no—
152C5×#120—21no—
153C5×#120—21no—
154C4×C5×Q8—21no—
155C4×C5×Q8—21no—
156C4×C5×Q8D411yescharacteristic
157C4×C5×Q8D411yescharacteristic
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×D4D411yescharacteristic
165C4×C5×D4D411yescharacteristic
166C5×#117—21no—
167C5×#117—21no—
168C5×#117—21no—
169C5×#117—21no—
170C5×#117—21no—
171C5×#117—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×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×#103—21no—
190C5×#103—21no—
191C5×#103—21no—
192C5×#103—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×#97C2311yescharacteristic
201C5×#97C2311yescharacteristic
202C5×#97C2311yescharacteristic
203C5×#97C2311yescharacteristic
204C5×#97C2311yescharacteristic
205C5×#97C2311yescharacteristic
206C4×C5×C8—21no—
207#3545C2×C511yescharacteristic
208#3240C2×C511yescharacteristic, complemented
209#3215C2×C511yescharacteristic, complemented
210#3172C2×C511yescharacteristic, complemented
211#1664C2×C511yescharacteristic, complemented
212#1662C2×C511yescharacteristic, complemented
213#1661C2×C511yescharacteristic, complemented
214#1661C2×C511yescharacteristic, complemented
215#1661C2×C511yescharacteristic, complemented
216#1660C2×C511yescharacteristic, complemented
217#1659C2×C511yescharacteristic, complemented
218#1659C2×C511yescharacteristic, complemented
219#1535C2×C511yescharacteristic, complemented
220#1529C2×C511yescharacteristic, complemented
221#1527C2×C511yescharacteristic, complemented
222C24×C5—21no—
223C24×C5—21no—
224C5×#41—82no—
225C2×C5×Q8—21no—
226C2×C5×Q8—21no—
227C2×C5×Q8—21no—
228C2×C5×Q8—21no—
229C2×C5×Q8—81no—
230C2×C5×Q8C2×D411yescharacteristic
231C2×C5×Q8C2×D411yescharacteristic
232C2×C5×Q8C2×D411yescharacteristic
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—81no—
245C2×C5×D4—82no—
246C2×C5×D4C2×D411yescharacteristic
247C2×C5×D4C2×D411yescharacteristic
248C2×C5×D4C2×D411yescharacteristic
249C2×C5×D4C2×D411yescharacteristic
250C22×C4×C5—21no—
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×C5C2×D411yescharacteristic
259C22×C4×C5C2×D411yescharacteristic
260C22×C4×C5C2×D411yescharacteristic
261C5×Q16—42no—
262C5×Q16—81no—
263C5×Q16—81no—
264C5×SD16—42no—
265C5×SD16—81no—
266C5×SD16—81no—
267C5×M16—42no—
268C2×C5×C8—21no—
269C2×C5×C8—21no—
270C2×C5×C8—21no—
271C2×C5×C8—21no—
272C2×C5×C8—21no—
273C2×C5×C8—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—41no—
293C5×C4⋊C4—41no—
294C5×C4⋊C4C2×D411yescharacteristic
295C5×C4⋊C4C2×D411yescharacteristic
296C5×C4⋊C4C2×D411yescharacteristic
297C5×C4⋊C4C2×D411yescharacteristic
298C5×C22⋊C4—21no—
299C5×C22⋊C4—21no—
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—21no—
321C5×C22⋊C4—21no—
322C5×C22⋊C4—21no—
323C5×C22⋊C4—21no—
324C5×C22⋊C4—21no—
325C5×C22⋊C4—21no—
326C5×C22⋊C4—41no—
327C42×C5—21no—
328C42×C5—21no—
329C42×C5—21no—
330C42×C5—21no—
331C42×C5—41no—
332C42×C5C2×D411yescharacteristic
333C42×C5C2×D411yescharacteristic
334C42×C5C2×D411yescharacteristic
335C42×C5C2411yescharacteristic
336#563C22×C511yescharacteristic
337#562C22×C511yescharacteristic
338#562C22×C511yescharacteristic
339H(3,𝔽4)C22×C511yescharacteristic
340#555—21no—
341#551—21no—
342#551—21no—
343#551—21no—
344#546—21no—
345#546—21no—
346#542—21no—
347#542—21no—
348#538—21no—
349#538—21no—
350#536—21no—
351#534—21no—
352#533C22×C511yescharacteristic, complemented
353#529C22×C511yescharacteristic
354#529C22×C511yescharacteristic
355C2×#124C22×C511yescharacteristic
356#501C22×C511yescharacteristic, complemented
357#501C22×C511yescharacteristic, complemented
358#501C22×C511yescharacteristic, complemented
359#497C22×C511yescharacteristic
360#497C22×C511yescharacteristic, complemented
361#497C22×C511yescharacteristic, complemented
362#491C22×C511yescharacteristic, complemented
363#489C22×C511yescharacteristic
364#489C22×C511yescharacteristic, complemented
365#489C22×C511yescharacteristic, complemented
366#489C22×C511yescharacteristic, complemented
367#489C22×C511yescharacteristic, complemented
368#485—21no—
369#482—21no—
370#479—21no—
371#478—21no—
372#470—21no—
373#468—21no—
374#464—21no—
375#464—21no—
376#451—21no—
377#450—21no—
378C4×Q16—21no—
379C4×SD16—21no—
380#432C22×C511yescharacteristic, complemented
381#432C22×C511yescharacteristic, complemented
382C4×M16C22×C511yescharacteristic, complemented
383#330C22×C511yescharacteristic, complemented
384#330C22×C511yescharacteristic, complemented
385#330C22×C511yescharacteristic, complemented
386#330C22×C511yescharacteristic, complemented
387#329C22×C511yescharacteristic
388#329C22×C511yescharacteristic
389#329C22×C511yescharacteristic, complemented
390#329C22×C511yescharacteristic, complemented
391#329C22×C511yescharacteristic, complemented
392#329C22×C511yescharacteristic, complemented
393#329C22×C511yescharacteristic, complemented
394#329C22×C511yescharacteristic, complemented
395C23×C5—21no—
396C23×C5—21no—
397C23×C5—21no—
398C23×C5—21no—
399C23×C5—42no—
400C23×C5—81no—
401C23×C5—81no—
402C23×C5—81no—
403C23×C5—81no—
404C23×C5—81no—
405C23×C5#12011yescharacteristic
406C5×Q8—41no—
407C5×Q8—41no—
408C5×Q8—41no—
409C5×Q8—41no—
410C5×Q8—41no—
411C5×Q8—41no—
412C5×Q8—41no—
413C5×Q8—41no—
414C5×Q8—81no—
415C5×Q8—81no—
416C5×D4—41no—
417C5×D4—41no—
418C5×D4—41no—
419C5×D4—41no—
420C5×D4—42no—
421C5×D4—42no—
422C5×D4—81no—
423C5×D4—81no—
424C5×D4—81no—
425C5×D4—81no—
426C5×D4—81no—
427C5×D4—81no—
428C5×D4—81no—
429C5×D4—81no—
430C2×C4×C5—21no—
431C2×C4×C5—21no—
432C2×C4×C5—21no—
433C2×C4×C5—21no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—41no—
439C2×C4×C5—41no—
440C2×C4×C5—41no—
441C2×C4×C5—42no—
442C2×C4×C5—41no—
443C2×C4×C5—41no—
444C2×C4×C5—81no—
445C2×C4×C5—81no—
446C2×C4×C5—81no—
447C2×C4×C5—81no—
448C2×C4×C5—81no—
449C2×C4×C5—81no—
450C2×C4×C5—81no—
451C2×C4×C5#12011yescharacteristic
452C2×C4×C5#12011yescharacteristic
453C2×C4×C5#12011yescharacteristic
454C2×C4×C5C22×D411yescharacteristic
455C2×C4×C5C22×D411yescharacteristic
456C2×C4×C5C22×D411yescharacteristic
457C5×C8—22no—
458C5×C8—41no—
459C5×C8—41no—
460C5×C8—41no—
461C5×C8—41no—
462C5×C8—41no—
463C2×#41—21no—
464C22×Q8C5×D411yescharacteristic
465C22×D4—21no—
466C22×D4C5×D411yescharacteristic
467C2×Q16—21no—
468C2×Q16—21no—
469C2×Q16—21no—
470C2×SD16—21no—
471C2×SD16—21no—
472C2×SD16—21no—
473C2×M16—21no—
474C4⋊Q8—21no—
475C4⋊Q8—21no—
476C4⋊Q8C23×C511yescharacteristic
477C4⋊Q8C23×C511yescharacteristic
478#126—21no—
479#126—21no—
480#126—21no—
481#126—21no—
482#126—21no—
483#126—21no—
484#125—21no—
485#125C23×C511yescharacteristic
486#125C23×C511yescharacteristic
487#124—21no—
488#124—21no—
489#124—21no—
490#124—21no—
491#124—21no—
492#124—21no—
493#124—21no—
494#124—21no—
495#124C5×D411yescharacteristic
496#124C5×D411yescharacteristic
497#124C23×C511yescharacteristic
498#124C23×C511yescharacteristic
499#124C23×C511yescharacteristic
500#124C23×C511yescharacteristic
501#123—21no—
502#123—21no—
503#123—21no—
504#123—21no—
505#123—21no—
506#123—21no—
507#123—21no—
508#123—21no—
509#123—21no—
510#123—21no—
511#123—21no—
512#123—21no—
513C22⋊Q8—21no—
514C22⋊Q8—21no—
515C22⋊Q8—21no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—21no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8C5×D411yescharacteristic
524C22⋊Q8C5×D411yescharacteristic
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—21no—
531#121—21no—
532#121—21no—
533#121C5×D411yescharacteristic
534#121C5×D411yescharacteristic
535#120—21no—
536#120—21no—
537#120—21no—
538#120—21no—
539#120—21no—
540#120—21no—
541C4×Q8—21no—
542C4×Q8—21no—
543C4×Q8C5×D411yescharacteristic
544C4×Q8C5×D411yescharacteristic
545C4×D4—21no—
546C4×D4—21no—
547C4×D4—21no—
548C4×D4—21no—
549C4×D4—21no—
550C4×D4—21no—
551C4×D4C5×D411yescharacteristic
552C4×D4C5×D411yescharacteristic
553#117—21no—
554#117—21no—
555#117—21no—
556#117—21no—
557#117—21no—
558#117—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C42C23×C511yescharacteristic
565#107—21no—
566#107—21no—
567#107—21no—
568#106—21no—
569#106—21no—
570#106—21no—
571C4⋊C8—21no—
572C4⋊C8—21no—
573#103—21no—
574#103—21no—
575#103—21no—
576#103—21no—
577#103—21no—
578#103—21no—
579#103—21no—
580#102—21no—
581#102—21no—
582#102—21no—
583#102—21no—
584#102—21no—
585C22⋊C8—21no—
586C22⋊C8—21no—
587#97C23×C511yescharacteristic
588#97C23×C511yescharacteristic
589#97C23×C511yescharacteristic
590#97C23×C511yescharacteristic
591#97C23×C511yescharacteristic
592#97C23×C511yescharacteristic
593C4×C8—21no—
594C22×C5—21no—
595C22×C5—21no—
596C22×C5—21no—
597C22×C5—41no—
598C22×C5—41no—
599C22×C5—41no—
600C22×C5—41no—
601C22×C5—41no—
602C22×C5—41no—
603C22×C5—41no—
604C22×C5—41no—
605C22×C5—41no—
606C22×C5—41no—
607C22×C5—41no—
608C22×C5—41no—
609C22×C5—162no—
610C22×C5—162no—
611C22×C5C2×#12011yescharacteristic
612C4×C5—21no—
613C4×C5—21no—
614C4×C5—21no—
615C4×C5—21no—
616C4×C5—21no—
617C4×C5—21no—
618C4×C5—41no—
619C4×C5—41no—
620C4×C5—41no—
621C4×C5—41no—
622C4×C5—41no—
623C4×C5—41no—
624C4×C5—41no—
625C4×C5—41no—
626C4×C5—81no—
627C4×C5—81no—
628C24—21no—
629C24—21no—
630#41—82no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—81no—
636C2×Q8C2×C5×D411yescharacteristic
637C2×Q8C2×C5×D411yescharacteristic
638C2×Q8C2×C5×D411yescharacteristic
639C2×Q8C2×C5×D411yescharacteristic
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—81no—
651C2×D4—82no—
652C2×D4C2×C5×D411yescharacteristic
653C2×D4C2×C5×D411yescharacteristic
654C2×D4C2×C5×D411yescharacteristic
655C2×D4C2×C5×D411yescharacteristic
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4C2×C5×D411yescharacteristic
665C22×C4C2×C5×D411yescharacteristic
666C22×C4C2×C5×D411yescharacteristic
667Q16—42no—
668Q16—81no—
669Q16—81no—
670SD16—42no—
671SD16—81no—
672SD16—81no—
673M16—42no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—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—41no—
699C4⋊C4—41no—
700C4⋊C4C2×C5×D411yescharacteristic
701C4⋊C4C2×C5×D411yescharacteristic
702C4⋊C4C2×C5×D411yescharacteristic
703C4⋊C4C2×C5×D411yescharacteristic
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
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—41no—
733C42—21no—
734C42—21no—
735C42—21no—
736C42—21no—
737C42—41no—
738C42C2×C5×D411yescharacteristic
739C42C2×C5×D411yescharacteristic
740C42C2×C5×D411yescharacteristic
741C42C24×C511yescharacteristic
742C2×C5—41no—
743C2×C5—81no—
744C2×C5—81no—
745C2×C5—81no—
746C2×C5—81no—
747C2×C5#301811yescharacteristic
748C2×C5#301911yescharacteristic
749C2×C5#302211yescharacteristic
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—42no—
755C23—81no—
756C23—81no—
757C23—81no—
758C23—81no—
759C23—81no—
760C23C5×#12011yescharacteristic
761Q8—41no—
762Q8—41no—
763Q8—41no—
764Q8—41no—
765Q8—41no—
766Q8—41no—
767Q8—41no—
768Q8—41no—
769Q8—81no—
770Q8—81no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4—41no—
775D4—42no—
776D4—42no—
777D4—81no—
778D4—81no—
779D4—81no—
780D4—81no—
781D4—81no—
782D4—81no—
783D4—81no—
784D4—81no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4C5×#12011yescharacteristic
807C2×C4C5×#12011yescharacteristic
808C2×C4C5×#12011yescharacteristic
809C2×C4C22×C5×D411yescharacteristic
810C2×C4C22×C5×D411yescharacteristic
811C2×C4C22×C5×D411yescharacteristic
812C8—22no—
813C8—41no—
814C8—41no—
815C8—41no—
816C8—41no—
817C8—41no—
818C5#1906911yescharacteristic, direct product factor, Sylow
819C22—21no—
820C22—21no—
821C22—21no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—162no—
835C22—162no—
836C22C2×C5×#12011yescharacteristic
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—81no—
852C4—81no—
853C2—41no—
854C2—81no—
855C2—81no—
856C2—81no—
857C2—81no—
858C2C5×#301811yescharacteristic
859C2C5×#301911yescharacteristic
860C2C5×#302211yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3545C2
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
2. C5×#3240C2semidirect
3. C5×#3215C2semidirect
4. C5×#3172C2semidirect
5. C5×#1664C2semidirect
6. C5×#1662C2semidirect
7. C5×#1661C2semidirect
8. C5×#1661C2semidirect
9. C5×#1661C2semidirect
10. C5×#1660C2semidirect
11. C5×#1659C2semidirect
12. C5×#1659C2semidirect
13. C5×#1535C2semidirect
14. C5×#1529C2semidirect
15. C5×#1527C2semidirect
32. C5×#533C22semidirect
36. C5×#501C22semidirect
37. C5×#501C22semidirect
38. C5×#501C22semidirect
40. C5×#497C22semidirect
41. C5×#497C22semidirect
42. C5×#491C22semidirect
44. C5×#489C22semidirect
45. C5×#489C22semidirect
46. C5×#489C22semidirect
47. C5×#489C22semidirect
60. C5×#432C22semidirect
61. C5×#432C22semidirect
62. C4×C5×M16C22semidirect
63. C5×#330C22semidirect
64. C5×#330C22semidirect
65. C5×#330C22semidirect
66. C5×#330C22semidirect
69. C5×#329C22semidirect
70. C5×#329C22semidirect
71. C5×#329C22semidirect
72. C5×#329C22semidirect
73. C5×#329C22semidirect
74. C5×#329C22semidirect
75. #19069C5direct (N × H)
208. #3240C2×C5semidirect
209. #3215C2×C5semidirect
210. #3172C2×C5semidirect
211. #1664C2×C5semidirect
212. #1662C2×C5semidirect
213. #1661C2×C5semidirect
214. #1661C2×C5semidirect
215. #1661C2×C5semidirect
216. #1660C2×C5semidirect
217. #1659C2×C5semidirect
218. #1659C2×C5semidirect
219. #1535C2×C5semidirect
220. #1529C2×C5semidirect
221. #1527C2×C5semidirect
352. #533C22×C5semidirect
356. #501C22×C5semidirect
357. #501C22×C5semidirect
358. #501C22×C5semidirect
360. #497C22×C5semidirect
361. #497C22×C5semidirect
362. #491C22×C5semidirect
364. #489C22×C5semidirect
365. #489C22×C5semidirect
366. #489C22×C5semidirect
367. #489C22×C5semidirect
380. #432C22×C5semidirect
381. #432C22×C5semidirect
382. C4×M16C22×C5semidirect
383. #330C22×C5semidirect
384. #330C22×C5semidirect
385. #330C22×C5semidirect
386. #330C22×C5semidirect
389. #329C22×C5semidirect
390. #329C22×C5semidirect
391. #329C22×C5semidirect
392. #329C22×C5semidirect
393. #329C22×C5semidirect
394. #329C22×C5semidirect
818. C5#19069direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35452
C5×#32402
C5×#32152
C5×#31722
C5×#16642
C5×#16622
C5×#16612
C5×#16602
C5×#16592
C5×#15352
C5×#15292
C5×#15272
#190695