Finite Group Databasebeta

← C5×#24166 #11946886

Subgroups — C5×#24166 #11946886

Order 1280.

1142 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#542C211yesmaximal, characteristic, complemented
2C2×C5×#476C211yesmaximal, characteristic, complemented
3C2×C5×#463C211yesmaximal, characteristic, complemented
4C5×#2324C211yesmaximal, characteristic, complemented
5C5×#2035C211yesmaximal, characteristic, complemented
6C5×#2034C211yesmaximal, characteristic, complemented
7C5×#2000C211yesmaximal, characteristic, complemented
8C5×#1999C211yesmaximal, characteristic
9C5×#1988C211yesmaximal, characteristic, complemented
10C5×#1983C211yesmaximal, characteristic, complemented
11C5×#1880C211yesmaximal, characteristic, complemented
12C5×#1879C211yesmaximal, characteristic, complemented
13C5×#1865C211yesmaximal, characteristic, complemented
14C5×#1864C211yesmaximal, characteristic, complemented
15C5×#1798C211yesmaximal, characteristic, complemented
16C22×C5×SD16C2211yescharacteristic
17C22×C5×D8C2211yescharacteristic
18C5×#542—24no—
19C5×#542—24no—
20C2×C5×C4⋊Q8C2211yescharacteristic
21C2×C5×#126—21no—
22C2×C5×#124—21no—
23C2×C5×#124C2211yescharacteristic
24C2×C5×#123—21no—
25C2×C5×C22⋊Q8—21no—
26C2×C5×C22⋊Q8C2211yescharacteristic
27C2×C5×#121C2211yescharacteristic
28C2×C5×#121C2211yescharacteristic
29C2×C4×C5×Q8C2211yescharacteristic
30C2×C4×C5×D4C2211yescharacteristic
31C2×C4×C5×D4C2211yescharacteristic
32C2×C5×#117C2211yescharacteristic
33C5×#476—24no—
34C5×#463—24no—
35C2×C5×#106C2211yescharacteristic
36C2×C5×#106C2211yescharacteristic
37C2×C5×C4⋊C8C2211yescharacteristic
38C2×C5×C4⋊C8C2211yescharacteristic
39C2×C5×#103C2211yescharacteristic
40C2×C5×#103C2211yescharacteristic
41C2×C5×#103C2211yescharacteristic
42C2×C5×#102C2211yescharacteristic
43C2×C5×#102C2211yescharacteristic
44C2×C5×#102C2211yescharacteristic
45C2×C5×#102C2211yescharacteristic
46C2×C5×#102C2211yescharacteristic
47C2×C5×C22⋊C8C2211yescharacteristic
48C2×C5×C22⋊C8C2211yescharacteristic
49C5×#390—21no—
50C5×#390C2211yescharacteristic
51C5×#389C2211yescharacteristic
52C5×#388—21no—
53C5×#386—21no—
54C5×#385—21no—
55C5×#380C2211yescharacteristic
56C4×C5×C4⋊C4C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#340C2211yescharacteristic
61C5×#336C2211yescharacteristic
62C5×#336C2211yescharacteristic
63#24166C511yesmaximal, characteristic, direct product factor, Sylow
64C22×C5×Q8—21no—
65C22×C5×Q8C2311yescharacteristic
66C22×C5×D4—21no—
67C22×C5×D4—21no—
68C22×C5×D4C2311yescharacteristic
69C22×C5×D4C2311yescharacteristic
70C23×C4×C5—21no—
71C23×C4×C5—21no—
72C23×C4×C5C2311yescharacteristic
73C2×C5×SD16—22no—
74C2×C5×SD16—22no—
75C2×C5×SD16—41no—
76C2×C5×D8—22no—
77C2×C5×D8—22no—
78C2×C5×D8—41no—
79C22×C5×C8C2311yescharacteristic
80C22×C5×C8C2311yescharacteristic
81C22×C5×C8C2311yescharacteristic
82C22×C5×C8C2311yescharacteristic
83C5×C4⋊Q8—22no—
84C5×C4⋊Q8D414yescomplemented
85C5×#126—28no—
86C5×#124—28no—
87C5×#124—22no—
88C5×#124D414yescomplemented
89C5×#123—28no—
90C5×C22⋊Q8—28no—
91C5×C22⋊Q8—22no—
92C5×C22⋊Q8—22no—
93C5×#121—22no—
94C5×#121—22no—
95C5×#121—22no—
96C5×#121—22no—
97C4×C5×Q8—22no—
98C4×C5×Q8—22no—
99C4×C5×D4—22no—
100C4×C5×D4—22no—
101C4×C5×D4—22no—
102C4×C5×D4—22no—
103C5×#117—22no—
104C5×#117—22no—
105C2×C5×C4⋊C4—21no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4D411yescharacteristic
110C2×C5×C4⋊C4D411yescharacteristic
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4—21no—
120C2×C5×C22⋊C4—21no—
121C2×C5×C22⋊C4—21no—
122C2×C5×C22⋊C4—21no—
123C2×C5×C22⋊C4—21no—
124C2×C5×C22⋊C4—21no—
125C2×C5×C22⋊C4—21no—
126C2×C5×C22⋊C4D411yescharacteristic
127C2×C5×C22⋊C4D411yescharacteristic
128C2×C42×C5—21no—
129C2×C42×C5—21no—
130C2×C42×C5C2311yescharacteristic
131C2×C42×C5C2311yescharacteristic
132C5×#106—22no—
133C5×#106—22no—
134C5×C4⋊C8—22no—
135C5×C4⋊C8—22no—
136C5×#103—22no—
137C5×#103—22no—
138C5×#103—41no—
139C5×#102—22no—
140C5×#102—22no—
141C5×#102—22no—
142C5×#102—22no—
143C5×#102—41no—
144C5×C22⋊C8—41no—
145C5×C22⋊C8—41no—
146C5×#95—21no—
147C5×#95—21no—
148C5×#95—21no—
149C2×#542C2×C511yescharacteristic, complemented
150C2×#476C2×C511yescharacteristic, complemented
151C2×#463C2×C511yescharacteristic, complemented
152#2324C2×C511yescharacteristic, complemented
153#2035C2×C511yescharacteristic, complemented
154#2034C2×C511yescharacteristic, complemented
155#2000C2×C511yescharacteristic, complemented
156#1999C2×C511yescharacteristic
157#1988C2×C511yescharacteristic, complemented
158#1983C2×C511yescharacteristic, complemented
159#1880C2×C511yescharacteristic, complemented
160#1879C2×C511yescharacteristic, complemented
161#1865C2×C511yescharacteristic, complemented
162#1864C2×C511yescharacteristic, complemented
163#1798C2×C511yescharacteristic, complemented
164C24×C5—21no—
165C24×C5—21no—
166C24×C5C2×D411yescharacteristic
167C2×C5×Q8—24no—
168C2×C5×Q8—21no—
169C2×C5×Q8—21no—
170C2×C5×Q8—21no—
171C2×C5×Q8—21no—
172C2×C5×Q8—21no—
173C2×C5×Q8—81no—
174C2×C5×Q8—81no—
175C2×C5×Q8C2×D412yes—
176C2×C5×D4—24no—
177C2×C5×D4—24no—
178C2×C5×D4—21no—
179C2×C5×D4—21no—
180C2×C5×D4—21no—
181C2×C5×D4—21no—
182C2×C5×D4—21no—
183C2×C5×D4—21no—
184C2×C5×D4—21no—
185C2×C5×D4—21no—
186C2×C5×D4—21no—
187C2×C5×D4—21no—
188C2×C5×D4—81no—
189C2×C5×D4—81no—
190C2×C5×D4—81no—
191C2×C5×D4—81no—
192C2×C5×D4C2×D412yes—
193C2×C5×D4#4112yes—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—24no—
199C22×C4×C5—21no—
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5—42no—
208C22×C4×C5—81no—
209C22×C4×C5—81no—
210C22×C4×C5—81no—
211C22×C4×C5—81no—
212C22×C4×C5C2×D411yescharacteristic
213C22×C4×C5C2×D411yescharacteristic
214C22×C4×C5C2×D411yescharacteristic
215C22×C4×C5C2×D411yescharacteristic
216C22×C4×C5C2×D411yescharacteristic
217C22×C4×C5C2411yescharacteristic
218C5×SD16—44no—
219C5×D8—44no—
220C2×C5×C8—21no—
221C2×C5×C8—21no—
222C2×C5×C8—21no—
223C2×C5×C8—21no—
224C2×C5×C8—21no—
225C2×C5×C8—21no—
226C2×C5×C8—21no—
227C2×C5×C8—21no—
228C2×C5×C8—21no—
229C2×C5×C8—21no—
230C2×C5×C8—21no—
231C2×C5×C8—21no—
232C5×C4⋊C4—24no—
233C5×C4⋊C4—24no—
234C5×C4⋊C4—24no—
235C5×C4⋊C4—22no—
236C5×C4⋊C4—22no—
237C5×C4⋊C4—21no—
238C5×C4⋊C4—21no—
239C5×C4⋊C4—21no—
240C5×C4⋊C4—21no—
241C5×C4⋊C4—21no—
242C5×C4⋊C4—21no—
243C5×C4⋊C4—21no—
244C5×C4⋊C4—81no—
245C5×C4⋊C4C2×D412yes—
246C5×C4⋊C4C2×D412yes—
247C5×C4⋊C4#4112yes—
248C5×C22⋊C4—24no—
249C5×C22⋊C4—24no—
250C5×C22⋊C4—24no—
251C5×C22⋊C4—24no—
252C5×C22⋊C4—24no—
253C5×C22⋊C4—24no—
254C5×C22⋊C4—22no—
255C5×C22⋊C4—22no—
256C5×C22⋊C4—42no—
257C5×C22⋊C4—81no—
258C5×C22⋊C4—81no—
259C5×C22⋊C4—81no—
260C42×C5—24no—
261C42×C5—21no—
262C42×C5—21no—
263C42×C5—81no—
264C42×C5C2×D412yes—
265C42×C5C2×D412yes—
266C22×SD16C22×C511yescharacteristic
267C22×D8C22×C511yescharacteristic
268#542—24no—
269#542—24no—
270C2×C4⋊Q8C22×C511yescharacteristic
271C2×#126—21no—
272C2×#124—21no—
273C2×#124C22×C511yescharacteristic
274C2×#123—21no—
275C2×C22⋊Q8—21no—
276C2×C22⋊Q8C22×C511yescharacteristic
277C2×#121C22×C511yescharacteristic
278C2×#121C22×C511yescharacteristic
279C2×C4×Q8C22×C511yescharacteristic
280C2×C4×D4C22×C511yescharacteristic
281C2×C4×D4C22×C511yescharacteristic
282C2×#117C22×C511yescharacteristic
283#476—24no—
284#463—24no—
285C2×#106C22×C511yescharacteristic
286C2×#106C22×C511yescharacteristic
287C2×C4⋊C8C22×C511yescharacteristic
288C2×C4⋊C8C22×C511yescharacteristic
289C2×#103C22×C511yescharacteristic
290C2×#103C22×C511yescharacteristic
291C2×#103C22×C511yescharacteristic
292C2×#102C22×C511yescharacteristic
293C2×#102C22×C511yescharacteristic
294C2×#102C22×C511yescharacteristic
295C2×#102C22×C511yescharacteristic
296C2×#102C22×C511yescharacteristic
297C2×C22⋊C8C22×C511yescharacteristic
298C2×C22⋊C8C22×C511yescharacteristic
299#390—21no—
300#390C22×C511yescharacteristic
301#389C22×C511yescharacteristic
302#388—21no—
303#386—21no—
304#385—21no—
305#380C22×C511yescharacteristic
306C4×C4⋊C4C22×C511yescharacteristic
307#340C22×C511yescharacteristic
308#340C22×C511yescharacteristic
309#340C22×C511yescharacteristic
310#340C22×C511yescharacteristic
311#336C22×C511yescharacteristic
312#336C22×C511yescharacteristic
313C23×C5—21no—
314C23×C5—22no—
315C23×C5—22no—
316C23×C5—21no—
317C23×C5—21no—
318C23×C5—21no—
319C23×C5—21no—
320C23×C5—21no—
321C23×C5—21no—
322C23×C5—41no—
323C23×C5—41no—
324C23×C5—41no—
325C23×C5—41no—
326C23×C5—41no—
327C23×C5—41no—
328C23×C5—41no—
329C23×C5—41no—
330C23×C5—41no—
331C23×C5—41no—
332C23×C5—41no—
333C23×C5—41no—
334C23×C5C22×D411yescharacteristic
335C5×Q8—22no—
336C5×Q8—22no—
337C5×Q8—41no—
338C5×Q8—41no—
339C5×Q8—84no—
340C5×D4—22no—
341C5×D4—22no—
342C5×D4—22no—
343C5×D4—22no—
344C5×D4—41no—
345C5×D4—41no—
346C5×D4—41no—
347C5×D4—41no—
348C5×D4—84no—
349C5×D4—84no—
350C2×C4×C5—21no—
351C2×C4×C5—21no—
352C2×C4×C5—21no—
353C2×C4×C5—21no—
354C2×C4×C5—21no—
355C2×C4×C5—22no—
356C2×C4×C5—21no—
357C2×C4×C5—22no—
358C2×C4×C5—21no—
359C2×C4×C5—22no—
360C2×C4×C5—21no—
361C2×C4×C5—22no—
362C2×C4×C5—21no—
363C2×C4×C5—21no—
364C2×C4×C5—21no—
365C2×C4×C5—21no—
366C2×C4×C5—21no—
367C2×C4×C5—41no—
368C2×C4×C5—41no—
369C2×C4×C5—41no—
370C2×C4×C5—41no—
371C2×C4×C5—41no—
372C2×C4×C5—41no—
373C2×C4×C5—41no—
374C2×C4×C5—41no—
375C2×C4×C5—41no—
376C2×C4×C5—41no—
377C2×C4×C5—41no—
378C2×C4×C5—41no—
379C2×C4×C5—41no—
380C2×C4×C5—41no—
381C2×C4×C5—41no—
382C2×C4×C5—41no—
383C2×C4×C5—41no—
384C2×C4×C5—41no—
385C2×C4×C5—84no—
386C2×C4×C5—84no—
387C2×C4×C5#12012yes—
388C2×C4×C5#12012yes—
389C2×C4×C5C22×D411yescharacteristic
390C2×C4×C5C22×D411yescharacteristic
391C2×C4×C5C2×#4111yescharacteristic
392C2×C4×C5C2×#4111yescharacteristic
393C2×C4×C5H(5,𝔽2)11yescharacteristic
394C2×C4×C52−1+411yescharacteristic
395C5×C8—41no—
396C5×C8—41no—
397C5×C8—41no—
398C5×C8—41no—
399C22×Q8—21no—
400C22×Q8C23×C511yescharacteristic
401C22×D4—21no—
402C22×D4—21no—
403C22×D4C23×C511yescharacteristic
404C22×D4C23×C511yescharacteristic
405C23×C4—21no—
406C23×C4—21no—
407C23×C4C23×C511yescharacteristic
408C2×SD16—22no—
409C2×SD16—22no—
410C2×SD16—41no—
411C2×D8—22no—
412C2×D8—22no—
413C2×D8—41no—
414C22×C8C23×C511yescharacteristic
415C22×C8C23×C511yescharacteristic
416C22×C8C23×C511yescharacteristic
417C22×C8C23×C511yescharacteristic
418C4⋊Q8—22no—
419C4⋊Q8C5×D414yescomplemented
420#126—28no—
421#124—28no—
422#124—22no—
423#124C5×D414yescomplemented
424#123—28no—
425C22⋊Q8—28no—
426C22⋊Q8—22no—
427C22⋊Q8—22no—
428#121—22no—
429#121—22no—
430#121—22no—
431#121—22no—
432C4×Q8—22no—
433C4×Q8—22no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—22no—
438#117—22no—
439#117—22no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4C5×D411yescharacteristic
445C2×C4⋊C4C5×D411yescharacteristic
446C2×C4⋊C4C23×C511yescharacteristic
447C2×C4⋊C4C23×C511yescharacteristic
448C2×C4⋊C4C23×C511yescharacteristic
449C2×C4⋊C4C23×C511yescharacteristic
450C2×C4⋊C4C23×C511yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4C5×D411yescharacteristic
462C2×C22⋊C4C5×D411yescharacteristic
463C2×C42—21no—
464C2×C42—21no—
465C2×C42C23×C511yescharacteristic
466C2×C42C23×C511yescharacteristic
467#106—22no—
468#106—22no—
469C4⋊C8—22no—
470C4⋊C8—22no—
471#103—22no—
472#103—22no—
473#103—41no—
474#102—22no—
475#102—22no—
476#102—22no—
477#102—22no—
478#102—41no—
479C22⋊C8—41no—
480C22⋊C8—41no—
481#95—21no—
482#95—21no—
483#95—21no—
484C22×C5—41no—
485C22×C5—42no—
486C22×C5—41no—
487C22×C5—42no—
488C22×C5—41no—
489C22×C5—42no—
490C22×C5—42no—
491C22×C5—41no—
492C22×C5—41no—
493C22×C5—41no—
494C22×C5—42no—
495C22×C5—42no—
496C22×C5—41no—
497C22×C5—81no—
498C22×C5—81no—
499C22×C5—81no—
500C22×C5—81no—
501C22×C5—81no—
502C22×C5—81no—
503C22×C5—81no—
504C22×C5—81no—
505C22×C5C2×#12011yescharacteristic
506C22×C5#52511yescharacteristic
507C22×C5#53711yescharacteristic
508C22×C5#57611yescharacteristic
509C22×C5#57711yescharacteristic
510C22×C5#57711yescharacteristic
511C22×C5#57711yescharacteristic
512C4×C5—22no—
513C4×C5—22no—
514C4×C5—42no—
515C4×C5—41no—
516C4×C5—42no—
517C4×C5—41no—
518C4×C5—41no—
519C4×C5—42no—
520C4×C5—42no—
521C4×C5—81no—
522C4×C5—81no—
523C4×C5#54611yescharacteristic
524C4×C5#54711yescharacteristic
525C4×C5#54811yescharacteristic
526C4×C5#55011yescharacteristic
527C24—21no—
528C24—21no—
529C24C2×C5×D411yescharacteristic
530C2×Q8—24no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—81no—
537C2×Q8—81no—
538C2×Q8C2×C5×D412yes—
539C2×D4—24no—
540C2×D4—24no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—81no—
552C2×D4—81no—
553C2×D4—81no—
554C2×D4—81no—
555C2×D4C2×C5×D412yes—
556C2×D4C5×#4112yes—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—42no—
571C22×C4—81no—
572C22×C4—81no—
573C22×C4—81no—
574C22×C4—81no—
575C22×C4C2×C5×D411yescharacteristic
576C22×C4C2×C5×D411yescharacteristic
577C22×C4C2×C5×D411yescharacteristic
578C22×C4C2×C5×D411yescharacteristic
579C22×C4C2×C5×D411yescharacteristic
580C22×C4C24×C511yescharacteristic
581SD16—44no—
582D8—44no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—81no—
608C4⋊C4C2×C5×D412yes—
609C4⋊C4C2×C5×D412yes—
610C4⋊C4C5×#4112yes—
611C22⋊C4—24no—
612C22⋊C4—24no—
613C22⋊C4—24no—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—42no—
620C22⋊C4—81no—
621C22⋊C4—81no—
622C22⋊C4—81no—
623C42—24no—
624C42—21no—
625C42—21no—
626C42—81no—
627C42C2×C5×D412yes—
628C42C2×C5×D412yes—
629C2×C5—81no—
630C2×C5—82no—
631C2×C5—82no—
632C2×C5#240711yescharacteristic
633C2×C5#301011yescharacteristic
634C2×C5#301211yescharacteristic
635C2×C5#311811yescharacteristic
636C2×C5#312511yescharacteristic
637C2×C5#325711yescharacteristic
638C2×C5#326311yescharacteristic
639C23—21no—
640C23—22no—
641C23—22no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23C22×C5×D411yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665Q8—84no—
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—84no—
675D4—84no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—84no—
712C2×C4—84no—
713C2×C4C5×#12012yes—
714C2×C4C5×#12012yes—
715C2×C4C22×C5×D411yescharacteristic
716C2×C4C22×C5×D411yescharacteristic
717C2×C4C2×C5×#4111yescharacteristic
718C2×C4C2×C5×#4111yescharacteristic
719C2×C4C5×H(5,𝔽2)11yescharacteristic
720C2×C4C5×2−1+411yescharacteristic
721C8—41no—
722C8—41no—
723C8—41no—
724C8—41no—
725C5#2416611yescharacteristic, direct product factor, Sylow
726C22—41no—
727C22—41no—
728C22—41no—
729C22—42no—
730C22—42no—
731C22—41no—
732C22—41no—
733C22—42no—
734C22—41no—
735C22—42no—
736C22—41no—
737C22—42no—
738C22—42no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22C2×C5×#12011yescharacteristic
748C22C5×#52511yescharacteristic
749C22C5×#53711yescharacteristic
750C22C5×#57611yescharacteristic
751C22C5×#57711yescharacteristic
752C22C5×#57711yescharacteristic
753C22C5×#57711yescharacteristic
754C4—22no—
755C4—22no—
756C4—41no—
757C4—41no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—41no—
762C4—42no—
763C4—81no—
764C4—81no—
765C4C5×#54611yescharacteristic
766C4C5×#54711yescharacteristic
767C4C5×#54811yescharacteristic
768C4C5×#55011yescharacteristic
769C2—81no—
770C2—82no—
771C2—82no—
772C2C5×#240711yescharacteristic
773C2C5×#301011yescharacteristic
774C2C5×#301211yescharacteristic
775C2C5×#311811yescharacteristic
776C2C5×#312511yescharacteristic
777C2C5×#325711yescharacteristic
778C2C5×#326311yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C5×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#542C2semidirect
2. C2×C5×#476C2semidirect
3. C2×C5×#463C2semidirect
4. C5×#2324C2semidirect
5. C5×#2035C2semidirect
6. C5×#2034C2semidirect
7. C5×#2000C2semidirect
9. C5×#1988C2semidirect
10. C5×#1983C2semidirect
11. C5×#1880C2semidirect
12. C5×#1879C2semidirect
13. C5×#1865C2semidirect
14. C5×#1864C2semidirect
15. C5×#1798C2semidirect
63. #24166C5direct (N × H)
84. C5×C4⋊Q8D4semidirect
88. C5×#124D4semidirect
149. C2×#542C2×C5semidirect
150. C2×#476C2×C5semidirect
151. C2×#463C2×C5semidirect
152. #2324C2×C5semidirect
153. #2035C2×C5semidirect
154. #2034C2×C5semidirect
155. #2000C2×C5semidirect
157. #1988C2×C5semidirect
158. #1983C2×C5semidirect
159. #1880C2×C5semidirect
160. #1879C2×C5semidirect
161. #1865C2×C5semidirect
162. #1864C2×C5semidirect
163. #1798C2×C5semidirect
419. C4⋊Q8C5×D4semidirect
423. #124C5×D4semidirect
725. C5#24166direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5422
C2×C5×#4762
C2×C5×#4632
C5×#23242
C5×#20352
C5×#20342
C5×#20002
C5×#19992
C5×#19882
C5×#19832
C5×#18802
C5×#18792
C5×#18652
C5×#18642
C5×#17982
#241665