Finite Group Databasebeta

← C2×#10618615 #13007705

Subgroups — C2×#10618615 #13007705

Order 1280.

11438 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×#41C211yesmaximal, characteristic, complemented
2C22×#4147C211yesmaximal, characteristic, complemented
3C2×C5×#548C211yesmaximal, characteristic, complemented
4C2×#66165C211yesmaximal, characteristic, complemented
5C2×Q8×C22⋊D5C211yesmaximal, characteristic, complemented
6#10618615C2132yesmaximal, direct product factor
7C2×#66010C213yesmaximal, complemented
8C2×#66009C213yesmaximal, complemented
9C2×#65965C213yesmaximal, complemented
10C2×D5×C22⋊Q8C213yesmaximal, complemented
11C2×#65946C213yesmaximal, complemented
12C2×#65942C213yesmaximal, complemented
13C2×Q8×D20C211yesmaximal, characteristic, complemented
14C2×#65908C211yesmaximal, characteristic, complemented
15C2×#65885C213yesmaximal, complemented
16C2×#65881C213yesmaximal, complemented
17C22×C5×#41C2211yescharacteristic
18C23×C5×Q8C2211yescharacteristic, complemented
19C2×D5×#41—216no—
20C2×D5×#41C22116yescomplemented
21C2×#4147—216no—
22C2×#4147C22116yescomplemented
23C22×#713C2211yescharacteristic
24C22×#713C2213yescomplemented
25C22×Q8×D5C2211yescharacteristic
26C22×Q8×D5C2213yescomplemented
27C22×Q8×D5C2211yescharacteristic, complemented
28C22×#711C2213yes—
29C22×D4×D5C2213yes—
30C22×#709C2213yes—
31C22×#709C2213yescomplemented
32C22×#709C2213yescomplemented
33C23×C4×D5C2213yes—
34C5×#548C22116yescomplemented
35C2×C5×#124C2213yescomplemented
36C2×C5×C22⋊Q8C2213yescomplemented
37C2×C5×#121C2213yescomplemented
38C2×C4×C5×Q8C2211yescharacteristic, complemented
39C2×C4×C5×D4C2213yescomplemented
40#66165C22116yescomplemented
41Q8×C22⋊D5C22116yescomplemented
42C2×#4092C2213yes—
43C2×Q8×Dic5C2211yescharacteristic, complemented
44C2×#4090C2213yescomplemented
45C2×#4085C2213yescomplemented
46C2×#4084C2213yescomplemented
47C2×#4084C2216yescomplemented
48C2×#4083C2213yes—
49C2×#4082C2213yescomplemented
50C2×C4×C22⋊D5C2213yes—
51C2×C4×C22⋊D5C2213yescomplemented
52C2×#4070C2213yescomplemented
53C2×#4070C2213yescomplemented
54#66010C22148yescomplemented
55#66009C22148yescomplemented
56#65965C22148yescomplemented
57D5×C22⋊Q8C22148yescomplemented
58#65946C22148yescomplemented
59#65942C22148yescomplemented
60Q8×D20C22116yescomplemented
61#65908C22116yescomplemented
62#65885C22148yescomplemented
63#65881C22148yescomplemented
64C2×#4043C2213yes—
65C2×#4043C2213yescomplemented
66C2×#4042C2213yes—
67C2×#4040C2213yescomplemented
68C2×#4039C2213yescomplemented
69C2×D5×C4⋊C4C2216yescomplemented
70C2×D5×C4⋊C4C2213yescomplemented
71C2×#4030C2211yescharacteristic
72C2×#4030C2216yescomplemented
73C2×#4029C2216yescomplemented
74C2×#4029C2213yescomplemented
75C2×#4029C2216yescomplemented
76C2×#4028C2213yes—
77C2×D5×C22⋊C4C2216yes—
78C2×#4024C2216yescomplemented
79C2×#4024C2213yescomplemented
80C2×C4×D20C2213yes—
81C2×C4×D20C2213yescomplemented
82C2×#4018C2213yescomplemented
83C2×#4015C2213yescomplemented
84C2×#3489—51nomaximal, Sylow
85C24×D5C2313yes—
86C2×C5×#41—28no—
87C2×C5×#41C2318yes—
88C22×C5×Q8—28no—
89C22×C5×Q8C2313yes—
90C22×C5×Q8C2311yescharacteristic
91C22×C5×Q8C2318yescomplemented
92C22×C5×D4C2313yes—
93C22×C5×D4C2313yes—
94C23×C4×C5C2313yes—
95C23×C4×C5C2313yes—
96C22×C22⋊D5C2316yes—
97C22×C22⋊D5C2313yes—
98C22×C22⋊D5C2311yescharacteristic
99C22×C22⋊D5C2311yescharacteristic
100C22×C22⋊D5C2313yes—
101C23×Dic5C2313yes—
102D5×#41—2128no—
103#4147—2128no—
104C2×#713—224no—
105C2×#713D4116yescomplemented
106C2×#713C2318yes—
107C2×#713C23124yescomplemented
108C2×Q8×D5—28no—
109C2×Q8×D5—28no—
110C2×Q8×D5—224no—
111C2×Q8×D5C2318yes—
112C2×Q8×D5C2318yescomplemented
113C2×Q8×D5C23124yescomplemented
114C2×#711—224no—
115C2×#711C23124yes—
116C2×D4×D5—224no—
117C2×D4×D5C23124yes—
118C2×#709—224no—
119C2×#709—224no—
120C2×#709—224no—
121C2×#709C23124yes—
122C2×#709C23124yescomplemented
123C2×#709C23124yescomplemented
124C22×D20C2311yescharacteristic
125C22×D20C2313yes—
126C22×D20C2313yes—
127C22×C4×D5—224no—
128C22×C4×D5C2313yes—
129C22×C4×D5C2313yes—
130C22×C4×D5C2316yes—
131C22×C4×D5C2313yes—
132C22×C4×D5C2311yescharacteristic
133C22×C4×D5C23124yes—
134C22×C4×D5C2316yes—
135C22×C4×D5C2313yes—
136C22×Dic10C2313yes—
137C22×Dic10C2313yes—
138C22×Dic10C2313yes—
139C5×#124C23124yescomplemented
140C5×C22⋊Q8C23124yescomplemented
141C5×#121C23124yescomplemented
142C4×C5×Q8C2318yescomplemented
143C4×C5×D4C23124yescomplemented
144C2×C5×C4⋊C4C2313yes—
145C2×C5×C4⋊C4C2313yes—
146C2×C5×C22⋊C4C2316yes—
147C2×C5×C22⋊C4C2313yes—
148C2×C5×C22⋊C4C2311yescharacteristic
149C2×C42×C5C2313yes—
150C2×C22⋊Dic5C2316yes—
151C2×C22⋊Dic5C2313yes—
152C2×C22⋊Dic5C2313yes—
153#4092C23124yes—
154Q8×Dic5C2318yescomplemented
155#4090C23124yescomplemented
156#4085C23124yescomplemented
157#4084C23148yescomplemented
158#4084C23124yescomplemented
159#4083C23124yes—
160#4082C23124yescomplemented
161C4×C22⋊D5C23124yes—
162C4×C22⋊D5C23124yescomplemented
163C2×#685C2313yes—
164C2×#685C2313yes—
165C2×#685C2313yes—
166C2×#685C2313yes—
167C2×#685C2313yes—
168C2×#685C2311yescharacteristic
169C2×C4⋊Dic5C2313yes—
170C2×C4⋊Dic5C2316yes—
171C2×C4⋊Dic5C2313yes—
172#4070C23124yescomplemented
173#4070C23124yescomplemented
174C2×#683C2311yescharacteristic
175C2×#683C2313yes—
176C2×#683C2313yes—
177C2×#683C2316yes—
178C2×#683C2313yes—
179C2×C4×Dic5C2313yes—
180#4043C23124yes—
181#4043C23124yescomplemented
182#4042C23124yes—
183#4040C23124yescomplemented
184#4039C23124yescomplemented
185D5×C4⋊C4C23148yescomplemented
186D5×C4⋊C4C23124yescomplemented
187#4030C2318yes—
188#4030C23148yescomplemented
189#4029C23124yescomplemented
190#4029C23148yescomplemented
191#4029C23148yescomplemented
192#4028C23124yes—
193D5×C22⋊C4C23148yes—
194#4024C23124yescomplemented
195#4024C23148yescomplemented
196C4×D20C23124yes—
197C4×D20C23124yescomplemented
198#4018C23124yescomplemented
199#4015C23124yescomplemented
200C22×2−1+4—51no—
201C23×#41—51no—
202#3489—532no—
203C2×D4×Q8—51no—
204C2×D4×Q8—51no—
205C2×#548—51no—
206C2×#548D511yescharacteristic, complemented
207C2×#547—53no—
208C2×#547—53no—
209C2×#546—53no—
210C2×#546—53no—
211C2×#537—53no—
212C2×#536—53no—
213C2×#525—53no—
214C22×C22⋊Q8—53no—
215C2×#520—51no—
216C24×C5C2413yes—
217C24×C5C2411yescharacteristic
218C23×D5—212no—
219C23×D5—212no—
220C23×D5—46no—
221C23×D5C2411yescharacteristic
222C23×D5C24112yes—
223C23×D5C2413yes—
224C23×D5C2411yescharacteristic
225C5×#41—232no—
226C2×C5×Q8—232no—
227C2×C5×Q8—212no—
228C2×C5×Q8C2×D418yes—
229C2×C5×Q8C24112yes—
230C2×C5×Q8C2414yes—
231C2×C5×D4—212no—
232C2×C5×D4—46no—
233C2×C5×D4C24112yes—
234C2×C5×D4C24112yes—
235C22×C4×C5—212no—
236C22×C4×C5—212no—
237C22×C4×C5C2411yescharacteristic
238C22×C4×C5C2413yes—
239C22×C4×C5C2413yes—
240C22×C4×C5C2411yescharacteristic
241C22×C4×C5C24112yes—
242C22×C4×C5C24112yes—
243C22×C4×C5C2413yes—
244C2×C22⋊D5—212no—
245C2×C22⋊D5—224no—
246C2×C22⋊D5—24no—
247C2×C22⋊D5—24no—
248C2×C22⋊D5—46no—
249C2×C22⋊D5C24124yes—
250C2×C22⋊D5C24112yes—
251C2×C22⋊D5C2414yes—
252C2×C22⋊D5C2414yes—
253C2×C22⋊D5C24112yes—
254C22×Dic5—212no—
255C22×Dic5C2413yes—
256C22×Dic5C2413yes—
257C22×Dic5C2411yescharacteristic
258C22×Dic5C2413yes—
259C22×Dic5C24112yes—
260C22×Dic5C2411yescharacteristic
261#713—296no—
262#713C2×D4164yescomplemented
263Q8×D5—232no—
264Q8×D5—232no—
265Q8×D5—296no—
266#711—296no—
267D4×D5—296no—
268#709—296no—
269#709—296no—
270#709—296no—
271C2×D20—212no—
272C2×D20—24no—
273C2×D20C2×D4124yes—
274C2×D20C24112yes—
275C2×D20C2414yes—
276C2×D20C24112yes—
277C2×C4×D5—212no—
278C2×C4×D5—224no—
279C2×C4×D5—212no—
280C2×C4×D5—212no—
281C2×C4×D5—24no—
282C2×C4×D5—296no—
283C2×C4×D5—412no—
284C2×C4×D5C2×D4124yes—
285C2×C4×D5C2414yes—
286C2×C4×D5C24112yes—
287C2×C4×D5C24112yes—
288C2×C4×D5C24112yes—
289C2×C4×D5C24124yes—
290C2×C4×D5C24124yes—
291C2×C4×D5C24112yes—
292C2×Dic10—212no—
293C2×Dic10—212no—
294C2×Dic10—212no—
295C2×Dic10C24112yes—
296C2×Dic10C24112yes—
297C2×Dic10C24112yes—
298C5×C4⋊C4C24112yes—
299C5×C4⋊C4C24112yes—
300C5×C22⋊C4C2414yes—
301C5×C22⋊C4C24112yes—
302C5×C22⋊C4C24124yes—
303C42×C5C24112yes—
304C22⋊Dic5C24124yes—
305C22⋊Dic5C24112yes—
306C22⋊Dic5C24112yes—
307#685C24112yes—
308#685C24112yes—
309#685C24112yes—
310#685C24112yes—
311#685C24112yes—
312#685C2414yes—
313C4⋊Dic5C24112yes—
314C4⋊Dic5C24124yes—
315C4⋊Dic5C24112yes—
316#683C2414yes—
317#683C24112yes—
318#683C24112yes—
319#683C24124yes—
320#683C24112yes—
321C4×Dic5C24112yes—
322C2×2−1+4—516no—
323C2×2−1+4—1016no—
324C22×#41—516no—
325C22×#41—51no—
326C22×#41—53no—
327C22×#41—53no—
328C22×#41—53no—
329C22×#41—53no—
330C22×#41—53no—
331C22×#41—1016no—
332C22×#41C2×D511yescharacteristic
333C23×Q8—51no—
334C23×Q8—53no—
335C23×Q8—51no—
336C23×Q8C2×D511yescharacteristic, complemented
337C23×D4—53no—
338C24×C4—53no—
339D4×Q8—516no—
340D4×Q8—516no—
341#548—516no—
342#548C2×D5116yescomplemented
343#547—548no—
344#547—548no—
345#546—548no—
346#546—548no—
347#537—548no—
348#536—548no—
349C2×C4⋊Q8—53no—
350C2×C4⋊Q8—53no—
351C2×#124—53no—
352C2×#124C2×D513yescomplemented
353#525—548no—
354C2×#123—53no—
355C2×#123—53no—
356C2×#123—56no—
357C2×#123—56no—
358C2×C22⋊Q8—53no—
359C2×C22⋊Q8—53no—
360C2×C22⋊Q8—53no—
361C2×C22⋊Q8—548no—
362C2×C22⋊Q8—53no—
363C2×C22⋊Q8—53no—
364C2×C22⋊Q8—53no—
365C2×C22⋊Q8—56no—
366C2×C22⋊Q8—53no—
367C2×C22⋊Q8C2×D513yescomplemented
368C2×#121—56no—
369C2×#121—53no—
370C2×#121—53no—
371C2×#121—51no—
372C2×#121—56no—
373C2×#121C2×D513yescomplemented
374C2×#120—53no—
375C2×#120—53no—
376#520—516no—
377C2×C4×Q8—51no—
378C2×C4×Q8C2×D511yescharacteristic, complemented
379C2×C4×D4—53no—
380C2×C4×D4—53no—
381C2×C4×D4—53no—
382C2×C4×D4—53no—
383C2×C4×D4—53no—
384C2×C4×D4C2×D513yescomplemented
385C2×#117—53no—
386C22×C4⋊C4—53no—
387C22×C4⋊C4—56no—
388C22×C22⋊C4—56no—
389C23×C5—26no—
390C23×C5—22no—
391C23×C5—22no—
392C23×C5—26no—
393C23×C5—26no—
394C23×C5—22no—
395C23×C5C2516yes—
396C23×C5C2512yes—
397C23×C5C2511yescharacteristic
398C22×D5—22no—
399C22×D5—26no—
400C22×D5—26no—
401C22×D5—22no—
402C22×D5—22no—
403C22×D5—22no—
404C22×D5—22no—
405C22×D5—224no—
406C22×D5—224no—
407C22×D5—412no—
408C22×D5—448no—
409C22×D5C22×D4112yes—
410C22×D52−1+414yescomplemented
411C22×D5C2512yes—
412C22×D5C2516yes—
413C22×D5C2512yes—
414C5×Q8—224no—
415C5×Q8C22×D4116yes—
416C5×D4—224no—
417C5×D4—412no—
418C2×C4×C5—26no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—26no—
422C2×C4×C5—224no—
423C2×C4×C5—224no—
424C2×C4×C5C22×D4112yes—
425C2×C4×C5C2516yes—
426C2×C4×C5C2512yes—
427C2×C4×C5C2512yes—
428C2×C4×C5C2516yes—
429C2×C4×C5C2516yes—
430C22⋊D5—224no—
431C22⋊D5—248no—
432C22⋊D5—28no—
433C22⋊D5—28no—
434C22⋊D5—412no—
435C2×Dic5—26no—
436C2×Dic5—26no—
437C2×Dic5—22no—
438C2×Dic5—26no—
439C2×Dic5—224no—
440C2×Dic5C22×D414yes—
441C2×Dic5C2512yes—
442C2×Dic5C2516yes—
443C2×Dic5C2516yes—
444C2×Dic5C2516yes—
445C2×Dic5C2512yes—
446D20—224no—
447D20—28no—
448D20C22×D4148yes—
449C4×D5—224no—
450C4×D5—248no—
451C4×D5—224no—
452C4×D5—224no—
453C4×D5—28no—
454C4×D5—424no—
455C4×D5C22×D4148yes—
456Dic10—224no—
457Dic10—224no—
458Dic10—224no—
459C25—53no—
4602−1+4—10128no—
461C2×#41—28no—
462C2×#41—516no—
463C2×#41—58no—
464C2×#41—524no—
465C2×#41—524no—
466C2×#41—524no—
467C2×#41—524no—
468C2×#41—524no—
469C2×#41—1024no—
470C2×#41—1024no—
471C2×#41—1024no—
472C2×#41—1024no—
473C2×#41—1024no—
474C2×#41—10128no—
475C2×#41C22×D518yes—
476C22×Q8—28no—
477C22×Q8—524no—
478C22×Q8—58no—
479C22×Q8—58no—
480C22×Q8—53no—
481C22×Q8—53no—
482C22×Q8—53no—
483C22×Q8—1024no—
484C22×Q8—108no—
485C22×Q8—108no—
486C22×Q8C22×D513yes—
487C22×Q8C22×D511yescharacteristic
488C22×Q8C22×D518yescomplemented
489C22×D4—51no—
490C22×D4—53no—
491C22×D4—51no—
492C22×D4—56no—
493C22×D4—53no—
494C22×D4—524no—
495C22×D4—53no—
496C22×D4—51no—
497C22×D4—53no—
498C22×D4—1024no—
499C22×D4C22×D513yes—
500C22×D4C22×D513yes—
501C23×C4—53no—
502C23×C4—53no—
503C23×C4—56no—
504C23×C4—53no—
505C23×C4—53no—
506C23×C4—53no—
507C23×C4—51no—
508C23×C4—524no—
509C23×C4—56no—
510C23×C4—1024no—
511C23×C4C22×D513yes—
512C23×C4C22×D513yes—
513C4⋊Q8—524no—
514C4⋊Q8—524no—
515#124—524no—
516#124C22×D5124yescomplemented
517#123—524no—
518#123—524no—
519#123—548no—
520#123—548no—
521C22⋊Q8—524no—
522C22⋊Q8—524no—
523C22⋊Q8—524no—
524C22⋊Q8—524no—
525C22⋊Q8—524no—
526C22⋊Q8—524no—
527C22⋊Q8—548no—
528C22⋊Q8—524no—
529C22⋊Q8C22×D5124yescomplemented
530#121—524no—
531#121—548no—
532#121—524no—
533#121—58no—
534#121—548no—
535#121C22×D5124yescomplemented
536#120—524no—
537#120—524no—
538C4×Q8—58no—
539C4×Q8C22×D518yescomplemented
540C4×D4—524no—
541C4×D4—524no—
542C4×D4—524no—
543C4×D4—524no—
544C4×D4—524no—
545C4×D4C22×D5124yescomplemented
546#117—524no—
547C2×C4⋊C4—53no—
548C2×C4⋊C4—53no—
549C2×C4⋊C4—53no—
550C2×C4⋊C4—56no—
551C2×C4⋊C4—56no—
552C2×C4⋊C4—51no—
553C2×C4⋊C4—53no—
554C2×C4⋊C4—53no—
555C2×C4⋊C4—524no—
556C2×C4⋊C4—548no—
557C2×C4⋊C4C22×D513yes—
558C2×C4⋊C4C22×D513yes—
559C2×C22⋊C4—56no—
560C2×C22⋊C4—53no—
561C2×C22⋊C4—53no—
562C2×C22⋊C4—53no—
563C2×C22⋊C4—53no—
564C2×C22⋊C4—53no—
565C2×C22⋊C4—53no—
566C2×C22⋊C4—51no—
567C2×C22⋊C4—53no—
568C2×C22⋊C4—548no—
569C2×C22⋊C4C22×D516yes—
570C2×C22⋊C4C22×D511yescharacteristic
571C2×C22⋊C4C22×D513yes—
572C2×C42—53no—
573C2×C42C22×D513yes—
574C22×C5—26no—
575C22×C5—22no—
576C22×C5—22no—
577C22×C5—26no—
578C22×C5—26no—
579C22×C5—22no—
580C22×C5—412no—
581C22×C5—44no—
582C22×C5C23×D412yes—
583C22×C5C2×2−1+412yes—
584C22×C5#58512yes—
585C22×C5C2611yescharacteristic
586C2×D5—22no—
587C2×D5—26no—
588C2×D5—26no—
589C2×D5—22no—
590C2×D5—28no—
591C2×D5—224no—
592C2×D5—22no—
593C2×D5—22no—
594C2×D5—22no—
595C2×D5—448no—
596C2×D5—44no—
597C2×D5C23×D4112yes—
598C2×D5C2×2−1+414yescomplemented
599C4×C5—26no—
600C4×C5—22no—
601C4×C5—22no—
602C4×C5—26no—
603C4×C5C23×D4112yes—
604Dic5—26no—
605Dic5—26no—
606Dic5—22no—
607Dic5—26no—
608Dic5C23×D414yes—
609C24—51no—
610C24—53no—
611C24—51no—
612C24—512no—
613C24—1012no—
614C24—1012no—
615C24—206no—
616C24C23×D513yes—
617C24C23×D511yescharacteristic
618#41—232no—
619#41—564no—
620#41—1096no—
621#41—1096no—
622#41—1096no—
623#41—1096no—
624#41—1096no—
625C2×Q8—232no—
626C2×Q8—212no—
627C2×Q8—512no—
628C2×Q8—512no—
629C2×Q8—512no—
630C2×Q8—1012no—
631C2×Q8—1096no—
632C2×Q8—1032no—
633C2×Q8—1032no—
634C2×Q8—1012no—
635C2×Q8—1012no—
636C2×Q8D4×D518yes—
637C2×Q8C23×D5112yes—
638C2×Q8C23×D514yes—
639C2×D4—212no—
640C2×D4—46no—
641C2×D4—54no—
642C2×D4—512no—
643C2×D4—54no—
644C2×D4—524no—
645C2×D4—512no—
646C2×D4—524no—
647C2×D4—512no—
648C2×D4—54no—
649C2×D4—512no—
650C2×D4—1012no—
651C2×D4—104no—
652C2×D4—104no—
653C2×D4—1096no—
654C2×D4—1024no—
655C2×D4—1012no—
656C2×D4—104no—
657C2×D4—206no—
658C2×D4C23×D5112yes—
659C2×D4C23×D5112yes—
660C22×C4—212no—
661C22×C4—212no—
662C22×C4—51no—
663C22×C4—524no—
664C22×C4—512no—
665C22×C4—512no—
666C22×C4—51no—
667C22×C4—53no—
668C22×C4—53no—
669C22×C4—53no—
670C22×C4—524no—
671C22×C4—512no—
672C22×C4—512no—
673C22×C4—512no—
674C22×C4—54no—
675C22×C4—524no—
676C22×C4—104no—
677C22×C4—1096no—
678C22×C4—1012no—
679C22×C4—1024no—
680C22×C4—1012no—
681C22×C4—1012no—
682C22×C4—1012no—
683C22×C4—2012no—
684C22×C4C23×D5112yes—
685C22×C4C23×D5112yes—
686C22×C4C23×D511yescharacteristic
687C22×C4C23×D513yes—
688C22×C4C23×D513yes—
689C22×C4C23×D511yescharacteristic
690C22×C4C23×D513yes—
691C4⋊C4—512no—
692C4⋊C4—512no—
693C4⋊C4—512no—
694C4⋊C4—524no—
695C4⋊C4—524no—
696C4⋊C4—54no—
697C4⋊C4—512no—
698C4⋊C4—512no—
699C4⋊C4C23×D5112yes—
700C4⋊C4C23×D5112yes—
701C22⋊C4—524no—
702C22⋊C4—512no—
703C22⋊C4—512no—
704C22⋊C4—512no—
705C22⋊C4—512no—
706C22⋊C4—512no—
707C22⋊C4—512no—
708C22⋊C4—54no—
709C22⋊C4—512no—
710C22⋊C4C23×D5124yes—
711C22⋊C4C23×D514yes—
712C22⋊C4C23×D5112yes—
713C42—512no—
714C42C23×D5112yes—
715C2×C5—46no—
716C2×C5—42no—
717C2×C5#348914yescomplemented
718C2×C5C24×D411yescharacteristic
719C2×C5C22×2−1+411yescharacteristic
720C2×C5C2×#58511yescharacteristic
721D5—24no—
722D5—212no—
723D5—42no—
724C23—22no—
725C23—26no—
726C23—22no—
727C23—26no—
728C23—22no—
729C23—26no—
730C23—512no—
731C23—54no—
732C23—52no—
733C23—56no—
734C23—52no—
735C23—1024no—
736C23—1024no—
737C23—102no—
738C23—106no—
739C23—102no—
740C23—106no—
741C23—102no—
742C23—102no—
743C23—102no—
744C23—2012no—
745C23—2048no—
746C23C24×D516yes—
747C23C24×D512yes—
748C23C24×D511yescharacteristic
749Q8—224no—
750Q8—1024no—
751Q8—1024no—
752Q8—1024no—
753Q8C2×D4×D5116yes—
754D4—224no—
755D4—412no—
756D4—548no—
757D4—1024no—
758D4—108no—
759D4—108no—
760D4—1048no—
761D4—1024no—
762D4—108no—
763D4—2012no—
764C2×C4—22no—
765C2×C4—26no—
766C2×C4—26no—
767C2×C4—22no—
768C2×C4—224no—
769C2×C4—224no—
770C2×C4—54no—
771C2×C4—52no—
772C2×C4—548no—
773C2×C4—52no—
774C2×C4—56no—
775C2×C4—56no—
776C2×C4—56no—
777C2×C4—108no—
778C2×C4—1024no—
779C2×C4—1048no—
780C2×C4—1024no—
781C2×C4—106no—
782C2×C4—106no—
783C2×C4—106no—
784C2×C4—102no—
785C2×C4—1024no—
786C2×C4—1024no—
787C2×C4—2024no—
788C2×C4C2×D4×D5112yes—
789C2×C4C24×D512yes—
790C2×C4C24×D516yes—
791C2×C4C24×D516yes—
792C2×C4C24×D512yes—
793C2×C4C24×D516yes—
794C5C2×#348911yescharacteristic, complemented, Sylow
795C22—22no—
796C22—26no—
797C22—22no—
798C22—26no—
799C22—22no—
800C22—26no—
801C22—412no—
802C22—44no—
803C22—512no—
804C22—54no—
805C22—102no—
806C22—106no—
807C22—102no—
808C22—106no—
809C22—108no—
810C22—1024no—
811C22—102no—
812C22—102no—
813C22—102no—
814C22—2048no—
815C22—204no—
816C22C22×D4×D512yes—
817C22#6628312yes—
818C22D5×2−1+412yes—
819C22C25×D511yescharacteristic
820C4—22no—
821C4—26no—
822C4—26no—
823C4—22no—
824C4—54no—
825C4—106no—
826C4—106no—
827C4—106no—
828C4—102no—
829C4C22×D4×D5112yes—
830C2—46no—
831C2—42no—
832C2—104no—
833C2—1012no—
834C2—202no—
835C2#1061861514yesdirect product factor
836C2C23×D4×D511yescharacteristic
837C2C2×#6628311yescharacteristic
838C2C2×D5×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#548C2
socleC23×C5C25
hypercenterC2×#548D5
hypocenterC5C2×#3489
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×D5×#41C2semidirect
2. C22×#4147C2semidirect
3. C2×C5×#548C2semidirect
4. C2×#66165C2semidirect
5. C2×Q8×C22⋊D5C2semidirect
6. #10618615C2direct (N × H)
7. C2×#66010C2semidirect
8. C2×#66009C2semidirect
9. C2×#65965C2semidirect
10. C2×D5×C22⋊Q8C2semidirect
11. C2×#65946C2semidirect
12. C2×#65942C2semidirect
13. C2×Q8×D20C2semidirect
14. C2×#65908C2semidirect
15. C2×#65885C2semidirect
16. C2×#65881C2semidirect
18. C23×C5×Q8C22semidirect
20. C2×D5×#41C22semidirect
22. C2×#4147C22semidirect
24. C22×#713C22semidirect
26. C22×Q8×D5C22semidirect
27. C22×Q8×D5C22semidirect
31. C22×#709C22semidirect
32. C22×#709C22semidirect
34. C5×#548C22semidirect
35. C2×C5×#124C22semidirect
36. C2×C5×C22⋊Q8C22semidirect
37. C2×C5×#121C22semidirect
38. C2×C4×C5×Q8C22semidirect
39. C2×C4×C5×D4C22semidirect
40. #66165C22semidirect
41. Q8×C22⋊D5C22semidirect
43. C2×Q8×Dic5C22semidirect
44. C2×#4090C22semidirect
45. C2×#4085C22semidirect
46. C2×#4084C22semidirect
47. C2×#4084C22semidirect
49. C2×#4082C22semidirect
51. C2×C4×C22⋊D5C22semidirect
52. C2×#4070C22semidirect
53. C2×#4070C22semidirect
54. #66010C22semidirect
55. #66009C22semidirect
56. #65965C22semidirect
57. D5×C22⋊Q8C22semidirect
58. #65946C22semidirect
59. #65942C22semidirect
60. Q8×D20C22semidirect
61. #65908C22semidirect
62. #65885C22semidirect
63. #65881C22semidirect
65. C2×#4043C22semidirect
67. C2×#4040C22semidirect
68. C2×#4039C22semidirect
69. C2×D5×C4⋊C4C22semidirect
70. C2×D5×C4⋊C4C22semidirect
72. C2×#4030C22semidirect
73. C2×#4029C22semidirect
74. C2×#4029C22semidirect
75. C2×#4029C22semidirect
78. C2×#4024C22semidirect
79. C2×#4024C22semidirect
81. C2×C4×D20C22semidirect
82. C2×#4018C22semidirect
83. C2×#4015C22semidirect
91. C22×C5×Q8C23semidirect
105. C2×#713D4semidirect
107. C2×#713C23semidirect
112. C2×Q8×D5C23semidirect
113. C2×Q8×D5C23semidirect
122. C2×#709C23semidirect
123. C2×#709C23semidirect
139. C5×#124C23semidirect
140. C5×C22⋊Q8C23semidirect
141. C5×#121C23semidirect
142. C4×C5×Q8C23semidirect
143. C4×C5×D4C23semidirect
154. Q8×Dic5C23semidirect
155. #4090C23semidirect
156. #4085C23semidirect
157. #4084C23semidirect
158. #4084C23semidirect
160. #4082C23semidirect
162. C4×C22⋊D5C23semidirect
172. #4070C23semidirect
173. #4070C23semidirect
181. #4043C23semidirect
183. #4040C23semidirect
184. #4039C23semidirect
185. D5×C4⋊C4C23semidirect
186. D5×C4⋊C4C23semidirect
188. #4030C23semidirect
189. #4029C23semidirect
190. #4029C23semidirect
191. #4029C23semidirect
194. #4024C23semidirect
195. #4024C23semidirect
197. C4×D20C23semidirect
198. #4018C23semidirect
199. #4015C23semidirect
206. C2×#548D5semidirect
262. #713C2×D4semidirect
336. C23×Q8C2×D5semidirect
342. #548C2×D5semidirect
352. C2×#124C2×D5semidirect
367. C2×C22⋊Q8C2×D5semidirect
373. C2×#121C2×D5semidirect
378. C2×C4×Q8C2×D5semidirect
384. C2×C4×D4C2×D5semidirect
410. C22×D52−1+4semidirect
488. C22×Q8C22×D5semidirect
516. #124C22×D5semidirect
529. C22⋊Q8C22×D5semidirect
535. #121C22×D5semidirect
539. C4×Q8C22×D5semidirect
545. C4×D4C22×D5semidirect
598. C2×D5C2×2−1+4semidirect
717. C2×C5#3489semidirect
794. C5C2×#3489semidirect
835. C2#10618615direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×#412
C22×#41472
C2×C5×#5482
C2×#661652
C2×Q8×C22⋊D52
#106186152
C2×#660102
C2×#660092
C2×#659652
C2×D5×C22⋊Q82
C2×#659462
C2×#659422
C2×Q8×D202
C2×#659082
C2×#658852
C2×#658812
C2×#34895