Finite Group Databasebeta

← C2×#10618636 #13007462

Subgroups — C2×#10618636 #13007462

Order 1280.

11254 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4150C211yesmaximal, characteristic, complemented
2C23×Q8×D5C211yesmaximal, characteristic, complemented
3C2×C5×#548C211yesmaximal, characteristic, complemented
4C2×#66165C211yesmaximal, characteristic, complemented
5C2×Q8×C22⋊D5C211yesmaximal, characteristic, complemented
6#10618636C2132yesmaximal, direct product factor
7C2×#66011C213yesmaximal, complemented
8C2×#66009C213yesmaximal, complemented
9C2×#65962C213yesmaximal, complemented
10C2×#65966C213yesmaximal, complemented
11C2×#65932C213yesmaximal, complemented
12C2×#65940C213yesmaximal, complemented
13C2×Q8×D20C211yesmaximal, characteristic, complemented
14C2×#65906C211yesmaximal, characteristic, complemented
15C2×#65881C213yesmaximal, complemented
16C2×D4×Dic10C213yesmaximal, complemented
17C22×C5×#41C2211yescharacteristic, complemented
18C23×C5×Q8C2211yescharacteristic
19C2×#4150—216no—
20C2×#4150C22116yescomplemented
21C22×Q8×D5—216no—
22C22×Q8×D5C2213yes—
23C22×Q8×D5C2213yes—
24C22×Q8×D5C2211yescharacteristic
25C22×Q8×D5C2211yescharacteristic
26C22×Q8×D5C22116yescomplemented
27C22×Q8×D5C2211yescharacteristic, complemented
28C22×#711C2213yes—
29C22×#711C2213yescomplemented
30C22×#709C2213yes—
31C23×C4×D5C2213yes—
32C23×Dic10C2213yes—
33C23×Dic10C2213yescomplemented
34C5×#548C22116yescomplemented
35C2×C5×#124C2213yescomplemented
36C2×C5×C22⋊Q8C2213yescomplemented
37C2×C5×#121C2213yes—
38C2×C4×C5×Q8C2211yescharacteristic, complemented
39C2×C4×C5×D4C2213yes—
40#66165C22116yescomplemented
41Q8×C22⋊D5C22116yescomplemented
42C2×#4092C2213yescomplemented
43C2×Q8×Dic5C2211yescharacteristic, complemented
44C2×#4090C2213yescomplemented
45C2×#4085C2213yes—
46C2×#4084C2213yes—
47C2×#4083C2213yes—
48C2×#4082C2213yescomplemented
49C2×D4×Dic5C2216yes—
50C2×C4×C22⋊D5C2213yes—
51C2×C4×C22⋊D5C2213yes—
52C2×#4070C2213yes—
53C2×#4070C2213yescomplemented
54#66011C22148yescomplemented
55#66009C22148yescomplemented
56#65966C22148yescomplemented
57#65962C22148yescomplemented
58#65940C22148yescomplemented
59#65932C22148yescomplemented
60Q8×D20C22116yescomplemented
61#65906C22116yescomplemented
62#65881C22148yescomplemented
63D4×Dic10C22148yescomplemented
64C2×#4043C2213yes—
65C2×#4043C2213yescomplemented
66C2×#4042C2213yes—
67C2×#4040C2213yes—
68C2×#4038C2213yes—
69C2×#4034C2216yescomplemented
70C2×#4033C2213yescomplemented
71C2×#4031C2216yescomplemented
72C2×#4030C2213yes—
73C2×#4029C2216yes—
74C2×#4029C2213yes—
75C2×#4028C2211yescharacteristic
76C2×#4027C2216yes—
77C2×#4024C2213yes—
78C2×#4024C2216yescomplemented
79C2×#4024C2216yescomplemented
80C2×C4×D20C2213yes—
81C2×#4018C2213yes—
82C2×#4015C2213yescomplemented
83C2×C4×Dic10C2213yescomplemented
84C2×#3486—51nomaximal, Sylow
85C24×D5C2311yescharacteristic
86C2×C5×#41—28no—
87C2×C5×#41C2318yescomplemented
88C22×C5×Q8—28no—
89C22×C5×Q8C2313yes—
90C22×C5×Q8C2318yes—
91C22×C5×Q8C2311yescharacteristic
92C22×C5×D4C2313yes—
93C22×C5×D4C2313yes—
94C23×C4×C5C2313yes—
95C23×C4×C5C2313yes—
96C22×C22⋊D5C2313yes—
97C22×C22⋊D5C2311yescharacteristic
98C22×C22⋊D5C2313yes—
99C22×C22⋊D5C2313yes—
100C23×Dic5C2313yes—
101C23×Dic5C2316yes—
102#4150—2128no—
103C2×Q8×D5—28no—
104C2×Q8×D5—28no—
105C2×Q8×D5—2128no—
106C2×Q8×D5—224no—
107C2×Q8×D5—224no—
108C2×Q8×D5D4116yescomplemented
109C2×Q8×D5C2318yes—
110C2×Q8×D5C23124yes—
111C2×Q8×D5C23124yes—
112C2×Q8×D5C2318yes—
113C2×Q8×D5C2318yescomplemented
114C2×#711—224no—
115C2×#711—224no—
116C2×#711C23124yes—
117C2×#711C23124yescomplemented
118C2×#709—224no—
119C2×#709C23124yes—
120C22×D20C2311yescharacteristic
121C22×D20C2311yescharacteristic
122C22×C4×D5—224no—
123C22×C4×D5C2313yes—
124C22×C4×D5C2313yes—
125C22×C4×D5C2313yes—
126C22×C4×D5C2313yes—
127C22×C4×D5C23124yes—
128C22×C4×D5C2313yes—
129C22×Dic10—224no—
130C22×Dic10—224no—
131C22×Dic10C2313yes—
132C22×Dic10C2313yes—
133C22×Dic10C2313yes—
134C22×Dic10C2316yes—
135C22×Dic10C23124yes—
136C22×Dic10C2313yes—
137C22×Dic10C23124yescomplemented
138C5×#124C23124yescomplemented
139C5×C22⋊Q8C23124yescomplemented
140C5×#121C23124yes—
141C4×C5×Q8C2318yescomplemented
142C4×C5×D4C23124yes—
143C2×C5×C4⋊C4C2313yes—
144C2×C5×C4⋊C4C2313yes—
145C2×C5×C22⋊C4C2311yescharacteristic
146C2×C5×C22⋊C4C2313yes—
147C2×C5×C22⋊C4C2316yes—
148C2×C42×C5C2313yes—
149C2×C22⋊Dic5C2313yes—
150C2×C22⋊Dic5C2313yes—
151C2×C22⋊Dic5C2316yes—
152#4092C23124yescomplemented
153Q8×Dic5C2318yescomplemented
154#4090C23124yescomplemented
155#4085C23124yes—
156#4084C23124yes—
157#4083C23124yes—
158#4082C23124yescomplemented
159D4×Dic5C23148yes—
160C4×C22⋊D5C23124yes—
161C4×C22⋊D5C23124yes—
162C2×#685C2311yescharacteristic
163C2×#685C2313yes—
164C2×#685C2313yes—
165C2×#685C2313yes—
166C2×#685C2311yescharacteristic
167C2×#685C2313yes—
168C2×C4⋊Dic5C2313yes—
169C2×C4⋊Dic5C2313yes—
170C2×C4⋊Dic5C2316yes—
171#4070C23124yes—
172#4070C23124yescomplemented
173C2×#683C2313yes—
174C2×#683C2313yes—
175C2×#683C2313yes—
176C2×#683C2313yes—
177C2×#683C2316yes—
178C2×C4×Dic5C2316yes—
179C2×C4×Dic5C2313yes—
180#4043C23124yes—
181#4043C23124yescomplemented
182#4042C23124yes—
183#4040C23124yes—
184#4038C23124yes—
185#4034C23148yescomplemented
186#4033C23124yescomplemented
187#4031C23148yescomplemented
188#4030C23124yes—
189#4029C23124yes—
190#4029C23148yes—
191#4028C2318yes—
192#4027C23148yes—
193#4024C23124yes—
194#4024C23148yescomplemented
195#4024C23148yescomplemented
196C4×D20C23124yes—
197#4018C23124yes—
198#4015C23124yescomplemented
199C4×Dic10C23124yescomplemented
200C22×2−1+4—51no—
201C24×Q8—51no—
202#3486—532no—
203C2×D4×Q8—51no—
204C2×D4×Q8—53no—
205C2×D4×Q8—51no—
206C2×D4×Q8—53no—
207C2×#548—51no—
208C2×#548—53no—
209C2×#548—53no—
210C2×#548D511yescharacteristic, complemented
211C2×#536—53no—
212C2×#536—53no—
213C2×#525—53no—
214C2×#525—53no—
215C2×#519—51no—
216C24×C5C2413yes—
217C24×C5C2411yescharacteristic
218C23×D5—24no—
219C23×D5—24no—
220C23×D5—24no—
221C23×D5C2414yes—
222C23×D5C2411yescharacteristic
223C23×D5C2411yescharacteristic
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—212no—
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—24no—
245C2×C22⋊D5—212no—
246C2×C22⋊D5—212no—
247C2×C22⋊D5—212no—
248C2×C22⋊D5C24112yes—
249C2×C22⋊D5C24112yes—
250C2×C22⋊D5C24112yes—
251C2×C22⋊D5C2414yes—
252C22×Dic5—212no—
253C22×Dic5—224no—
254C22×Dic5C2413yes—
255C22×Dic5C2411yescharacteristic
256C22×Dic5C2413yes—
257C22×Dic5C2413yes—
258C22×Dic5C24112yes—
259C22×Dic5C24124yes—
260C22×Dic5C2413yes—
261Q8×D5—232no—
262Q8×D5—232no—
263Q8×D5—296no—
264Q8×D5—296no—
265Q8×D5C2×D4164yescomplemented
266#711—296no—
267#711—296no—
268#709—296no—
269C2×D20—24no—
270C2×D20—24no—
271C2×D20C2414yes—
272C2×D20C2414yes—
273C2×C4×D5—212no—
274C2×C4×D5—212no—
275C2×C4×D5—212no—
276C2×C4×D5—212no—
277C2×C4×D5—296no—
278C2×C4×D5C2×D4124yes—
279C2×C4×D5C24112yes—
280C2×C4×D5C24112yes—
281C2×C4×D5C24112yes—
282C2×C4×D5C24112yes—
283C2×C4×D5C24112yes—
284C2×Dic10—212no—
285C2×Dic10—212no—
286C2×Dic10—212no—
287C2×Dic10—224no—
288C2×Dic10—296no—
289C2×Dic10—296no—
290C2×Dic10C2×D4124yes—
291C2×Dic10C24112yes—
292C2×Dic10C24124yes—
293C2×Dic10C24112yes—
294C2×Dic10C24112yes—
295C2×Dic10C24112yes—
296C5×C4⋊C4C24112yes—
297C5×C4⋊C4C24112yes—
298C5×C22⋊C4C2414yes—
299C5×C22⋊C4C24112yes—
300C5×C22⋊C4C24124yes—
301C42×C5C24112yes—
302C22⋊Dic5C24112yes—
303C22⋊Dic5C24112yes—
304C22⋊Dic5C24124yes—
305#685C2414yes—
306#685C24112yes—
307#685C24112yes—
308#685C24112yes—
309#685C2414yes—
310#685C24112yes—
311C4⋊Dic5C24112yes—
312C4⋊Dic5C24112yes—
313C4⋊Dic5C24124yes—
314#683C24112yes—
315#683C24112yes—
316#683C24112yes—
317#683C24112yes—
318#683C24124yes—
319C4×Dic5C24124yes—
320C4×Dic5C24112yes—
321C2×2−1+4—516no—
322C2×2−1+4—1016no—
323C22×#41—53no—
324C22×#41—53no—
325C22×#41—53no—
326C22×#41C2×D511yescharacteristic, complemented
327C23×Q8—51no—
328C23×Q8—53no—
329C23×Q8—53no—
330C23×Q8—51no—
331C23×Q8—516no—
332C23×Q8—51no—
333C23×Q8—53no—
334C23×Q8—53no—
335C23×Q8—1016no—
336C23×Q8C2×D511yescharacteristic
337C24×C4—53no—
338D4×Q8—516no—
339D4×Q8—548no—
340D4×Q8—516no—
341D4×Q8—548no—
342#548—516no—
343#548—548no—
344#548—548no—
345#548C2×D5116yescomplemented
346#536—548no—
347#536—548no—
348C2×C4⋊Q8—53no—
349C2×C4⋊Q8—56no—
350C2×C4⋊Q8—53no—
351C2×#124—53no—
352C2×#124—56no—
353C2×#124C2×D513yescomplemented
354#525—548no—
355#525—548no—
356C2×#123—53no—
357C2×#123—56no—
358C2×#123—53no—
359C2×C22⋊Q8—53no—
360C2×C22⋊Q8—53no—
361C2×C22⋊Q8—53no—
362C2×C22⋊Q8—53no—
363C2×C22⋊Q8—53no—
364C2×C22⋊Q8—53no—
365C2×C22⋊Q8—53no—
366C2×C22⋊Q8—56no—
367C2×C22⋊Q8—56no—
368C2×C22⋊Q8C2×D513yescomplemented
369C2×#121—53no—
370C2×#121—53no—
371C2×#121—53no—
372C2×#121C2×D513yes—
373C2×#120—53no—
374C2×#120—51no—
375#519—516no—
376C2×C4×Q8—51no—
377C2×C4×Q8—53no—
378C2×C4×Q8—53no—
379C2×C4×Q8C2×D511yescharacteristic, complemented
380C2×C4×D4—56no—
381C2×C4×D4—53no—
382C2×C4×D4—53no—
383C2×C4×D4—56no—
384C2×C4×D4—53no—
385C2×C4×D4C2×D513yes—
386C2×#117—53no—
387C2×#117—53no—
388C23×C5—22no—
389C23×C5—22no—
390C23×C5—26no—
391C23×C5—26no—
392C23×C5—26no—
393C23×C52−1+414yescomplemented
394C23×C5C2516yes—
395C23×C5C2512yes—
396C23×C5C2511yescharacteristic
397C22×D5—232no—
398C22×D5—22no—
399C22×D5—22no—
400C22×D5—22no—
401C22×D5—22no—
402C22×D5—28no—
403C22×D5—28no—
404C22×D5—28no—
405C22×D5—22no—
406C22×D5—22no—
407C22×D5—22no—
408C22×D5C22×D414yes—
409C22×D52−1+414yescomplemented
410C22×D5C2512yes—
411C22×D5C2512yes—
412C22×D5C2512yes—
413C5×Q8—224no—
414C5×Q8C22×D4116yes—
415C5×D4—224no—
416C5×D4—224no—
417C2×C4×C5—22no—
418C2×C4×C5—26no—
419C2×C4×C5—22no—
420C2×C4×C5—26no—
421C2×C4×C5—224no—
422C2×C4×C5—224no—
423C2×C4×C5C22×D4112yes—
424C2×C4×C5C2516yes—
425C2×C4×C5C2512yes—
426C2×C4×C5C2516yes—
427C2×C4×C5C2512yes—
428C2×C4×C5C2516yes—
429C22⋊D5—28no—
430C22⋊D5—224no—
431C22⋊D5—224no—
432C22⋊D5—224no—
433C2×Dic5—26no—
434C2×Dic5—26no—
435C2×Dic5—22no—
436C2×Dic5—26no—
437C2×Dic5—224no—
438C2×Dic5—248no—
439C2×Dic5C22×D4112yes—
440C2×Dic5C2512yes—
441C2×Dic5C2516yes—
442C2×Dic5C2516yes—
443C2×Dic5C2516yes—
444C2×Dic5C2516yes—
445D20—28no—
446D20—28no—
447C4×D5—224no—
448C4×D5—224no—
449C4×D5—224no—
450C4×D5—224no—
451C4×D5C22×D4148yes—
452Dic10—224no—
453Dic10—224no—
454Dic10—224no—
455Dic10—248no—
456Dic10C22×D4148yes—
457C25—51no—
4582−1+4—10128no—
459C2×#41—28no—
460C2×#41—524no—
461C2×#41—524no—
462C2×#41—524no—
463C2×#41—1024no—
464C2×#41—1024no—
465C2×#41—1024no—
466C2×#41C22×D518yescomplemented
467C22×Q8—28no—
468C22×Q8—516no—
469C22×Q8—58no—
470C22×Q8—524no—
471C22×Q8—524no—
472C22×Q8—58no—
473C22×Q8—58no—
474C22×Q8—53no—
475C22×Q8—56no—
476C22×Q8—53no—
477C22×Q8—53no—
478C22×Q8—53no—
479C22×Q8—524no—
480C22×Q8—524no—
481C22×Q8—1024no—
482C22×Q8—1024no—
483C22×Q8—1024no—
484C22×Q8—10128no—
485C22×Q8—1024no—
486C22×Q8—108no—
487C22×Q8—108no—
488C22×Q8C22×D513yes—
489C22×Q8C22×D518yes—
490C22×Q8C22×D511yescharacteristic
491C22×D4—53no—
492C22×D4—51no—
493C22×D4—53no—
494C22×D4—53no—
495C22×D4—51no—
496C22×D4—51no—
497C22×D4C22×D513yes—
498C22×D4C22×D513yes—
499C23×C4—53no—
500C23×C4—53no—
501C23×C4—56no—
502C23×C4—53no—
503C23×C4—53no—
504C23×C4—53no—
505C23×C4—53no—
506C23×C4—524no—
507C23×C4—1024no—
508C23×C4C22×D513yes—
509C23×C4C22×D513yes—
510C4⋊Q8—524no—
511C4⋊Q8—548no—
512C4⋊Q8—524no—
513#124—524no—
514#124—548no—
515#124C22×D5124yescomplemented
516#123—524no—
517#123—548no—
518#123—524no—
519C22⋊Q8—524no—
520C22⋊Q8—524no—
521C22⋊Q8—524no—
522C22⋊Q8—524no—
523C22⋊Q8—524no—
524C22⋊Q8—524no—
525C22⋊Q8—524no—
526C22⋊Q8—548no—
527C22⋊Q8—548no—
528C22⋊Q8C22×D5124yescomplemented
529#121—524no—
530#121—524no—
531#121—524no—
532#121C22×D5124yes—
533#120—524no—
534#120—58no—
535C4×Q8—58no—
536C4×Q8—524no—
537C4×Q8—524no—
538C4×Q8C22×D518yescomplemented
539C4×D4—548no—
540C4×D4—524no—
541C4×D4—524no—
542C4×D4—548no—
543C4×D4—524no—
544C4×D4C22×D5124yes—
545#117—524no—
546#117—524no—
547C2×C4⋊C4—53no—
548C2×C4⋊C4—53no—
549C2×C4⋊C4—53no—
550C2×C4⋊C4—53no—
551C2×C4⋊C4—53no—
552C2×C4⋊C4—56no—
553C2×C4⋊C4—56no—
554C2×C4⋊C4—53no—
555C2×C4⋊C4C22×D513yes—
556C2×C4⋊C4C22×D513yes—
557C2×C22⋊C4—53no—
558C2×C22⋊C4—53no—
559C2×C22⋊C4—56no—
560C2×C22⋊C4—53no—
561C2×C22⋊C4—51no—
562C2×C22⋊C4—51no—
563C2×C22⋊C4—53no—
564C2×C22⋊C4—53no—
565C2×C22⋊C4—53no—
566C2×C22⋊C4C22×D516yes—
567C2×C22⋊C4C22×D511yescharacteristic
568C2×C22⋊C4C22×D513yes—
569C2×C42—56no—
570C2×C42—53no—
571C2×C42C22×D513yes—
572C22×C5—22no—
573C22×C5—22no—
574C22×C5—28no—
575C22×C5—26no—
576C22×C5—26no—
577C22×C5—26no—
578C22×C5—412no—
579C22×C5C23×D412yes—
580C22×C5C2×2−1+412yes—
581C22×C5C2×2−1+412yes—
582C22×C5C2×2−1+414yescomplemented
583C22×C5C2611yescharacteristic
584C2×D5—232no—
585C2×D5—22no—
586C2×D5—22no—
587C2×D5—22no—
588C2×D5—22no—
589C2×D5—28no—
590C2×D5—28no—
591C2×D5—22no—
592C2×D5—22no—
593C2×D5—22no—
594C2×D5—44no—
595C2×D5C23×D414yes—
596C2×D5C2×2−1+414yescomplemented
597C4×C5—22no—
598C4×C5—26no—
599C4×C5—22no—
600C4×C5—26no—
601C4×C5C23×D4112yes—
602Dic5—26no—
603Dic5—26no—
604Dic5—22no—
605Dic5—26no—
606Dic5C23×D4112yes—
607C24—51no—
608C24—51no—
609C24—54no—
610C24—51no—
611C24—104no—
612C24—104no—
613C24—104no—
614C24C23×D513yes—
615C24C23×D511yescharacteristic
616#41—232no—
617#41—1096no—
618#41—1096no—
619#41—1096no—
620C2×Q8—232no—
621C2×Q8—212no—
622C2×Q8—564no—
623C2×Q8—524no—
624C2×Q8—512no—
625C2×Q8—524no—
626C2×Q8—512no—
627C2×Q8—512no—
628C2×Q8—512no—
629C2×Q8—1024no—
630C2×Q8—1012no—
631C2×Q8—1096no—
632C2×Q8—1096no—
633C2×Q8—1096no—
634C2×Q8—1096no—
635C2×Q8—1032no—
636C2×Q8—1032no—
637C2×Q8—1012no—
638C2×Q8—1012no—
639C2×Q8D4×D518yes—
640C2×Q8C23×D5112yes—
641C2×Q8C23×D514yes—
642C2×D4—212no—
643C2×D4—212no—
644C2×D4—512no—
645C2×D4—54no—
646C2×D4—512no—
647C2×D4—512no—
648C2×D4—54no—
649C2×D4—54no—
650C2×D4—104no—
651C2×D4—104no—
652C2×D4—1012no—
653C2×D4—1012no—
654C2×D4—1012no—
655C2×D4—104no—
656C2×D4C23×D5112yes—
657C2×D4C23×D5112yes—
658C22×C4—212no—
659C22×C4—212no—
660C22×C4—53no—
661C22×C4—524no—
662C22×C4—512no—
663C22×C4—512no—
664C22×C4—524no—
665C22×C4—51no—
666C22×C4—53no—
667C22×C4—53no—
668C22×C4—53no—
669C22×C4—512no—
670C22×C4—512no—
671C22×C4—512no—
672C22×C4—512no—
673C22×C4—1012no—
674C22×C4—1096no—
675C22×C4—1012no—
676C22×C4—1012no—
677C22×C4—1024no—
678C22×C4—1012no—
679C22×C4—1012no—
680C22×C4C23×D5112yes—
681C22×C4C23×D5112yes—
682C22×C4C23×D513yes—
683C22×C4C23×D511yescharacteristic
684C22×C4C23×D513yes—
685C22×C4C23×D511yescharacteristic
686C22×C4C23×D513yes—
687C4⋊C4—512no—
688C4⋊C4—512no—
689C4⋊C4—512no—
690C4⋊C4—512no—
691C4⋊C4—512no—
692C4⋊C4—524no—
693C4⋊C4—524no—
694C4⋊C4—512no—
695C4⋊C4C23×D5112yes—
696C4⋊C4C23×D5112yes—
697C22⋊C4—512no—
698C22⋊C4—524no—
699C22⋊C4—512no—
700C22⋊C4—512no—
701C22⋊C4—54no—
702C22⋊C4—54no—
703C22⋊C4—512no—
704C22⋊C4—512no—
705C22⋊C4—512no—
706C22⋊C4C23×D5124yes—
707C22⋊C4C23×D514yes—
708C22⋊C4C23×D5112yes—
709C42—524no—
710C42—512no—
711C42C23×D5112yes—
712C2×C5—24no—
713C2×C5—46no—
714C2×C5#348614yescomplemented
715C2×C5C24×D411yescharacteristic
716C2×C5C22×2−1+411yescharacteristic
717C2×C5C22×2−1+411yescharacteristic
718D5—24no—
719D5—24no—
720D5—42no—
721C23—22no—
722C23—22no—
723C23—26no—
724C23—26no—
725C23—26no—
726C23—54no—
727C23—54no—
728C23—52no—
729C23—52no—
730C23—52no—
731C23—108no—
732C23—108no—
733C23—1032no—
734C23—102no—
735C23—102no—
736C23—102no—
737C23—108no—
738C23—102no—
739C23—102no—
740C23—102no—
741C23—102no—
742C23#415014yescomplemented
743C23C24×D516yes—
744C23C24×D512yes—
745C23C24×D511yescharacteristic
746Q8—224no—
747Q8—548no—
748Q8—1048no—
749Q8—1024no—
750Q8—1024no—
751Q8—1024no—
752Q8C2×D4×D5116yes—
753D4—224no—
754D4—224no—
755D4—108no—
756D4—108no—
757D4—1024no—
758D4—1024no—
759D4—1024no—
760D4—108no—
761C2×C4—22no—
762C2×C4—26no—
763C2×C4—26no—
764C2×C4—22no—
765C2×C4—224no—
766C2×C4—224no—
767C2×C4—512no—
768C2×C4—56no—
769C2×C4—548no—
770C2×C4—52no—
771C2×C4—56no—
772C2×C4—56no—
773C2×C4—56no—
774C2×C4—1024no—
775C2×C4—1024no—
776C2×C4—1024no—
777C2×C4—1048no—
778C2×C4—106no—
779C2×C4—106no—
780C2×C4—102no—
781C2×C4—106no—
782C2×C4—1024no—
783C2×C4—1024no—
784C2×C4C2×D4×D5112yes—
785C2×C4C24×D516yes—
786C2×C4C24×D512yes—
787C2×C4C24×D516yes—
788C2×C4C24×D512yes—
789C2×C4C24×D516yes—
790C5C2×#348611yescharacteristic, complemented, Sylow
791C22—28no—
792C22—22no—
793C22—22no—
794C22—26no—
795C22—26no—
796C22—26no—
797C22—412no—
798C22—54no—
799C22—54no—
800C22—1032no—
801C22—108no—
802C22—108no—
803C22—102no—
804C22—102no—
805C22—102no—
806C22—102no—
807C22—102no—
808C22—102no—
809C22—102no—
810C22—204no—
811C22C22×D4×D512yes—
812C22C2×#415012yes—
813C22C2×#415014yescomplemented
814C22D5×2−1+412yes—
815C22C25×D511yescharacteristic
816C4—22no—
817C4—26no—
818C4—26no—
819C4—22no—
820C4—512no—
821C4—106no—
822C4—106no—
823C4—102no—
824C4—106no—
825C4C22×D4×D5112yes—
826C2—24no—
827C2—46no—
828C2—104no—
829C2—104no—
830C2—202no—
831C2#1061863614yesdirect product factor
832C2C23×D4×D511yescharacteristic
833C2C22×#415011yescharacteristic
834C2C2×D5×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#548C2
socleC23×C5C25
hypercenterC2×#548D5
hypocenterC5C2×#3486
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#4150C2semidirect
2. C23×Q8×D5C2semidirect
3. C2×C5×#548C2semidirect
4. C2×#66165C2semidirect
5. C2×Q8×C22⋊D5C2semidirect
6. #10618636C2direct (N × H)
7. C2×#66011C2semidirect
8. C2×#66009C2semidirect
9. C2×#65962C2semidirect
10. C2×#65966C2semidirect
11. C2×#65932C2semidirect
12. C2×#65940C2semidirect
13. C2×Q8×D20C2semidirect
14. C2×#65906C2semidirect
15. C2×#65881C2semidirect
16. C2×D4×Dic10C2semidirect
17. C22×C5×#41C22semidirect
20. C2×#4150C22semidirect
26. C22×Q8×D5C22semidirect
27. C22×Q8×D5C22semidirect
29. C22×#711C22semidirect
33. C23×Dic10C22semidirect
34. C5×#548C22semidirect
35. C2×C5×#124C22semidirect
36. C2×C5×C22⋊Q8C22semidirect
38. C2×C4×C5×Q8C22semidirect
40. #66165C22semidirect
41. Q8×C22⋊D5C22semidirect
42. C2×#4092C22semidirect
43. C2×Q8×Dic5C22semidirect
44. C2×#4090C22semidirect
48. C2×#4082C22semidirect
53. C2×#4070C22semidirect
54. #66011C22semidirect
55. #66009C22semidirect
56. #65966C22semidirect
57. #65962C22semidirect
58. #65940C22semidirect
59. #65932C22semidirect
60. Q8×D20C22semidirect
61. #65906C22semidirect
62. #65881C22semidirect
63. D4×Dic10C22semidirect
65. C2×#4043C22semidirect
69. C2×#4034C22semidirect
70. C2×#4033C22semidirect
71. C2×#4031C22semidirect
78. C2×#4024C22semidirect
79. C2×#4024C22semidirect
82. C2×#4015C22semidirect
83. C2×C4×Dic10C22semidirect
87. C2×C5×#41C23semidirect
108. C2×Q8×D5D4semidirect
113. C2×Q8×D5C23semidirect
117. C2×#711C23semidirect
137. C22×Dic10C23semidirect
138. C5×#124C23semidirect
139. C5×C22⋊Q8C23semidirect
141. C4×C5×Q8C23semidirect
152. #4092C23semidirect
153. Q8×Dic5C23semidirect
154. #4090C23semidirect
158. #4082C23semidirect
172. #4070C23semidirect
181. #4043C23semidirect
185. #4034C23semidirect
186. #4033C23semidirect
187. #4031C23semidirect
194. #4024C23semidirect
195. #4024C23semidirect
198. #4015C23semidirect
199. C4×Dic10C23semidirect
210. C2×#548D5semidirect
265. Q8×D5C2×D4semidirect
326. C22×#41C2×D5semidirect
345. #548C2×D5semidirect
353. C2×#124C2×D5semidirect
368. C2×C22⋊Q8C2×D5semidirect
379. C2×C4×Q8C2×D5semidirect
393. C23×C52−1+4semidirect
409. C22×D52−1+4semidirect
466. C2×#41C22×D5semidirect
515. #124C22×D5semidirect
528. C22⋊Q8C22×D5semidirect
538. C4×Q8C22×D5semidirect
582. C22×C5C2×2−1+4semidirect
596. C2×D5C2×2−1+4semidirect
714. C2×C5#3486semidirect
742. C23#4150semidirect
790. C5C2×#3486semidirect
813. C22C2×#4150semidirect
831. C2#10618636direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41502
C23×Q8×D52
C2×C5×#5482
C2×#661652
C2×Q8×C22⋊D52
#106186362
C2×#660112
C2×#660092
C2×#659622
C2×#659662
C2×#659322
C2×#659402
C2×Q8×D202
C2×#659062
C2×#658812
C2×D4×Dic102
C2×#34865