Finite Group Databasebeta

← Q8×D5×#67 #14482920

Subgroups — Q8×D5×#67 #14482920

Order 1920.

3136 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×C3×Q8×D5C211yesmaximal, characteristic, complemented
2C2×D3×Q8×D5C211yesmaximal, characteristic, complemented
3Q8×#1220C211yesmaximal, characteristic, complemented
4C5×Q8×#67C211yesmaximal, characteristic, complemented
5D5×#946C213yesmaximal, complemented
6Q8×#1202C211yesmaximal, characteristic, complemented
7Q8×#1201C211yesmaximal, characteristic, complemented
8#11755228C213yesmaximal, complemented
9#11755225C213yesmaximal, complemented
10Q8×D5×Dic3C211yesmaximal, characteristic, complemented
11D5×#944C213yesmaximal, complemented
12C4×D5×#67C213yesmaximal
13#67×Dic10C213yesmaximal, complemented
14D5×#924C213yesmaximal, complemented
15#11754167C213yesmaximal, complemented
16D4×Q8×D5—31nomaximal, Hall
17C22×C3×C5×Q8C2211yescharacteristic, complemented
18C2×Q8×D15C2211yescharacteristic, complemented
19C2×C5×D3×Q8C2211yescharacteristic, complemented
20C2×C3×Q8×D5—28no—
21C2×C3×Q8×D5C2213yes—
22C2×C3×Q8×D5C2211yescharacteristic
23C2×C3×Q8×D5C2213yescomplemented
24C2×C3×Q8×D5C2211yescharacteristic, complemented
25C22×C3×C4×D5C2213yes—
26C22×C3×Dic10C2213yescomplemented
27C2×D5×#67C2211yescharacteristic
28D3×Q8×D5—28no—
29C2×C4×D3×D5C2213yes—
30C2×D15⋊Q8C2213yescomplemented
31C2×D3×Dic10C2213yescomplemented
32C2×D5×Dic6C2213yes—
33#91835C2213yescomplemented
34Q8×Dic15C2211yescharacteristic, complemented
35#91833C2213yescomplemented
36C4×#1220C2213yes—
37#91813C2213yescomplemented
38C5×#946C2213yescomplemented
39C5×Q8×Dic3C2211yescharacteristic, complemented
40C5×#944C2213yescomplemented
41C4×C5×#67C2213yes—
42C5×#924C2213yescomplemented
43#91574C2216yescomplemented
44#91552C2213yes—
45Dic5×#67C2213yes—
46D5×#217C2213yes—
47D5×(C2×D3)⋊C4C2213yes—
48#91444C2213yes—
49C4×#1202C2213yes—
50#91440C2213yes—
51C4×#1201C2213yes—
52D5×C4⋊Dic3C2213yes—
53#91411C2216yescomplemented
54#91410C2216yescomplemented
55D5×Dic3⋊C4C2216yes—
56D5×Dic3⋊C4C2213yes—
57C4×D5×Dic3C2213yes—
58#91390C2213yescomplemented
59#91389C2213yescomplemented
60#91385C2213yescomplemented
61#91369C2213yescomplemented
62#91360C2213yescomplemented
63#91359C2213yescomplemented
64#91349C2216yescomplemented
65#91331C2213yescomplemented
66Dic3×Dic10C2213yescomplemented
67#91327C2216yescomplemented
68#91327C2216yescomplemented
69C2×Q8×#67—51nomaximal, Hall
70C22×Q8×D5—31no—
71C22×Q8×D5D311yescharacteristic, complemented
72C5×D4×Q8—31no—
73Q8×C22⋊D5—31no—
74Q8×C22⋊D5—31no—
75#66061—33no—
76D5×C4⋊Q8—33no—
77#65966—33no—
78#65966—33no—
79D5×C22⋊Q8—33no—
80D5×C22⋊Q8—33no—
81Q8×D20—31no—
82C4×Q8×D5—31no—
83C4×D4×D5—33no—
84D4×Dic10—33no—
85C23×C3×D5C2311yescharacteristic
86C22×D3×D5C2311yescharacteristic
87C2×C3×C5×Q8—24no—
88C2×C3×C5×Q8C2313yes—
89C2×C3×C5×Q8C2311yescharacteristic
90C22×C3×C4×C5C2313yes—
91C2×#1220C2311yescharacteristic
92Q8×D15—24no—
93C2×C4×D15C2313yes—
94C2×Dic30C2313yes—
95C2×C5×#67C2311yescharacteristic
96C5×D3×Q8—24no—
97C2×C4×C5×D3C2313yes—
98C2×C5×Dic6C2313yes—
99C22×C3×Dic5C2313yes—
100C3×Q8×D5—24no—
101C3×Q8×D5—212no—
102C3×Q8×D5—212no—
103C3×Q8×D5D418yescomplemented
104C2×C3×C4×D5—212no—
105C2×C3×C4×D5C2313yes—
106C2×C3×C4×D5C2313yes—
107C2×C3×C4×D5C2313yes—
108C2×C3×C4×D5C2313yes—
109C2×C3×Dic10—212no—
110C2×C3×Dic10C2316yes—
111C2×C3×Dic10C2313yes—
112C2×C3×Dic10C2313yes—
113D5×#67Q818yesdirect product factor
114C2×#1204C2316yes—
115C2×#1202C2311yescharacteristic
116C2×#1201C2311yescharacteristic
117C2×#1200C2313yes—
118C2×D3×Dic5C2313yes—
119C2×D5×Dic3C2313yes—
120C2×D5×Dic3C2313yes—
121C2×D5×Dic3C2311yescharacteristic
122C4×D3×D5—212no—
123D15⋊Q8—212no—
124D3×Dic10—212no—
125D5×Dic6—212no—
126#6719C2313yes—
127#6714C2313yes—
128C4⋊Dic15C2313yes—
129#6712C2316yes—
130#6712C2313yes—
131C4×Dic15C2313yes—
132C5×#217C2313yes—
133C5×(C2×D3)⋊C4C2313yes—
134C5×C4⋊Dic3C2313yes—
135C5×Dic3⋊C4C2316yes—
136C5×Dic3⋊C4C2313yes—
137C4×C5×Dic3C2313yes—
138Dic3⋊Dic5C2316yes—
139Dic3⋊Dic5C2313yes—
140#6669C2316yes—
141#6669C2313yes—
142#6668C2316yes—
143#6667C2313yes—
144(C2×D3)⋊Dic5C2313yes—
145#6665C2313yes—
146#6665C2313yes—
147Dic3×Dic5C2313yes—
148Dic3×Dic5C2313yes—
149C23×C3×Q8—51no—
150C22×D3×Q8—51no—
151Q8×#67—51no—
152Q8×#67—51no—
153Q8×#67—53no—
154Q8×#67—51no—
155Q8×#67—53no—
156Q8×#67—53no—
157Q8×#67—53no—
158Q8×#67D511yescharacteristic, direct product factor
159C2×#946—53no—
160C2×Q8×Dic3—51no—
161C2×#944—53no—
162C2×C4×#67—53no—
163C2×#924—53no—
164C22×C5×Q8—31no—
165C22×C5×Q8C2×D311yescharacteristic, complemented
166C2×Q8×D5—28no—
167C2×Q8×D5—31no—
168C2×Q8×D5—33no—
169C2×Q8×D5—33no—
170C2×Q8×D5—68no—
171C2×Q8×D5C2×D313yes—
172C2×Q8×D5C2×D311yescharacteristic
173C2×Q8×D5C2×D313yescomplemented
174C2×Q8×D5C2×D311yescharacteristic, complemented
175C2×D4×D5—31no—
176C22×C4×D5—33no—
177C22×C4×D5C2×D313yes—
178C22×Dic10—33no—
179C22×Dic10C2×D313yescomplemented
180C5×C4⋊Q8—33no—
181C5×C22⋊Q8—33no—
182C5×C22⋊Q8—33no—
183C4×C5×Q8—31no—
184C4×C5×D4—33no—
185#4092—33no—
186#4092—33no—
187Q8×Dic5—31no—
188#4090—33no—
189#4090—33no—
190D4×Dic5—33no—
191C4×C22⋊D5—33no—
192C4×C22⋊D5—33no—
193#4070—33no—
194#4070—33no—
195#4043—33no—
196#4043—33no—
197#4042—36no—
198#4042—36no—
199#4039—33no—
200D5×C4⋊C4—33no—
201D5×C4⋊C4—36no—
202D5×C4⋊C4—33no—
203#4034—36no—
204#4034—36no—
205#4033—33no—
206#4027—33no—
207#4027—33no—
208D5×C22⋊C4—33no—
209D5×C22⋊C4—33no—
210#4024—36no—
211#4024—36no—
212C4×D20—33no—
213C42×D5—33no—
214#4015—33no—
215C4×Dic10—33no—
216C2×D4×Q8—151noSylow
217C23×C3×C5C2411yescharacteristic
218C22×D15C2411yescharacteristic
219C22×C5×D3C2411yescharacteristic
220C22×C3×D5—22no—
221C22×C3×D5—22no—
222C22×C3×D5C2×Q814yescomplemented
223C22×C3×D5C2411yescharacteristic
224C22×C3×D5C2411yescharacteristic
225C2×D3×D5—22no—
226C2×D3×D5—22no—
227C2×D3×D5C2×Q814yescomplemented
228C3×C5×Q8—26no—
229C3×C5×Q8C2×D414yescomplemented
230C2×C3×C4×C5—26no—
231C2×C3×C4×C5C2413yes—
232C2×C3×C4×C5C2413yes—
233#1220C2×Q814yescomplemented
234C2×Dic15C2413yes—
235C2×Dic15C2413yes—
236C2×Dic15C2411yescharacteristic
237C4×D15—26no—
238Dic30—26no—
239C5×#67C2×Q814yescomplemented
240C2×C5×Dic3C2413yes—
241C2×C5×Dic3C2413yes—
242C2×C5×Dic3C2411yescharacteristic
243C4×C5×D3—26no—
244C5×Dic6—26no—
245C2×C3×Dic5—26no—
246C2×C3×Dic5C2413yes—
247C2×C3×Dic5C2413yes—
248C3×C4×D5—26no—
249C3×C4×D5—26no—
250C3×C4×D5—26no—
251C3×C4×D5C2×D4112yes—
252C3×Dic10—26no—
253C3×Dic10—212no—
254C3×Dic10C2×D4112yescomplemented
255#1204—212no—
256#1202C2×Q814yescomplemented
257#1201C2×Q814yescomplemented
258#1200—26no—
259D3×Dic5—26no—
260D5×Dic3—26no—
261D5×Dic3—26no—
262D5×Dic3C2×Q814yescomplemented
263C22×C3×Q8—51no—
264C22×C3×Q8—53no—
265C22×C3×Q8—53no—
266C22×C3×Q8—51no—
267C22×C3×Q8—53no—
268C22×C3×Q8—108no—
269C22×C3×Q8C2×D511yescharacteristic, complemented
270C23×C3×C4—53no—
271C22×#67—51no—
272C2×D3×Q8—51no—
273C2×D3×Q8—53no—
274C2×D3×Q8—53no—
275C2×D3×Q8—108no—
276C2×D3×Q8C2×D511yescharacteristic, complemented
277C22×C4×D3—53no—
278C22×Dic6—53no—
279C2×#217—53no—
280#946—53no—
281#946—53no—
282#946—56no—
283#946—53no—
284#946—56no—
285#946C2×D513yescomplemented
286Q8×Dic3—51no—
287Q8×Dic3—53no—
288Q8×Dic3—53no—
289Q8×Dic3C2×D511yescharacteristic, complemented
290#944—53no—
291#944—53no—
292#944—56no—
293#944—56no—
294#944—53no—
295#944C2×D513yescomplemented
296C4×#67—53no—
297C4×#67—53no—
298C4×#67—53no—
299C4×#67—53no—
300C4×#67—53no—
301C4×#67—53no—
302C4×#67—53no—
303C4×#67C2×D513yes—
304C2×(C2×D3)⋊C4—53no—
305C2×C4⋊Dic3—53no—
306#924—53no—
307#924—53no—
308#924—56no—
309#924—53no—
310#924—56no—
311#924C2×D513yescomplemented
312C2×Dic3⋊C4—56no—
313C2×Dic3⋊C4—53no—
314C2×C4×Dic3—53no—
315C23×D5—31no—
316C23×D5C22×D311yescharacteristic
317C2×C5×Q8—24no—
318C2×C5×Q8—33no—
319C2×C5×Q8—64no—
320C2×C5×Q8C22×D313yes—
321C2×C5×Q8C22×D311yescharacteristic
322C2×C5×D4—31no—
323C22×C4×C5—33no—
324C22×C4×C5C22×D313yes—
325C2×C22⋊D5—31no—
326C2×C22⋊D5—31no—
327C22×Dic5—33no—
328C22×Dic5C22×D313yes—
329Q8×D5—24no—
330Q8×D5—212no—
331Q8×D5—212no—
332Q8×D5—64no—
333Q8×D5—612no—
334Q8×D5—612no—
335Q8×D5#6718yesdirect product factor
336D4×D5—38no—
337C2×D20—31no—
338C2×C4×D5—212no—
339C2×C4×D5—31no—
340C2×C4×D5—33no—
341C2×C4×D5—33no—
342C2×C4×D5—33no—
343C2×C4×D5—33no—
344C2×C4×D5—612no—
345C2×C4×D5C22×D313yes—
346C2×C4×D5C22×D313yes—
347C2×C4×D5C22×D313yes—
348C2×C4×D5C22×D313yes—
349C2×Dic10—212no—
350C2×Dic10—33no—
351C2×Dic10—36no—
352C2×Dic10—612no—
353C2×Dic10C22×D313yes—
354C2×Dic10C22×D316yes—
355C2×Dic10C22×D313yes—
356C5×C4⋊C4—33no—
357C5×C4⋊C4—33no—
358C5×C4⋊C4—36no—
359C5×C22⋊C4—33no—
360C5×C22⋊C4—33no—
361C42×C5—33no—
362C22⋊Dic5—33no—
363C22⋊Dic5—33no—
364#685—33no—
365#685—33no—
366#685—33no—
367#685—33no—
368C4⋊Dic5—33no—
369C4⋊Dic5—33no—
370C4⋊Dic5—36no—
371#683—36no—
372#683—33no—
373#683—36no—
374#683—36no—
375#683—33no—
376C4×Dic5—33no—
377C4×Dic5—33no—
378C4×Dic5—33no—
379C23×Q8—51no—
380C23×Q8—151no—
381D4×Q8—31no—
382D4×Q8—153no—
383D4×Q8—151no—
384D4×Q8—153no—
385D4×Q8—153no—
386D4×Q8—153no—
387D4×Q8—151no—
388D4×Q8—151no—
389C2×C4⋊Q8—153no—
390C2×C22⋊Q8—153no—
391C2×C22⋊Q8—153no—
392C2×C4×Q8—151no—
393C2×C4×D4—153no—
394C22×C3×C5—21no—
395C22×C3×C5—21no—
396C22×C3×C5C22×Q812yescomplemented
397C22×C3×C5C2511yescharacteristic
398C2×D15—21no—
399C2×D15—21no—
400C2×D15C22×Q812yescomplemented
401C2×C5×D3—21no—
402C2×C5×D3—21no—
403C2×C5×D3C22×Q812yescomplemented
404C2×C3×D5—21no—
405C2×C3×D5—21no—
406C2×C3×D5—28no—
407C2×C3×D5C22×D412yes—
408C2×C3×D5C22×Q812yes—
409C2×C3×D5C22×Q812yescomplemented
410C2×C3×D52−1+412yes—
411D3×D5—28no—
412C3×C4×C5—23no—
413C3×C4×C5C22×D416yes—
414Dic15—23no—
415Dic15—23no—
416Dic15C22×Q812yescomplemented
417C3×Dic5—23no—
418C3×Dic5C22×D416yes—
419C5×Dic3—23no—
420C5×Dic3—23no—
421C5×Dic3C22×Q812yescomplemented
422C24×C3—51no—
423C23×D3—51no—
424C2×C3×Q8—24no—
425C2×C3×Q8—58no—
426C2×C3×Q8—53no—
427C2×C3×Q8—56no—
428C2×C3×Q8—53no—
429C2×C3×Q8—1012no—
430C2×C3×Q8—1012no—
431C2×C3×Q8—1012no—
432C2×C3×Q8—104no—
433C2×C3×Q8C22×D513yes—
434C2×C3×Q8C22×D511yescharacteristic
435C22×C3×C4—53no—
436C22×C3×C4—53no—
437C22×C3×C4—53no—
438C22×C3×C4—53no—
439C22×C3×C4—53no—
440C22×C3×C4—1012no—
441C22×C3×C4C22×D513yes—
442C2×#67—51no—
443C2×#67—51no—
444C2×#67—58no—
445C2×#67—51no—
446C2×#67C22×D511yescharacteristic
447C22×Dic3—51no—
448C22×Dic3—53no—
449C22×Dic3—53no—
450D3×Q8—24no—
451D3×Q8—1012no—
452D3×Q8—1012no—
453D3×Q8—104no—
454C2×C4×D3—53no—
455C2×C4×D3—53no—
456C2×C4×D3—53no—
457C2×C4×D3—1012no—
458C2×C4×D3C22×D513yes—
459C2×Dic6—53no—
460C2×Dic6—56no—
461C2×Dic6—1012no—
462C2×Dic6C22×D513yes—
463#217—53no—
464#217—53no—
465#217—53no—
466#217C22×D513yes—
467(C2×D3)⋊C4—53no—
468(C2×D3)⋊C4—53no—
469(C2×D3)⋊C4—53no—
470(C2×D3)⋊C4C22×D513yes—
471C4⋊Dic3—53no—
472C4⋊Dic3—56no—
473C4⋊Dic3C22×D513yes—
474Dic3⋊C4—56no—
475Dic3⋊C4—53no—
476Dic3⋊C4—56no—
477Dic3⋊C4—53no—
478Dic3⋊C4—56no—
479Dic3⋊C4—53no—
480Dic3⋊C4C22×D516yes—
481Dic3⋊C4C22×D513yes—
482C4×Dic3—53no—
483C4×Dic3—53no—
484C4×Dic3—53no—
485C4×Dic3C22×D513yes—
486C23×C5—31no—
487C23×C5C23×D311yescharacteristic
488C22×D5—22no—
489C22×D5—22no—
490C22×D5—31no—
491C22×D5—34no—
492C22×D5—62no—
493C22×D5—62no—
494C22×D5D3×Q814yescomplemented
495C22×D5C23×D311yescharacteristic
496C22×D5C23×D311yescharacteristic
497C5×Q8—26no—
498C5×Q8—66no—
499C5×Q8C2×#6714yescomplemented
500C5×D4—34no—
501C2×C4×C5—26no—
502C2×C4×C5—31no—
503C2×C4×C5—33no—
504C2×C4×C5—33no—
505C2×C4×C5—66no—
506C2×C4×C5C23×D313yes—
507C2×C4×C5C23×D313yes—
508C22⋊D5—34no—
509C22⋊D5—34no—
510C2×Dic5—26no—
511C2×Dic5—31no—
512C2×Dic5—33no—
513C2×Dic5—33no—
514C2×Dic5—66no—
515C2×Dic5C23×D313yes—
516C2×Dic5C23×D313yes—
517D20—34no—
518C4×D5—26no—
519C4×D5—26no—
520C4×D5—26no—
521C4×D5—34no—
522C4×D5—66no—
523C4×D5—66no—
524C4×D5—66no—
525C4×D5—66no—
526C4×D5C2×#67112yes—
527Dic10—26no—
528Dic10—212no—
529Dic10—66no—
530Dic10—612no—
531Dic10C2×#67112yescomplemented
532C22×Q8—31no—
533C22×Q8—51no—
534C22×Q8—53no—
535C22×Q8—53no—
536C22×Q8—51no—
537C22×Q8—53no—
538C22×Q8—108no—
539C22×Q8—153no—
540C22×Q8—153no—
541C22×Q8—153no—
542C22×Q8—151no—
543C22×Q8—308no—
544C22×Q8D3×D511yescharacteristic, complemented
545C22×D4—151no—
546C23×C4—53no—
547C23×C4—153no—
548C4⋊Q8—33no—
549C4⋊Q8—153no—
550C4⋊Q8—156no—
551C4⋊Q8—156no—
552C4⋊Q8—153no—
553C4⋊Q8—153no—
554C22⋊Q8—33no—
555C22⋊Q8—33no—
556C22⋊Q8—156no—
557C22⋊Q8—156no—
558C22⋊Q8—156no—
559C22⋊Q8—153no—
560C22⋊Q8—156no—
561C22⋊Q8—153no—
562C22⋊Q8—153no—
563C22⋊Q8—153no—
564C22⋊Q8—153no—
565C22⋊Q8—153no—
566C4×Q8—31no—
567C4×Q8—153no—
568C4×Q8—153no—
569C4×Q8—151no—
570C4×D4—33no—
571C4×D4—153no—
572C4×D4—153no—
573C4×D4—153no—
574C4×D4—153no—
575C4×D4—153no—
576C4×D4—153no—
577C4×D4—153no—
578C2×C4⋊C4—153no—
579C2×C4⋊C4—153no—
580C2×C4⋊C4—156no—
581C2×C22⋊C4—153no—
582C2×C22⋊C4—153no—
583C2×C42—153no—
584C2×C3×C5—22no—
585C2×C3×C5C23×D411yescharacteristic
586C2×C3×C5C23×Q811yescharacteristic
587C2×C3×C5C2×2−1+411yescharacteristic
588D15—22no—
589C3×D5—22no—
590C3×D5D4×Q814yescomplemented
591C5×D3—22no—
592C23×C3—51no—
593C23×C3—54no—
594C23×C3—51no—
595C23×C3—102no—
596C23×C3—102no—
597C23×C3C23×D511yescharacteristic
598C22×D3—51no—
599C22×D3—54no—
600C22×D3—102no—
601C22×D3—102no—
602C22×D3C23×D511yescharacteristic
603C3×Q8—26no—
604C3×Q8—512no—
605C3×Q8—1012no—
606C3×Q8—106no—
607C3×Q8D4×D514yescomplemented
608C2×C3×C4—26no—
609C2×C3×C4—53no—
610C2×C3×C4—512no—
611C2×C3×C4—53no—
612C2×C3×C4—106no—
613C2×C3×C4—106no—
614C2×C3×C4—106no—
615C2×C3×C4—106no—
616C2×C3×C4C23×D513yes—
617C2×C3×C4C23×D513yes—
618#67—54no—
619#67—54no—
620#67—54no—
621#67Q8×D514yesdirect product factor
622C2×Dic3—51no—
623C2×Dic3—54no—
624C2×Dic3—53no—
625C2×Dic3—53no—
626C2×Dic3—106no—
627C2×Dic3—106no—
628C2×Dic3C23×D513yes—
629C2×Dic3C23×D513yes—
630C2×Dic3C23×D511yescharacteristic
631C4×D3—26no—
632C4×D3—106no—
633C4×D3—106no—
634C4×D3—106no—
635Dic6—26no—
636Dic6—1012no—
637Dic6—106no—
638C22×C5—21no—
639C22×C5—21no—
640C22×C5—32no—
641C22×C5—61no—
642C22×C5—61no—
643C22×C5C2×D3×Q812yescomplemented
644C22×C5C24×D311yescharacteristic
645C2×D5—21no—
646C2×D5—21no—
647C2×D5—28no—
648C2×D5—32no—
649C2×D5—61no—
650C2×D5—61no—
651C2×D5—68no—
652C2×D5C2×D3×Q812yes—
653C2×D5C2×D3×Q812yescomplemented
654C2×D5#100712yes—
655C2×D5C22×#6712yes—
656C4×C5—23no—
657C4×C5—32no—
658C4×C5—63no—
659C4×C5—63no—
660C4×C5C22×#6716yes—
661Dic5—23no—
662Dic5—32no—
663Dic5—63no—
664Dic5—63no—
665Dic5C22×#6716yes—
666C24—51no—
667C24—151no—
668C2×Q8—24no—
669C2×Q8—33no—
670C2×Q8—58no—
671C2×Q8—53no—
672C2×Q8—56no—
673C2×Q8—53no—
674C2×Q8—64no—
675C2×Q8—1012no—
676C2×Q8—1012no—
677C2×Q8—1012no—
678C2×Q8—104no—
679C2×Q8—156no—
680C2×Q8—153no—
681C2×Q8—3012no—
682C2×Q8—3012no—
683C2×Q8—3012no—
684C2×Q8—304no—
685C2×Q8C2×D3×D513yes—
686C2×Q8C2×D3×D511yescharacteristic
687C2×D4—31no—
688C2×D4—151no—
689C2×D4—158no—
690C2×D4—151no—
691C2×D4—151no—
692C22×C4—33no—
693C22×C4—53no—
694C22×C4—53no—
695C22×C4—53no—
696C22×C4—53no—
697C22×C4—53no—
698C22×C4—1012no—
699C22×C4—153no—
700C22×C4—151no—
701C22×C4—153no—
702C22×C4—153no—
703C22×C4—153no—
704C22×C4—153no—
705C22×C4—3012no—
706C22×C4C2×D3×D513yes—
707C4⋊C4—33no—
708C4⋊C4—33no—
709C4⋊C4—36no—
710C4⋊C4—153no—
711C4⋊C4—153no—
712C4⋊C4—156no—
713C4⋊C4—156no—
714C4⋊C4—156no—
715C4⋊C4—153no—
716C4⋊C4—153no—
717C4⋊C4—156no—
718C22⋊C4—33no—
719C22⋊C4—33no—
720C22⋊C4—153no—
721C22⋊C4—153no—
722C22⋊C4—153no—
723C22⋊C4—153no—
724C22⋊C4—153no—
725C22⋊C4—153no—
726C42—33no—
727C42—153no—
728C42—153no—
729C42—153no—
730C3×C5C2×D4×Q811yescharacteristic, complemented, Hall
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—52no—
734C22×C3—52no—
735C22×C3—52no—
736C22×C3—52no—
737C22×C3—108no—
738C22×C3—101no—
739C22×C3—101no—
740C22×C3C2×Q8×D512yescomplemented
741C22×C3C24×D511yescharacteristic
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—52no—
745C2×D3—108no—
746C2×D3—101no—
747C2×D3—101no—
748C2×D3C2×Q8×D512yescomplemented
749C3×C4—23no—
750C3×C4—56no—
751C3×C4—103no—
752C3×C4C2×D4×D516yes—
753Dic3—23no—
754Dic3—23no—
755Dic3—52no—
756Dic3—103no—
757Dic3—103no—
758Dic3C2×Q8×D512yescomplemented
759C2×C5—22no—
760C2×C5—62no—
761C2×C5C22×D3×Q811yescharacteristic
762C2×C5C2×#100711yescharacteristic
763C2×C5C23×#6711yescharacteristic
764D5—22no—
765D5—62no—
766D5Q8×#6714yesdirect product factor
767C23—31no—
768C23—51no—
769C23—54no—
770C23—51no—
771C23—102no—
772C23—102no—
773C23—154no—
774C23—151no—
775C23—302no—
776C23—302no—
777C23C22×D3×D511yescharacteristic
778Q8—26no—
779Q8—512no—
780Q8—66no—
781Q8—1012no—
782Q8—106no—
783Q8—3012no—
784Q8—306no—
785Q8D5×#6714yesdirect product factor
786D4—34no—
787D4—154no—
788D4—154no—
789D4—154no—
790C2×C4—26no—
791C2×C4—31no—
792C2×C4—33no—
793C2×C4—33no—
794C2×C4—53no—
795C2×C4—512no—
796C2×C4—53no—
797C2×C4—66no—
798C2×C4—106no—
799C2×C4—106no—
800C2×C4—106no—
801C2×C4—106no—
802C2×C4—154no—
803C2×C4—151no—
804C2×C4—153no—
805C2×C4—153no—
806C2×C4—306no—
807C2×C4—306no—
808C2×C4—306no—
809C2×C4—306no—
810C2×C4—306no—
811C2×C4C22×D3×D513yes—
812C2×C4C22×D3×D513yes—
813C2×C3—22no—
814C2×C3—54no—
815C2×C3—102no—
816C2×C3C22×D4×D511yescharacteristic
817C2×C3C22×Q8×D511yescharacteristic
818C2×C3D5×2−1+411yescharacteristic
819D3—22no—
820D3—102no—
821C5C2×Q8×#6711yescharacteristic, complemented, Sylow
822C22—21no—
823C22—21no—
824C22—32no—
825C22—52no—
826C22—52no—
827C22—52no—
828C22—52no—
829C22—61no—
830C22—61no—
831C22—108no—
832C22—101no—
833C22—101no—
834C22—152no—
835C22—308no—
836C22—301no—
837C22—301no—
838C22D3×Q8×D512yescomplemented
839C22C23×D3×D511yescharacteristic
840C4—23no—
841C4—32no—
842C4—56no—
843C4—63no—
844C4—63no—
845C4—103no—
846C4—152no—
847C4—303no—
848C4—303no—
849C4C2×D5×#6716yes—
850C3D4×Q8×D511yescharacteristic, complemented, Sylow
851C2—22no—
852C2—54no—
853C2—62no—
854C2—102no—
855C2—302no—
856C2C2×D3×Q8×D511yescharacteristic
857C2D5×#100711yescharacteristic
858C2C22×D5×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC22×C3×C5×Q8C22
prime radicalC2×D5×#67C22
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×D4×Q8
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×Q8×D5C2semidirect
2. C2×D3×Q8×D5C2semidirect
3. Q8×#1220C2semidirect
4. C5×Q8×#67C2semidirect
5. D5×#946C2semidirect
6. Q8×#1202C2semidirect
7. Q8×#1201C2semidirect
8. #11755228C2semidirect
9. #11755225C2semidirect
10. Q8×D5×Dic3C2semidirect
11. D5×#944C2semidirect
13. #67×Dic10C2semidirect
14. D5×#924C2semidirect
15. #11754167C2semidirect
17. C22×C3×C5×Q8C22semidirect
18. C2×Q8×D15C22semidirect
19. C2×C5×D3×Q8C22semidirect
23. C2×C3×Q8×D5C22semidirect
24. C2×C3×Q8×D5C22semidirect
26. C22×C3×Dic10C22semidirect
30. C2×D15⋊Q8C22semidirect
31. C2×D3×Dic10C22semidirect
33. #91835C22semidirect
34. Q8×Dic15C22semidirect
35. #91833C22semidirect
37. #91813C22semidirect
38. C5×#946C22semidirect
39. C5×Q8×Dic3C22semidirect
40. C5×#944C22semidirect
42. C5×#924C22semidirect
43. #91574C22semidirect
53. #91411C22semidirect
54. #91410C22semidirect
58. #91390C22semidirect
59. #91389C22semidirect
60. #91385C22semidirect
61. #91369C22semidirect
62. #91360C22semidirect
63. #91359C22semidirect
64. #91349C22semidirect
65. #91331C22semidirect
66. Dic3×Dic10C22semidirect
67. #91327C22semidirect
68. #91327C22semidirect
71. C22×Q8×D5D3semidirect
103. C3×Q8×D5D4semidirect
113. D5×#67Q8direct (N × H)
158. Q8×#67D5direct (N × H)
165. C22×C5×Q8C2×D3semidirect
173. C2×Q8×D5C2×D3semidirect
174. C2×Q8×D5C2×D3semidirect
179. C22×Dic10C2×D3semidirect
222. C22×C3×D5C2×Q8semidirect
227. C2×D3×D5C2×Q8semidirect
229. C3×C5×Q8C2×D4semidirect
233. #1220C2×Q8semidirect
239. C5×#67C2×Q8semidirect
254. C3×Dic10C2×D4semidirect
256. #1202C2×Q8semidirect
257. #1201C2×Q8semidirect
262. D5×Dic3C2×Q8semidirect
269. C22×C3×Q8C2×D5semidirect
276. C2×D3×Q8C2×D5semidirect
285. #946C2×D5semidirect
289. Q8×Dic3C2×D5semidirect
295. #944C2×D5semidirect
311. #924C2×D5semidirect
335. Q8×D5#67direct (N × H)
396. C22×C3×C5C22×Q8semidirect
400. C2×D15C22×Q8semidirect
403. C2×C5×D3C22×Q8semidirect
409. C2×C3×D5C22×Q8semidirect
416. Dic15C22×Q8semidirect
421. C5×Dic3C22×Q8semidirect
494. C22×D5D3×Q8semidirect
499. C5×Q8C2×#67semidirect
531. Dic10C2×#67semidirect
544. C22×Q8D3×D5semidirect
590. C3×D5D4×Q8semidirect
607. C3×Q8D4×D5semidirect
621. #67Q8×D5direct (N × H)
643. C22×C5C2×D3×Q8semidirect
653. C2×D5C2×D3×Q8semidirect
730. C3×C5C2×D4×Q8semidirect
740. C22×C3C2×Q8×D5semidirect
748. C2×D3C2×Q8×D5semidirect
758. Dic3C2×Q8×D5semidirect
766. D5Q8×#67direct (N × H)
785. Q8D5×#67direct (N × H)
821. C5C2×Q8×#67semidirect
838. C22D3×Q8×D5semidirect
850. C3D4×Q8×D5semidirect

Maximal subgroups

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

subgroupindex
C22×C3×Q8×D52
C2×D3×Q8×D52
Q8×#12202
C5×Q8×#672
D5×#9462
Q8×#12022
Q8×#12012
#117552282
#117552252
Q8×D5×Dic32
D5×#9442
C4×D5×#672
#67×Dic102
D5×#9242
#117541672
D4×Q8×D53
C2×Q8×#675