Finite Group Databasebeta

← C2×D5×#548 #13006230

Subgroups — C2×D5×#548 #13006230

Order 1280.

12142 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×#41C211yesmaximal, characteristic, complemented
2C23×Q8×D5C211yesmaximal, characteristic, complemented
3C2×C5×#548C211yesmaximal, characteristic, complemented
4C2×#66165C211yesmaximal, characteristic, complemented
5C2×#66151C211yesmaximal, characteristic, complemented
6D5×#548C2132yesmaximal, direct product factor
7C2×#66011C213yesmaximal, complemented
8C2×D5×#124C213yesmaximal, complemented
9C2×#65967C213yesmaximal, complemented
10C2×D5×C22⋊Q8C213yesmaximal, complemented
11C2×D5×#121C213yesmaximal, complemented
12C2×#65932C213yesmaximal, complemented
13C2×#65910C211yesmaximal, characteristic, complemented
14C2×C4×Q8×D5C211yesmaximal, characteristic, complemented
15C2×C4×D4×D5C213yesmaximal, complemented
16C2×#65886C213yesmaximal, complemented
17C22×C5×#41C2211yescharacteristic, complemented
18C23×C5×Q8C2211yescharacteristic, complemented
19C2×D5×#41—216no—
20C2×D5×#41C22116yescomplemented
21C22×#713C2211yescharacteristic, complemented
22C22×Q8×D5—216no—
23C22×Q8×D5C2213yes—
24C22×Q8×D5C2211yescharacteristic
25C22×Q8×D5C2213yescomplemented
26C22×Q8×D5C2211yescharacteristic, complemented
27C22×Q8×D5C22116yescomplemented
28C22×#711C2213yescomplemented
29C22×D4×D5C2213yes—
30C22×D4×D5C2213yes—
31C22×#709C2213yescomplemented
32C23×C4×D5C2213yes—
33C23×C4×D5C2213yes—
34C23×Dic10C2213yescomplemented
35C5×#548C22116yescomplemented
36C2×C5×#124C2213yescomplemented
37C2×C5×C22⋊Q8C2213yescomplemented
38C2×C5×#121C2213yescomplemented
39C2×C4×C5×Q8C2211yescharacteristic, complemented
40C2×C4×C5×D4C2213yescomplemented
41#66165C22116yescomplemented
42#66151C22116yescomplemented
43C2×#4093C2213yescomplemented
44C2×#4092C2213yescomplemented
45C2×Q8×Dic5C2211yescharacteristic, complemented
46C2×#4085C2216yescomplemented
47C2×#4084C2213yescomplemented
48C2×#4082C2213yescomplemented
49C2×D4×Dic5C2213yescomplemented
50C2×#4076C2213yescomplemented
51C2×C4×C22⋊D5C2213yescomplemented
52C2×C4×C22⋊D5C2213yescomplemented
53C2×#4070C2213yescomplemented
54#66011C22148yescomplemented
55D5×#124C22148yescomplemented
56#65967C22148yescomplemented
57D5×C22⋊Q8C22148yescomplemented
58D5×#121C22148yescomplemented
59#65932C22148yescomplemented
60#65910C22116yescomplemented
61C4×Q8×D5C22116yescomplemented
62#65886C22148yescomplemented
63C4×D4×D5C22148yescomplemented
64C2×#4043C2213yescomplemented
65C2×#4042C2216yescomplemented
66C2×#4041C2213yescomplemented
67C2×#4039C2213yescomplemented
68C2×D5×C4⋊C4C2213yes—
69C2×D5×C4⋊C4C2213yes—
70C2×#4033C2213yescomplemented
71C2×#4031C2216yescomplemented
72C2×#4031C2216yescomplemented
73C2×#4030C2216yescomplemented
74C2×#4027C2213yescomplemented
75C2×#4027C2213yescomplemented
76C2×D5×C22⋊C4C2216yes—
77C2×D5×C22⋊C4C2211yescharacteristic
78C2×D5×C22⋊C4C2213yes—
79C2×#4024C2216yescomplemented
80C2×#4021C2213yescomplemented
81C2×C4×D20C2213yescomplemented
82C2×C42×D5C2213yes—
83C2×C4×Dic10C2213yescomplemented
84C22×#548—51nomaximal, Sylow
85C24×D5C2313yes—
86C24×D5C2311yescharacteristic
87C2×C5×#41—28no—
88C2×C5×#41C2318yescomplemented
89C22×C5×Q8—28no—
90C22×C5×Q8C2313yes—
91C22×C5×Q8C2311yescharacteristic
92C22×C5×Q8C2318yescomplemented
93C22×C5×D4C2313yes—
94C22×C5×D4C2313yes—
95C23×C4×C5C2313yes—
96C23×C4×C5C2313yes—
97C22×C22⋊D5C2313yes—
98C22×C22⋊D5C2313yes—
99C22×C22⋊D5C2316yes—
100C23×Dic5C2313yes—
101C23×Dic5C2313yes—
102D5×#41—2128no—
103C2×#713—28no—
104C2×#713C2318yescomplemented
105C2×Q8×D5—28no—
106C2×Q8×D5—2128no—
107C2×Q8×D5—224no—
108C2×Q8×D5—224no—
109C2×Q8×D5D4116yescomplemented
110C2×Q8×D5C23124yes—
111C2×Q8×D5C2318yes—
112C2×Q8×D5C2318yescomplemented
113C2×Q8×D5C23124yescomplemented
114C2×#711—224no—
115C2×#711C23124yescomplemented
116C2×D4×D5—224no—
117C2×D4×D5—224no—
118C2×D4×D5C23124yes—
119C2×D4×D5C23124yes—
120C2×#709—224no—
121C2×#709C23124yescomplemented
122C22×D20C2313yes—
123C22×D20C2313yes—
124C22×C4×D5—224no—
125C22×C4×D5—224no—
126C22×C4×D5C2311yescharacteristic
127C22×C4×D5C2313yes—
128C22×C4×D5C2313yes—
129C22×C4×D5C2313yes—
130C22×C4×D5C2313yes—
131C22×C4×D5C2311yescharacteristic
132C22×C4×D5C2313yes—
133C22×C4×D5C2313yes—
134C22×C4×D5C23124yes—
135C22×C4×D5C23124yes—
136C22×C4×D5C2313yes—
137C22×Dic10—224no—
138C22×Dic10C2313yes—
139C22×Dic10C2316yes—
140C22×Dic10C2313yes—
141C22×Dic10C23124yescomplemented
142C5×#124C23124yescomplemented
143C5×C22⋊Q8C23124yescomplemented
144C5×#121C23124yescomplemented
145C4×C5×Q8C2318yescomplemented
146C4×C5×D4C23124yescomplemented
147C2×C5×C4⋊C4C2313yes—
148C2×C5×C4⋊C4C2313yes—
149C2×C5×C22⋊C4C2316yes—
150C2×C5×C22⋊C4C2311yescharacteristic
151C2×C5×C22⋊C4C2313yes—
152C2×C42×C5C2313yes—
153C2×C22⋊Dic5C2316yes—
154C2×C22⋊Dic5C2313yes—
155C2×C22⋊Dic5C2311yescharacteristic
156#4093C23124yescomplemented
157#4092C23124yescomplemented
158Q8×Dic5C2318yescomplemented
159#4085C23148yescomplemented
160#4084C23124yescomplemented
161#4082C23124yescomplemented
162D4×Dic5C23124yescomplemented
163#4076C23124yescomplemented
164C4×C22⋊D5C23124yescomplemented
165C4×C22⋊D5C23124yescomplemented
166C2×#685C2311yescharacteristic
167C2×#685C2313yes—
168C2×#685C2316yes—
169C2×#685C2316yes—
170C2×#685C2313yes—
171C2×#685C2311yescharacteristic
172C2×C4⋊Dic5C2313yes—
173C2×C4⋊Dic5C2313yes—
174#4070C23124yescomplemented
175C2×#683C2316yes—
176C2×#683C2313yes—
177C2×#683C2313yes—
178C2×C4×Dic5C2313yes—
179C2×C4×Dic5C2313yes—
180C2×C4×Dic5C2313yes—
181#4043C23124yescomplemented
182#4042C23148yescomplemented
183#4041C23124yescomplemented
184#4039C23124yescomplemented
185D5×C4⋊C4C23124yes—
186D5×C4⋊C4C23124yes—
187#4033C23124yescomplemented
188#4031C23148yescomplemented
189#4031C23148yescomplemented
190#4030C23148yescomplemented
191#4027C23124yescomplemented
192#4027C23124yescomplemented
193D5×C22⋊C4C2318yes—
194D5×C22⋊C4C23124yes—
195D5×C22⋊C4C23148yes—
196#4024C23148yescomplemented
197#4021C23124yescomplemented
198C4×D20C23124yescomplemented
199C42×D5C23124yes—
200C4×Dic10C23124yescomplemented
201C23×#41—51no—
202C24×Q8—51no—
203C2×#548—51no—
204C2×#548—51no—
205C2×#548—532no—
206C2×#548—53no—
207C2×#548—53no—
208C2×#548—53no—
209C2×#548—51no—
210C2×#548—53no—
211C2×#548D511yescharacteristic, direct product factor
212C22×#124—53no—
213C22×C22⋊Q8—53no—
214C22×#121—53no—
215C22×C4×Q8—51no—
216C22×C4×D4—53no—
217C24×C5C2413yes—
218C24×C5C2411yescharacteristic
219C23×D5—24no—
220C23×D5—24no—
221C23×D5—212no—
222C23×D5—212no—
223C23×D5—212no—
224C23×D5#4118yescomplemented
225C23×D5C2413yes—
226C23×D5C24112yes—
227C23×D5C2411yescharacteristic
228C23×D5C2414yes—
229C23×D5C2411yescharacteristic
230C5×#41—232no—
231C2×C5×Q8—232no—
232C2×C5×Q8—212no—
233C2×C5×Q8C2×D418yescomplemented
234C2×C5×Q8C24112yes—
235C2×C5×Q8C2414yes—
236C2×C5×D4—212no—
237C2×C5×D4—212no—
238C2×C5×D4C24112yes—
239C2×C5×D4C24112yes—
240C22×C4×C5—212no—
241C22×C4×C5—212no—
242C22×C4×C5C2411yescharacteristic
243C22×C4×C5C2413yes—
244C22×C4×C5C2413yes—
245C22×C4×C5C2411yescharacteristic
246C22×C4×C5C24112yes—
247C22×C4×C5C24112yes—
248C22×C4×C5C2413yes—
249C2×C22⋊D5—212no—
250C2×C22⋊D5—212no—
251C2×C22⋊D5—224no—
252C2×C22⋊D5C24124yes—
253C2×C22⋊D5C24112yes—
254C2×C22⋊D5C24112yes—
255C22×Dic5—212no—
256C22×Dic5—212no—
257C22×Dic5C2411yescharacteristic
258C22×Dic5C2413yes—
259C22×Dic5C2413yes—
260C22×Dic5C2411yescharacteristic
261C22×Dic5C24112yes—
262C22×Dic5C24112yes—
263C22×Dic5C2413yes—
264#713—232no—
265Q8×D5—232no—
266Q8×D5—296no—
267Q8×D5—296no—
268Q8×D5C2×D4164yescomplemented
269#711—296no—
270D4×D5—296no—
271D4×D5—296no—
272#709—296no—
273C2×D20—212no—
274C2×D20—212no—
275C2×D20C24112yes—
276C2×D20C24112yes—
277C2×C4×D5—24no—
278C2×C4×D5—212no—
279C2×C4×D5—212no—
280C2×C4×D5—24no—
281C2×C4×D5—212no—
282C2×C4×D5—212no—
283C2×C4×D5—212no—
284C2×C4×D5—212no—
285C2×C4×D5—296no—
286C2×C4×D5—296no—
287C2×C4×D5C2×D4124yes—
288C2×C4×D5C2414yes—
289C2×C4×D5C24112yes—
290C2×C4×D5C24112yes—
291C2×C4×D5C24112yes—
292C2×C4×D5C24112yes—
293C2×C4×D5C24112yes—
294C2×C4×D5C24112yes—
295C2×C4×D5C2414yes—
296C2×C4×D5C24112yes—
297C2×Dic10—212no—
298C2×Dic10—224no—
299C2×Dic10—296no—
300C2×Dic10C2×D4124yescomplemented
301C2×Dic10C24112yes—
302C2×Dic10C24124yes—
303C2×Dic10C24112yes—
304C5×C4⋊C4C24112yes—
305C5×C4⋊C4C24112yes—
306C5×C22⋊C4C2414yes—
307C5×C22⋊C4C24112yes—
308C5×C22⋊C4C24124yes—
309C42×C5C24112yes—
310C22⋊Dic5C24124yes—
311C22⋊Dic5C24112yes—
312C22⋊Dic5C2414yes—
313#685C2414yes—
314#685C24112yes—
315#685C24124yes—
316#685C24124yes—
317#685C24112yes—
318#685C2414yes—
319C4⋊Dic5C24112yes—
320C4⋊Dic5C24112yes—
321#683C24124yes—
322#683C24112yes—
323#683C24112yes—
324C4×Dic5C24112yes—
325C4×Dic5C24112yes—
326C4×Dic5C24112yes—
327C22×#41—516no—
328C22×#41—51no—
329C22×#41—53no—
330C22×#41—53no—
331C22×#41—1016no—
332C22×#41C2×D511yescharacteristic, complemented
333C23×Q8—51no—
334C23×Q8—53no—
335C23×Q8—53no—
336C23×Q8—51no—
337C23×Q8—516no—
338C23×Q8—53no—
339C23×Q8—1016no—
340C23×Q8C2×D511yescharacteristic, complemented
341C23×D4—53no—
342C23×D4—53no—
343C24×C4—53no—
344C24×C4—53no—
345#548—516no—
346#548—516no—
347#548—548no—
348#548—548no—
349#548—548no—
350#548—516no—
351#548—548no—
352#548C2×D5116yesdirect product factor
353C2×#124—53no—
354C2×#124—53no—
355C2×#124—548no—
356C2×#124—56no—
357C2×#124—56no—
358C2×#124—53no—
359C2×#124C2×D513yescomplemented
360C2×C22⋊Q8—53no—
361C2×C22⋊Q8—53no—
362C2×C22⋊Q8—548no—
363C2×C22⋊Q8—56no—
364C2×C22⋊Q8—53no—
365C2×C22⋊Q8—56no—
366C2×C22⋊Q8C2×D513yescomplemented
367C2×#121—53no—
368C2×#121—56no—
369C2×#121—53no—
370C2×#121—548no—
371C2×#121—53no—
372C2×#121—56no—
373C2×#121C2×D513yescomplemented
374C2×C4×Q8—51no—
375C2×C4×Q8—516no—
376C2×C4×Q8—53no—
377C2×C4×Q8—53no—
378C2×C4×Q8C2×D511yescharacteristic, complemented
379C2×C4×D4—53no—
380C2×C4×D4—53no—
381C2×C4×D4—53no—
382C2×C4×D4—548no—
383C2×C4×D4—53no—
384C2×C4×D4—53no—
385C2×C4×D4—53no—
386C2×C4×D4—53no—
387C2×C4×D4C2×D513yescomplemented
388C22×C4⋊C4—53no—
389C22×C4⋊C4—53no—
390C22×C22⋊C4—51no—
391C22×C22⋊C4—53no—
392C22×C22⋊C4—56no—
393C22×C42—53no—
394C23×C5—22no—
395C23×C5—22no—
396C23×C5—26no—
397C23×C5—26no—
398C23×C5—26no—
399C23×C5C2×#4114yescomplemented
400C23×C5C2516yes—
401C23×C5C2512yes—
402C23×C5C2511yescharacteristic
403C22×D5—22no—
404C22×D5—22no—
405C22×D5—232no—
406C22×D5—28no—
407C22×D5—28no—
408C22×D5—26no—
409C22×D5—26no—
410C22×D5—26no—
411C22×D5—224no—
412C22×D5—224no—
413C22×D5—224no—
414C22×D5—448no—
415C22×D5C22×D414yes—
416C22×D5C2×#4114yes—
417C22×D5C2×#41116yescomplemented
418C22×D5C2×#4114yescomplemented
419C22×D52−1+414yes—
420C22×D5C2516yes—
421C22×D5C2512yes—
422C22×D5C2512yes—
423C5×Q8—224no—
424C5×Q8C22×D4116yescomplemented
425C5×D4—224no—
426C5×D4—224no—
427C2×C4×C5—26no—
428C2×C4×C5—22no—
429C2×C4×C5—26no—
430C2×C4×C5—22no—
431C2×C4×C5—224no—
432C2×C4×C5—224no—
433C2×C4×C5C22×D4112yes—
434C2×C4×C5C2512yes—
435C2×C4×C5C2516yes—
436C2×C4×C5C2512yes—
437C2×C4×C5C2516yes—
438C2×C4×C5C2516yes—
439C22⋊D5—224no—
440C22⋊D5—224no—
441C22⋊D5—248no—
442C2×Dic5—26no—
443C2×Dic5—22no—
444C2×Dic5—26no—
445C2×Dic5—22no—
446C2×Dic5—224no—
447C2×Dic5—224no—
448C2×Dic5C22×D4112yes—
449C2×Dic5C2512yes—
450C2×Dic5C2516yes—
451C2×Dic5C2512yes—
452C2×Dic5C2516yes—
453C2×Dic5C2516yes—
454D20—224no—
455D20—224no—
456C4×D5—28no—
457C4×D5—224no—
458C4×D5—224no—
459C4×D5—28no—
460C4×D5—224no—
461C4×D5—224no—
462C4×D5—224no—
463C4×D5—224no—
464C4×D5C22×D4148yes—
465Dic10—224no—
466Dic10—248no—
467Dic10C22×D4148yescomplemented
468C25—51no—
469C25—53no—
470C2×#41—28no—
471C2×#41—58no—
472C2×#41—524no—
473C2×#41—524no—
474C2×#41—1024no—
475C2×#41—1024no—
476C2×#41—10128no—
477C2×#41—108no—
478C2×#41C22×D518yescomplemented
479C22×Q8—28no—
480C22×Q8—516no—
481C22×Q8—58no—
482C22×Q8—524no—
483C22×Q8—524no—
484C22×Q8—58no—
485C22×Q8—53no—
486C22×Q8—56no—
487C22×Q8—53no—
488C22×Q8—524no—
489C22×Q8—1024no—
490C22×Q8—1024no—
491C22×Q8—10128no—
492C22×Q8—1024no—
493C22×Q8—108no—
494C22×Q8C22×D513yes—
495C22×Q8C22×D511yescharacteristic
496C22×Q8C22×D518yescomplemented
497C22×D4—53no—
498C22×D4—53no—
499C22×D4—56no—
500C22×D4—524no—
501C22×D4—524no—
502C22×D4—53no—
503C22×D4—53no—
504C22×D4—1024no—
505C22×D4—1024no—
506C22×D4C22×D513yes—
507C22×D4C22×D513yes—
508C23×C4—53no—
509C23×C4—53no—
510C23×C4—53no—
511C23×C4—51no—
512C23×C4—53no—
513C23×C4—53no—
514C23×C4—51no—
515C23×C4—53no—
516C23×C4—524no—
517C23×C4—53no—
518C23×C4—53no—
519C23×C4—524no—
520C23×C4—53no—
521C23×C4—1024no—
522C23×C4—1024no—
523C23×C4C22×D513yes—
524C23×C4C22×D513yes—
525#124—524no—
526#124—524no—
527#124—548no—
528#124—548no—
529#124—524no—
530#124C22×D5124yescomplemented
531C22⋊Q8—524no—
532C22⋊Q8—524no—
533C22⋊Q8—548no—
534C22⋊Q8—524no—
535C22⋊Q8—548no—
536C22⋊Q8C22×D5124yescomplemented
537#121—524no—
538#121—548no—
539#121—524no—
540#121—524no—
541#121—548no—
542#121C22×D5124yescomplemented
543C4×Q8—58no—
544C4×Q8—524no—
545C4×Q8—524no—
546C4×Q8C22×D518yescomplemented
547C4×D4—524no—
548C4×D4—524no—
549C4×D4—524no—
550C4×D4—524no—
551C4×D4—524no—
552C4×D4—524no—
553C4×D4—524no—
554C4×D4C22×D5124yescomplemented
555C2×C4⋊C4—53no—
556C2×C4⋊C4—53no—
557C2×C4⋊C4—53no—
558C2×C4⋊C4—56no—
559C2×C4⋊C4—53no—
560C2×C4⋊C4—524no—
561C2×C4⋊C4—524no—
562C2×C4⋊C4C22×D513yes—
563C2×C4⋊C4C22×D513yes—
564C2×C22⋊C4—51no—
565C2×C22⋊C4—53no—
566C2×C22⋊C4—56no—
567C2×C22⋊C4—51no—
568C2×C22⋊C4—51no—
569C2×C22⋊C4—53no—
570C2×C22⋊C4—53no—
571C2×C22⋊C4—56no—
572C2×C22⋊C4—56no—
573C2×C22⋊C4—58no—
574C2×C22⋊C4—524no—
575C2×C22⋊C4—548no—
576C2×C22⋊C4C22×D511yescharacteristic
577C2×C22⋊C4C22×D513yes—
578C2×C22⋊C4C22×D516yes—
579C2×C42—53no—
580C2×C42—53no—
581C2×C42—53no—
582C2×C42—524no—
583C2×C42C22×D513yes—
584C22×C5—22no—
585C22×C5—22no—
586C22×C5—28no—
587C22×C5—26no—
588C22×C5—26no—
589C22×C5—26no—
590C22×C5—412no—
591C22×C5C23×D412yes—
592C22×C5C22×#4112yes—
593C22×C5C22×#4114yescomplemented
594C22×C5C2×2−1+412yes—
595C22×C5C2611yescharacteristic
596C2×D5—22no—
597C2×D5—22no—
598C2×D5—28no—
599C2×D5—232no—
600C2×D5—26no—
601C2×D5—26no—
602C2×D5—26no—
603C2×D5—412no—
604C2×D5—448no—
605C2×D5#548116yesdirect product factor
606C2×D5C23×D414yes—
607C2×D5C22×#4114yes—
608C2×D5C22×#4114yescomplemented
609C2×D5C2×2−1+414yes—
610C4×C5—26no—
611C4×C5—22no—
612C4×C5—26no—
613C4×C5—22no—
614C4×C5C23×D4112yes—
615Dic5—26no—
616Dic5—22no—
617Dic5—26no—
618Dic5—22no—
619Dic5C23×D4112yes—
620C24—51no—
621C24—58no—
622C24—54no—
623C24—51no—
624C24—512no—
625C24—53no—
626C24—104no—
627C24—104no—
628C24—1012no—
629C24—1012no—
630C24—1012no—
631C24C23×D513yes—
632C24C23×D511yescharacteristic
633#41—232no—
634#41—1096no—
635#41—1096no—
636#41—1032no—
637C2×Q8—232no—
638C2×Q8—212no—
639C2×Q8—564no—
640C2×Q8—524no—
641C2×Q8—512no—
642C2×Q8—524no—
643C2×Q8—512no—
644C2×Q8—1024no—
645C2×Q8—1096no—
646C2×Q8—1096no—
647C2×Q8—1096no—
648C2×Q8—1032no—
649C2×Q8—1012no—
650C2×Q8D4×D518yescomplemented
651C2×Q8C23×D5112yes—
652C2×Q8C23×D514yes—
653C2×D4—212no—
654C2×D4—212no—
655C2×D4—512no—
656C2×D4—512no—
657C2×D4—524no—
658C2×D4—512no—
659C2×D4—512no—
660C2×D4—1012no—
661C2×D4—1096no—
662C2×D4—1024no—
663C2×D4—1096no—
664C2×D4—1012no—
665C2×D4—1012no—
666C2×D4—1012no—
667C2×D4C23×D5112yes—
668C2×D4C23×D5112yes—
669C22×C4—212no—
670C22×C4—212no—
671C22×C4—53no—
672C22×C4—524no—
673C22×C4—512no—
674C22×C4—512no—
675C22×C4—512no—
676C22×C4—51no—
677C22×C4—53no—
678C22×C4—53no—
679C22×C4—51no—
680C22×C4—54no—
681C22×C4—512no—
682C22×C4—512no—
683C22×C4—54no—
684C22×C4—512no—
685C22×C4—512no—
686C22×C4—512no—
687C22×C4—512no—
688C22×C4—1012no—
689C22×C4—1096no—
690C22×C4—1012no—
691C22×C4—1096no—
692C22×C4—104no—
693C22×C4—1012no—
694C22×C4—1012no—
695C22×C4—104no—
696C22×C4—1012no—
697C22×C4—1012no—
698C22×C4—1012no—
699C22×C4—1012no—
700C22×C4C23×D5112yes—
701C22×C4C23×D5112yes—
702C22×C4C23×D511yescharacteristic
703C22×C4C23×D513yes—
704C22×C4C23×D513yes—
705C22×C4C23×D511yescharacteristic
706C22×C4C23×D513yes—
707C4⋊C4—512no—
708C4⋊C4—512no—
709C4⋊C4—512no—
710C4⋊C4—524no—
711C4⋊C4—512no—
712C4⋊C4C23×D5112yes—
713C4⋊C4C23×D5112yes—
714C22⋊C4—54no—
715C22⋊C4—512no—
716C22⋊C4—524no—
717C22⋊C4—54no—
718C22⋊C4—54no—
719C22⋊C4—512no—
720C22⋊C4—512no—
721C22⋊C4—524no—
722C22⋊C4—524no—
723C22⋊C4C23×D514yes—
724C22⋊C4C23×D5112yes—
725C22⋊C4C23×D5124yes—
726C42—512no—
727C42—512no—
728C42—512no—
729C42C23×D5112yes—
730C2×C5—24no—
731C2×C5—46no—
732C2×C5C2×#54814yescomplemented
733C2×C5C24×D411yescharacteristic
734C2×C5C23×#4111yescharacteristic
735C2×C5C22×2−1+411yescharacteristic
736D5—24no—
737D5—46no—
738D5C2×#54818yesdirect product factor
739C23—22no—
740C23—22no—
741C23—26no—
742C23—26no—
743C23—26no—
744C23—54no—
745C23—54no—
746C23—54no—
747C23—52no—
748C23—54no—
749C23—516no—
750C23—52no—
751C23—56no—
752C23—108no—
753C23—1032no—
754C23—108no—
755C23—1024no—
756C23—1024no—
757C23—1024no—
758C23—102no—
759C23—102no—
760C23—106no—
761C23—106no—
762C23—106no—
763C23—2048no—
764C23D5×#4114yescomplemented
765C23C24×D516yes—
766C23C24×D512yes—
767C23C24×D511yescharacteristic
768Q8—224no—
769Q8—548no—
770Q8—1048no—
771Q8—1024no—
772Q8C2×D4×D5116yescomplemented
773D4—224no—
774D4—224no—
775D4—1024no—
776D4—1048no—
777D4—1024no—
778D4—1024no—
779D4—1024no—
780C2×C4—22no—
781C2×C4—26no—
782C2×C4—26no—
783C2×C4—22no—
784C2×C4—224no—
785C2×C4—224no—
786C2×C4—512no—
787C2×C4—56no—
788C2×C4—548no—
789C2×C4—52no—
790C2×C4—56no—
791C2×C4—56no—
792C2×C4—52no—
793C2×C4—1024no—
794C2×C4—1024no—
795C2×C4—108no—
796C2×C4—1024no—
797C2×C4—1024no—
798C2×C4—108no—
799C2×C4—1024no—
800C2×C4—1024no—
801C2×C4—102no—
802C2×C4—106no—
803C2×C4—106no—
804C2×C4—102no—
805C2×C4—1024no—
806C2×C4—1024no—
807C2×C4C2×D4×D5112yes—
808C2×C4C24×D512yes—
809C2×C4C24×D516yes—
810C2×C4C24×D516yes—
811C2×C4C24×D512yes—
812C2×C4C24×D516yes—
813C5C22×#54811yescharacteristic, complemented, Sylow
814C22—28no—
815C22—22no—
816C22—22no—
817C22—26no—
818C22—26no—
819C22—26no—
820C22—412no—
821C22—516no—
822C22—54no—
823C22—54no—
824C22—54no—
825C22—54no—
826C22—1032no—
827C22—108no—
828C22—102no—
829C22—102no—
830C22—106no—
831C22—106no—
832C22—106no—
833C22—2048no—
834C22—2012no—
835C22C22×D4×D512yes—
836C22C2×D5×#4112yes—
837C22C2×D5×#4114yescomplemented
838C22D5×2−1+412yes—
839C22C25×D511yescharacteristic
840C4—22no—
841C4—26no—
842C4—26no—
843C4—22no—
844C4—512no—
845C4—102no—
846C4—106no—
847C4—106no—
848C4—102no—
849C4C22×D4×D5112yes—
850C2—24no—
851C2—46no—
852C2—58no—
853C2—104no—
854C2—206no—
855C2D5×#54814yesdirect product factor
856C2C23×D4×D511yescharacteristic
857C2C22×D5×#4111yescharacteristic
858C2C2×D5×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#548C2
socleC23×C5C25
hypercenterC2×#548D5
hypocenterC5C22×#548
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. C23×Q8×D5C2semidirect
3. C2×C5×#548C2semidirect
4. C2×#66165C2semidirect
5. C2×#66151C2semidirect
6. D5×#548C2direct (N × H)
7. C2×#66011C2semidirect
8. C2×D5×#124C2semidirect
9. C2×#65967C2semidirect
10. C2×D5×C22⋊Q8C2semidirect
11. C2×D5×#121C2semidirect
12. C2×#65932C2semidirect
13. C2×#65910C2semidirect
14. C2×C4×Q8×D5C2semidirect
15. C2×C4×D4×D5C2semidirect
16. C2×#65886C2semidirect
17. C22×C5×#41C22semidirect
18. C23×C5×Q8C22semidirect
20. C2×D5×#41C22semidirect
21. C22×#713C22semidirect
25. C22×Q8×D5C22semidirect
26. C22×Q8×D5C22semidirect
27. C22×Q8×D5C22semidirect
28. C22×#711C22semidirect
31. C22×#709C22semidirect
34. C23×Dic10C22semidirect
35. C5×#548C22semidirect
36. C2×C5×#124C22semidirect
37. C2×C5×C22⋊Q8C22semidirect
38. C2×C5×#121C22semidirect
39. C2×C4×C5×Q8C22semidirect
40. C2×C4×C5×D4C22semidirect
41. #66165C22semidirect
42. #66151C22semidirect
43. C2×#4093C22semidirect
44. C2×#4092C22semidirect
45. C2×Q8×Dic5C22semidirect
46. C2×#4085C22semidirect
47. C2×#4084C22semidirect
48. C2×#4082C22semidirect
49. C2×D4×Dic5C22semidirect
50. C2×#4076C22semidirect
51. C2×C4×C22⋊D5C22semidirect
52. C2×C4×C22⋊D5C22semidirect
53. C2×#4070C22semidirect
54. #66011C22semidirect
55. D5×#124C22semidirect
56. #65967C22semidirect
57. D5×C22⋊Q8C22semidirect
58. D5×#121C22semidirect
59. #65932C22semidirect
60. #65910C22semidirect
61. C4×Q8×D5C22semidirect
62. #65886C22semidirect
63. C4×D4×D5C22semidirect
64. C2×#4043C22semidirect
65. C2×#4042C22semidirect
66. C2×#4041C22semidirect
67. C2×#4039C22semidirect
70. C2×#4033C22semidirect
71. C2×#4031C22semidirect
72. C2×#4031C22semidirect
73. C2×#4030C22semidirect
74. C2×#4027C22semidirect
75. C2×#4027C22semidirect
79. C2×#4024C22semidirect
80. C2×#4021C22semidirect
81. C2×C4×D20C22semidirect
83. C2×C4×Dic10C22semidirect
88. C2×C5×#41C23semidirect
92. C22×C5×Q8C23semidirect
104. C2×#713C23semidirect
109. C2×Q8×D5D4semidirect
112. C2×Q8×D5C23semidirect
113. C2×Q8×D5C23semidirect
115. C2×#711C23semidirect
121. C2×#709C23semidirect
141. C22×Dic10C23semidirect
142. C5×#124C23semidirect
143. C5×C22⋊Q8C23semidirect
144. C5×#121C23semidirect
145. C4×C5×Q8C23semidirect
146. C4×C5×D4C23semidirect
156. #4093C23semidirect
157. #4092C23semidirect
158. Q8×Dic5C23semidirect
159. #4085C23semidirect
160. #4084C23semidirect
161. #4082C23semidirect
162. D4×Dic5C23semidirect
163. #4076C23semidirect
164. C4×C22⋊D5C23semidirect
165. C4×C22⋊D5C23semidirect
174. #4070C23semidirect
181. #4043C23semidirect
182. #4042C23semidirect
183. #4041C23semidirect
184. #4039C23semidirect
187. #4033C23semidirect
188. #4031C23semidirect
189. #4031C23semidirect
190. #4030C23semidirect
191. #4027C23semidirect
192. #4027C23semidirect
196. #4024C23semidirect
197. #4021C23semidirect
198. C4×D20C23semidirect
200. C4×Dic10C23semidirect
211. C2×#548D5direct (N × H)
224. C23×D5#41semidirect
233. C2×C5×Q8C2×D4semidirect
268. Q8×D5C2×D4semidirect
300. C2×Dic10C2×D4semidirect
332. C22×#41C2×D5semidirect
340. C23×Q8C2×D5semidirect
352. #548C2×D5direct (N × H)
359. C2×#124C2×D5semidirect
366. C2×C22⋊Q8C2×D5semidirect
373. C2×#121C2×D5semidirect
378. C2×C4×Q8C2×D5semidirect
387. C2×C4×D4C2×D5semidirect
399. C23×C5C2×#41semidirect
417. C22×D5C2×#41semidirect
418. C22×D5C2×#41semidirect
424. C5×Q8C22×D4semidirect
467. Dic10C22×D4semidirect
478. C2×#41C22×D5semidirect
496. C22×Q8C22×D5semidirect
530. #124C22×D5semidirect
536. C22⋊Q8C22×D5semidirect
542. #121C22×D5semidirect
546. C4×Q8C22×D5semidirect
554. C4×D4C22×D5semidirect
593. C22×C5C22×#41semidirect
605. C2×D5#548direct (N × H)
608. C2×D5C22×#41semidirect
650. C2×Q8D4×D5semidirect
732. C2×C5C2×#548semidirect
738. D5C2×#548direct (N × H)
764. C23D5×#41semidirect
772. Q8C2×D4×D5semidirect
813. C5C22×#548semidirect
837. C22C2×D5×#41semidirect
855. C2D5×#548direct (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
C23×Q8×D52
C2×C5×#5482
C2×#661652
C2×#661512
D5×#5482
C2×#660112
C2×D5×#1242
C2×#659672
C2×D5×C22⋊Q82
C2×D5×#1212
C2×#659322
C2×#659102
C2×C4×Q8×D52
C2×C4×D4×D52
C2×#658862
C22×#5485