Finite Group Databasebeta

← D5×#5817 #14482829

Subgroups — D5×#5817 #14482829

Order 1920.

3240 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×D5×#239C211yesmaximal, characteristic, complemented
3#11756576C211yesmaximal, characteristic, complemented
4C5×#5817C211yesmaximal, characteristic, complemented
5D5×#947C213yesmaximal, complemented
6D5×#946C213yesmaximal, complemented
7#11755244C211yesmaximal, characteristic, complemented
8#11755227C213yesmaximal, complemented
9#11755226C213yesmaximal, complemented
10Q8×D5×Dic3C211yesmaximal, characteristic, complemented
11#11755128C211yesmaximal, characteristic, complemented
12D5×#930C213yesmaximal, complemented
13C4×D5×#67C213yesmaximal, complemented
14#11754321C213yesmaximal, complemented
15#11754319C213yesmaximal, complemented
16D5×#548—31nomaximal, Hall
17C22×C3×C5×Q8C2211yescharacteristic, complemented
18C2×#6821C2211yescharacteristic, complemented
19C2×C5×#239C2211yescharacteristic, complemented
20C2×C3×Q8×D5—28no—
21C2×C3×Q8×D5C2213yes—
22C2×C3×Q8×D5C2211yescharacteristic
23C2×C3×Q8×D5C2211yescharacteristic, complemented
24C2×C3×Q8×D5C2213yescomplemented
25C22×C3×C4×D5C2213yes—
26C22×C3×Dic10C2213yescomplemented
27C2×D5×#67C2213yes—
28D5×#239—28no—
29C2×D5×D12C2213yes—
30C2×C4×D3×D5C2213yes—
31C2×#6769C2213yescomplemented
32C2×#6768C2213yescomplemented
33#91836C2213yescomplemented
34#91835C2213yescomplemented
35Q8×Dic15C2211yescharacteristic, complemented
36#91819C2213yescomplemented
37C4×#1220C2213yescomplemented
38C5×#947C2213yescomplemented
39C5×#946C2213yescomplemented
40C5×Q8×Dic3C2211yescharacteristic, complemented
41C5×#930C2213yescomplemented
42C4×C5×#67C2213yescomplemented
43#91566C2216yescomplemented
44#91552C2213yescomplemented
45Dic5×#67C2213yescomplemented
46D5×#217C2211yescharacteristic
47D5×(C2×D3)⋊C4C2216yes—
48D5×(C2×D3)⋊C4C2213yes—
49#91450C2213yescomplemented
50#91449C2213yescomplemented
51#91448C2216yescomplemented
52#91444C2213yescomplemented
53C4×#1202C2213yescomplemented
54#91440C2213yescomplemented
55C4×#1201C2213yescomplemented
56D5×C4⋊Dic3C2213yes—
57#91411C2216yescomplemented
58#91410C2216yescomplemented
59D5×Dic3⋊C4C2213yes—
60C4×D5×Dic3C2213yes—
61#91390C2213yescomplemented
62#91374C2213yescomplemented
63#91370C2213yescomplemented
64#91369C2213yescomplemented
65#91331C2213yescomplemented
66Dic3×Dic10C2213yescomplemented
67#91326C2216yescomplemented
68#91326C2216yescomplemented
69C2×#5817—51nomaximal, Hall
70C2×D5×#41—31no—
71C22×Q8×D5D311yescharacteristic, complemented
72C5×#548—31no—
73#66165—31no—
74#66151—31no—
75#66011—33no—
76D5×#124—33no—
77#65967—33no—
78D5×C22⋊Q8—33no—
79D5×#121—33no—
80#65932—33no—
81#65910—31no—
82C4×Q8×D5—31no—
83#65886—33no—
84C4×D4×D5—33no—
85C23×C3×D5C2311yescharacteristic
86C22×D3×D5C2313yes—
87C2×C3×C5×Q8—24no—
88C2×C3×C5×Q8C2313yes—
89C2×C3×C5×Q8C2311yescharacteristic
90C22×C3×C4×C5C2313yes—
91C2×#1220C2313yes—
92#6821—24no—
93C2×D60C2313yes—
94C2×C4×D15C2313yes—
95C2×C5×#67C2313yes—
96C5×#239—24no—
97C2×C5×D12C2313yes—
98C2×C4×C5×D3C2313yes—
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×#67—212no—
114C2×#1203C2316yes—
115C2×#1202C2313yes—
116C2×#1201C2313yes—
117C2×#1200C2313yes—
118C2×D3×Dic5C2313yes—
119C2×D5×Dic3C2311yescharacteristic
120C2×D5×Dic3C2313yes—
121C2×D5×Dic3C2311yescharacteristic
122D5×D12—212no—
123C4×D3×D5—212no—
124#6769—212no—
125#6768—212no—
126#6719C2311yescharacteristic
127#6714C2316yes—
128#6714C2313yes—
129C4⋊Dic15C2313yes—
130#6712C2313yes—
131C4×Dic15C2313yes—
132C5×#217C2311yescharacteristic
133C5×(C2×D3)⋊C4C2316yes—
134C5×(C2×D3)⋊C4C2313yes—
135C5×C4⋊Dic3C2313yes—
136C5×Dic3⋊C4C2313yes—
137C4×C5×Dic3C2313yes—
138Dic3⋊Dic5C2313yes—
139#6669C2313yes—
140#6668C2316yes—
141#6667C2316yes—
142#6667C2313yes—
143(C2×D3)⋊Dic5C2316yes—
144(C2×D3)⋊Dic5C2313yes—
145#6665C2311yescharacteristic
146#6665C2311yescharacteristic
147Dic3×Dic5C2313yes—
148Dic3×Dic5C2313yes—
149C23×C3×Q8—51no—
150C22×#239—51no—
151#5817—51no—
152#5817—51no—
153#5817—53no—
154#5817—53no—
155#5817—51no—
156#5817—53no—
157#5817—53no—
158#5817D511yescharacteristic, direct product factor
159C2×#947—53no—
160C2×#946—53no—
161C2×Q8×Dic3—51no—
162C2×#930—53no—
163C2×C4×#67—53no—
164C2×C5×#41—31no—
165C22×C5×Q8C2×D311yescharacteristic, complemented
166D5×#41—68no—
167C2×#713—31no—
168C2×Q8×D5—28no—
169C2×Q8×D5C2×D313yes—
170C2×Q8×D5C2×D311yescharacteristic
171C2×Q8×D5C2×D311yescharacteristic, complemented
172C2×Q8×D5C2×D313yescomplemented
173C2×#711—33no—
174C2×D4×D5—33no—
175C2×D4×D5—33no—
176C2×#709—33no—
177C22×C4×D5—33no—
178C22×C4×D5C2×D313yes—
179C22×Dic10C2×D313yescomplemented
180C5×#124—33no—
181C5×C22⋊Q8—33no—
182C5×#121—33no—
183C4×C5×Q8—31no—
184C4×C5×D4—33no—
185#4093—33no—
186#4092—33no—
187Q8×Dic5—31no—
188#4085—36no—
189#4084—33no—
190#4082—33no—
191D4×Dic5—33no—
192#4076—33no—
193C4×C22⋊D5—33no—
194C4×C22⋊D5—33no—
195#4070—33no—
196#4043—33no—
197#4042—36no—
198#4041—33no—
199#4039—33no—
200D5×C4⋊C4—33no—
201D5×C4⋊C4—33no—
202#4033—33no—
203#4031—36no—
204#4031—36no—
205#4030—36no—
206#4027—33no—
207#4027—33no—
208D5×C22⋊C4—31no—
209D5×C22⋊C4—33no—
210D5×C22⋊C4—36no—
211#4024—36no—
212#4021—33no—
213C4×D20—33no—
214C42×D5—33no—
215C4×Dic10—33no—
216C2×#548—151noSylow
217C23×C3×C5C2411yescharacteristic
218C22×D15C2413yes—
219C22×C5×D3C2413yes—
220C22×C3×D5—22no—
221C22×C3×D5—22no—
222C22×C3×D5#4114yescomplemented
223C22×C3×D5C2411yescharacteristic
224C22×C3×D5C2411yescharacteristic
225C2×D3×D5—26no—
226C2×D3×D5—26no—
227C2×D3×D5—26no—
228C3×C5×Q8—26no—
229C3×C5×Q8C2×D414yescomplemented
230C2×C3×C4×C5—26no—
231C2×C3×C4×C5C2413yes—
232C2×C3×C4×C5C2413yes—
233#1220—26no—
234C2×Dic15C2411yescharacteristic
235C2×Dic15C2413yes—
236C2×Dic15C2411yescharacteristic
237D60—26no—
238C4×D15—26no—
239C5×#67—26no—
240C2×C5×Dic3C2411yescharacteristic
241C2×C5×Dic3C2413yes—
242C2×C5×Dic3C2411yescharacteristic
243C5×D12—26no—
244C4×C5×D3—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#1203—212no—
256#1202—26no—
257#1201—26no—
258#1200—26no—
259D3×Dic5—26no—
260D5×Dic3—22no—
261D5×Dic3—26no—
262D5×Dic3—22no—
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—53no—
272C2×#239—51no—
273C2×#239—53no—
274C2×#239—53no—
275C2×#239—108no—
276C2×#239C2×D511yescharacteristic, complemented
277C22×D12—53no—
278C22×C4×D3—53no—
279C2×#217—51no—
280#947—53no—
281#947—53no—
282#947—56no—
283#947—56no—
284#947—53no—
285#947C2×D513yescomplemented
286#946—53no—
287#946—53no—
288#946—56no—
289#946—53no—
290#946—56no—
291#946C2×D513yescomplemented
292Q8×Dic3—51no—
293Q8×Dic3—53no—
294Q8×Dic3—53no—
295Q8×Dic3C2×D511yescharacteristic, complemented
296#930—53no—
297#930—56no—
298#930—53no—
299#930—56no—
300#930—53no—
301#930C2×D513yescomplemented
302C4×#67—53no—
303C4×#67—53no—
304C4×#67—53no—
305C4×#67—53no—
306C4×#67—53no—
307C4×#67—53no—
308C4×#67—53no—
309C4×#67C2×D513yescomplemented
310C2×(C2×D3)⋊C4—53no—
311C2×(C2×D3)⋊C4—56no—
312C2×C4⋊Dic3—53no—
313C2×Dic3⋊C4—53no—
314C2×C4×Dic3—53no—
315C23×D5—33no—
316C23×D5C22×D311yescharacteristic
317C5×#41—64no—
318C2×C5×Q8—24no—
319C2×C5×Q8C22×D313yes—
320C2×C5×Q8C22×D311yescharacteristic
321C2×C5×D4—33no—
322C2×C5×D4—33no—
323C22×C4×C5—33no—
324C22×C4×C5C22×D313yes—
325C2×C22⋊D5—33no—
326C2×C22⋊D5—33no—
327C2×C22⋊D5—36no—
328C22×Dic5—33no—
329C22×Dic5C22×D313yes—
330#713—64no—
331Q8×D5—24no—
332Q8×D5—212no—
333Q8×D5—212no—
334Q8×D5#6718yescomplemented
335#711—612no—
336D4×D5—612no—
337D4×D5—612no—
338#709—612no—
339C2×D20—33no—
340C2×D20—33no—
341C2×C4×D5—212no—
342C2×C4×D5—31no—
343C2×C4×D5—33no—
344C2×C4×D5—31no—
345C2×C4×D5—33no—
346C2×C4×D5—33no—
347C2×C4×D5—612no—
348C2×C4×D5C22×D313yes—
349C2×C4×D5C22×D313yes—
350C2×C4×D5C22×D313yes—
351C2×C4×D5C22×D313yes—
352C2×Dic10—212no—
353C2×Dic10C22×D313yes—
354C2×Dic10C22×D316yes—
355C2×Dic10C22×D313yes—
356C5×C4⋊C4—33no—
357C5×C4⋊C4—33no—
358C5×C22⋊C4—31no—
359C5×C22⋊C4—33no—
360C5×C22⋊C4—36no—
361C42×C5—33no—
362C22⋊Dic5—31no—
363C22⋊Dic5—36no—
364C22⋊Dic5—33no—
365#685—31no—
366#685—31no—
367#685—36no—
368#685—33no—
369#685—33no—
370#685—36no—
371C4⋊Dic5—33no—
372C4⋊Dic5—33no—
373#683—33no—
374#683—36no—
375#683—33no—
376C4×Dic5—33no—
377C4×Dic5—33no—
378C4×Dic5—33no—
379C22×#41—151no—
380C23×Q8—51no—
381#548—31no—
382#548—153no—
383#548—151no—
384#548—153no—
385#548—153no—
386#548—153no—
387#548—151no—
388#548—151no—
389C2×#124—153no—
390C2×C22⋊Q8—153no—
391C2×#121—153no—
392C2×C4×Q8—151no—
393C2×C4×D4—153no—
394C22×C3×C5—21no—
395C22×C3×C5—21no—
396C22×C3×C5C2×#4112yescomplemented
397C22×C3×C5C2511yescharacteristic
398C2×D15—23no—
399C2×D15—23no—
400C2×D15—23no—
401C2×C5×D3—23no—
402C2×C5×D3—23no—
403C2×C5×D3—23no—
404C2×C3×D5—21no—
405C2×C3×D5—21no—
406C2×C3×D5—28no—
407C2×C3×D5C22×D412yes—
408C2×C3×D5C2×#4112yes—
409C2×C3×D5C2×#4112yescomplemented
410C2×C3×D52−1+412yes—
411D3×D5—412no—
412C3×C4×C5—23no—
413C3×C4×C5C22×D416yes—
414Dic15—21no—
415Dic15—23no—
416Dic15—21no—
417C3×Dic5—23no—
418C3×Dic5C22×D416yes—
419C5×Dic3—21no—
420C5×Dic3—23no—
421C5×Dic3—21no—
422C24×C3—51no—
423C23×D3—53no—
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—53no—
443C2×#67—53no—
444C2×#67—53no—
445C2×#67—1012no—
446C2×#67C22×D513yes—
447C22×Dic3—51no—
448C22×Dic3—53no—
449C22×Dic3—51no—
450#239—24no—
451#239—1012no—
452#239—1012no—
453#239—104no—
454C2×D12—56no—
455C2×D12—53no—
456C2×D12—1012no—
457C2×D12C22×D513yes—
458C2×C4×D3—53no—
459C2×C4×D3—53no—
460C2×C4×D3—53no—
461C2×C4×D3—1012no—
462C2×C4×D3C22×D513yes—
463#217—51no—
464#217—51no—
465#217—51no—
466#217C22×D511yescharacteristic
467(C2×D3)⋊C4—53no—
468(C2×D3)⋊C4—56no—
469(C2×D3)⋊C4—53no—
470(C2×D3)⋊C4—56no—
471(C2×D3)⋊C4—53no—
472(C2×D3)⋊C4—56no—
473(C2×D3)⋊C4C22×D513yes—
474(C2×D3)⋊C4C22×D516yes—
475C4⋊Dic3—53no—
476C4⋊Dic3—56no—
477C4⋊Dic3C22×D513yes—
478Dic3⋊C4—53no—
479Dic3⋊C4—53no—
480Dic3⋊C4—53no—
481Dic3⋊C4C22×D513yes—
482C4×Dic3—53no—
483C4×Dic3—53no—
484C4×Dic3—53no—
485C4×Dic3C22×D513yes—
486C23×C5—33no—
487C23×C5C23×D311yescharacteristic
488C22×D5—22no—
489C22×D5—22no—
490C22×D5—33no—
491C22×D5—66no—
492C22×D5—66no—
493C22×D5—66no—
494C22×D5#23914yescomplemented
495C22×D5C23×D311yescharacteristic
496C22×D5C23×D311yescharacteristic
497C5×Q8—26no—
498C5×Q8C2×#6714yescomplemented
499C5×D4—66no—
500C5×D4—66no—
501C2×C4×C5—26no—
502C2×C4×C5—31no—
503C2×C4×C5—33no—
504C2×C4×C5—31no—
505C2×C4×C5—66no—
506C2×C4×C5C23×D313yes—
507C2×C4×C5C23×D313yes—
508C22⋊D5—66no—
509C22⋊D5—66no—
510C22⋊D5—612no—
511C2×Dic5—26no—
512C2×Dic5—31no—
513C2×Dic5—33no—
514C2×Dic5—31no—
515C2×Dic5—66no—
516C2×Dic5C23×D313yes—
517C2×Dic5C23×D313yes—
518D20—66no—
519D20—66no—
520C4×D5—26no—
521C4×D5—26no—
522C4×D5—26no—
523C4×D5—66no—
524C4×D5—62no—
525C4×D5—62no—
526C4×D5—66no—
527C4×D5—66no—
528C4×D5C2×#67112yes—
529Dic10—26no—
530Dic10—212no—
531Dic10C2×#67112yescomplemented
532C2×#41—31no—
533C2×#41—153no—
534C2×#41—153no—
535C2×#41—151no—
536C2×#41—308no—
537C22×Q8—51no—
538C22×Q8—53no—
539C22×Q8—53no—
540C22×Q8—51no—
541C22×Q8—53no—
542C22×Q8—108no—
543C22×Q8D3×D511yescharacteristic, complemented
544C22×D4—153no—
545C22×D4—153no—
546C23×C4—53no—
547C23×C4—153no—
548#124—33no—
549#124—153no—
550#124—156no—
551#124—156no—
552#124—153no—
553#124—153no—
554C22⋊Q8—33no—
555C22⋊Q8—156no—
556C22⋊Q8—156no—
557C22⋊Q8—153no—
558C22⋊Q8—153no—
559C22⋊Q8—153no—
560#121—33no—
561#121—156no—
562#121—153no—
563#121—153no—
564#121—156no—
565#121—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×C22⋊C4—153no—
581C2×C22⋊C4—156no—
582C2×C22⋊C4—151no—
583C2×C42—153no—
584C2×C3×C5—22no—
585C2×C3×C5C23×D411yescharacteristic
586C2×C3×C5C22×#4111yescharacteristic
587C2×C3×C5C2×2−1+411yescharacteristic
588D15—43no—
589C3×D5—22no—
590C3×D5#54814yescomplemented
591C5×D3—43no—
592C23×C3—51no—
593C23×C3—54no—
594C23×C3—51no—
595C23×C3—102no—
596C23×C3—102no—
597C23×C3C23×D511yescharacteristic
598C22×D3—53no—
599C22×D3—106no—
600C22×D3—106no—
601C22×D3—106no—
602C22×D3C23×D513yes—
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—26no—
619#67—106no—
620#67—106no—
621#67—106no—
622C2×Dic3—51no—
623C2×Dic3—53no—
624C2×Dic3—51no—
625C2×Dic3—102no—
626C2×Dic3—102no—
627C2×Dic3—106no—
628C2×Dic3C23×D511yescharacteristic
629C2×Dic3C23×D513yes—
630C2×Dic3C23×D511yescharacteristic
631D12—26no—
632D12—1012no—
633D12—106no—
634C4×D3—26no—
635C4×D3—106no—
636C4×D3—106no—
637C4×D3—106no—
638C22×C5—21no—
639C22×C5—21no—
640C22×C5—63no—
641C22×C5—63no—
642C22×C5—63no—
643C22×C5C2×#23912yescomplemented
644C22×C5C24×D311yescharacteristic
645C2×D5—21no—
646C2×D5—21no—
647C2×D5—28no—
648C2×D5—63no—
649C2×D5—63no—
650C2×D5—63no—
651C2×D5—1212no—
652C2×D5C2×#23912yes—
653C2×D5C2×#23912yescomplemented
654C2×D5#100712yes—
655C2×D5C22×#6712yes—
656C4×C5—23no—
657C4×C5—63no—
658C4×C5—61no—
659C4×C5—61no—
660C4×C5C22×#6716yes—
661Dic5—23no—
662Dic5—63no—
663Dic5—61no—
664Dic5—61no—
665Dic5C22×#6716yes—
666C24—51no—
667C24—153no—
668#41—64no—
669#41—3012no—
670#41—3012no—
671#41—304no—
672C2×Q8—24no—
673C2×Q8—58no—
674C2×Q8—53no—
675C2×Q8—56no—
676C2×Q8—53no—
677C2×Q8—1012no—
678C2×Q8—1012no—
679C2×Q8—1012no—
680C2×Q8—104no—
681C2×Q8C2×D3×D513yes—
682C2×Q8C2×D3×D511yescharacteristic
683C2×D4—33no—
684C2×D4—33no—
685C2×D4—153no—
686C2×D4—156no—
687C2×D4—153no—
688C2×D4—153no—
689C2×D4—153no—
690C2×D4—3012no—
691C2×D4—3012no—
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—151no—
703C22×C4—153no—
704C22×C4—153no—
705C22×C4—3012no—
706C22×C4C2×D3×D513yes—
707C4⋊C4—33no—
708C4⋊C4—33no—
709C4⋊C4—153no—
710C4⋊C4—153no—
711C4⋊C4—156no—
712C4⋊C4—153no—
713C4⋊C4—153no—
714C22⋊C4—31no—
715C22⋊C4—33no—
716C22⋊C4—36no—
717C22⋊C4—153no—
718C22⋊C4—156no—
719C22⋊C4—151no—
720C22⋊C4—151no—
721C22⋊C4—153no—
722C22⋊C4—156no—
723C22⋊C4—151no—
724C22⋊C4—153no—
725C22⋊C4—156no—
726C42—33no—
727C42—153no—
728C42—153no—
729C42—153no—
730C3×C5C2×#54811yescharacteristic, 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×C3D5×#4112yescomplemented
741C22×C3C24×D511yescharacteristic
742C2×D3—23no—
743C2×D3—23no—
744C2×D3—23no—
745C2×D3—103no—
746C2×D3—103no—
747C2×D3—103no—
748C2×D3—2012no—
749C3×C4—23no—
750C3×C4—56no—
751C3×C4—103no—
752C3×C4C2×D4×D516yes—
753Dic3—21no—
754Dic3—23no—
755Dic3—21no—
756Dic3—101no—
757Dic3—103no—
758Dic3—101no—
759C2×C5—22no—
760C2×C5—123no—
761C2×C5C22×#23911yescharacteristic
762C2×C5C2×#100711yescharacteristic
763C2×C5C23×#6711yescharacteristic
764D5—22no—
765D5—123no—
766D5#581714yesdirect product factor
767C23—33no—
768C23—51no—
769C23—54no—
770C23—51no—
771C23—102no—
772C23—102no—
773C23—153no—
774C23—306no—
775C23—306no—
776C23—306no—
777C23C22×D3×D511yescharacteristic
778Q8—26no—
779Q8—512no—
780Q8—1012no—
781Q8—106no—
782Q8D5×#6714yescomplemented
783D4—66no—
784D4—66no—
785D4—3012no—
786D4—306no—
787D4—306no—
788D4—306no—
789D4—306no—
790C2×C4—26no—
791C2×C4—31no—
792C2×C4—33no—
793C2×C4—31no—
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—151no—
803C2×C4—153no—
804C2×C4—151no—
805C2×C4—306no—
806C2×C4—306no—
807C2×C4—302no—
808C2×C4—306no—
809C2×C4—302no—
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×C3C2×D5×#4111yescharacteristic
818C2×C3D5×2−1+411yescharacteristic
819D3—43no—
820D3—203no—
821C5C2×#581711yescharacteristic, complemented, Sylow
822C22—21no—
823C22—21no—
824C22—52no—
825C22—52no—
826C22—52no—
827C22—52no—
828C22—63no—
829C22—63no—
830C22—63no—
831C22—108no—
832C22—101no—
833C22—101no—
834C22—303no—
835C22—303no—
836C22—303no—
837C22—6012no—
838C22D5×#23912yescomplemented
839C22C23×D3×D511yescharacteristic
840C4—23no—
841C4—56no—
842C4—61no—
843C4—63no—
844C4—61no—
845C4—103no—
846C4—301no—
847C4—303no—
848C4—301no—
849C4C2×D5×#6716yes—
850C3D5×#54811yescharacteristic, complemented, Sylow
851C2—22no—
852C2—54no—
853C2—102no—
854C2—123no—
855C2—603no—
856C2C2×D5×#23911yescharacteristic
857C2D5×#100711yescharacteristic
858C2C22×D5×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC22×C3×C5×Q8C22
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#548
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×D5×#239C2semidirect
3. #11756576C2semidirect
4. C5×#5817C2semidirect
5. D5×#947C2semidirect
6. D5×#946C2semidirect
7. #11755244C2semidirect
8. #11755227C2semidirect
9. #11755226C2semidirect
10. Q8×D5×Dic3C2semidirect
11. #11755128C2semidirect
12. D5×#930C2semidirect
13. C4×D5×#67C2semidirect
14. #11754321C2semidirect
15. #11754319C2semidirect
17. C22×C3×C5×Q8C22semidirect
18. C2×#6821C22semidirect
19. C2×C5×#239C22semidirect
23. C2×C3×Q8×D5C22semidirect
24. C2×C3×Q8×D5C22semidirect
26. C22×C3×Dic10C22semidirect
31. C2×#6769C22semidirect
32. C2×#6768C22semidirect
33. #91836C22semidirect
34. #91835C22semidirect
35. Q8×Dic15C22semidirect
36. #91819C22semidirect
37. C4×#1220C22semidirect
38. C5×#947C22semidirect
39. C5×#946C22semidirect
40. C5×Q8×Dic3C22semidirect
41. C5×#930C22semidirect
42. C4×C5×#67C22semidirect
43. #91566C22semidirect
44. #91552C22semidirect
45. Dic5×#67C22semidirect
49. #91450C22semidirect
50. #91449C22semidirect
51. #91448C22semidirect
52. #91444C22semidirect
53. C4×#1202C22semidirect
54. #91440C22semidirect
55. C4×#1201C22semidirect
57. #91411C22semidirect
58. #91410C22semidirect
61. #91390C22semidirect
62. #91374C22semidirect
63. #91370C22semidirect
64. #91369C22semidirect
65. #91331C22semidirect
66. Dic3×Dic10C22semidirect
67. #91326C22semidirect
68. #91326C22semidirect
71. C22×Q8×D5D3semidirect
103. C3×Q8×D5D4semidirect
158. #5817D5direct (N × H)
165. C22×C5×Q8C2×D3semidirect
171. C2×Q8×D5C2×D3semidirect
172. C2×Q8×D5C2×D3semidirect
179. C22×Dic10C2×D3semidirect
222. C22×C3×D5#41semidirect
229. C3×C5×Q8C2×D4semidirect
254. C3×Dic10C2×D4semidirect
269. C22×C3×Q8C2×D5semidirect
276. C2×#239C2×D5semidirect
285. #947C2×D5semidirect
291. #946C2×D5semidirect
295. Q8×Dic3C2×D5semidirect
301. #930C2×D5semidirect
309. C4×#67C2×D5semidirect
334. Q8×D5#67semidirect
396. C22×C3×C5C2×#41semidirect
409. C2×C3×D5C2×#41semidirect
494. C22×D5#239semidirect
498. C5×Q8C2×#67semidirect
531. Dic10C2×#67semidirect
543. C22×Q8D3×D5semidirect
590. C3×D5#548semidirect
607. C3×Q8D4×D5semidirect
643. C22×C5C2×#239semidirect
653. C2×D5C2×#239semidirect
730. C3×C5C2×#548semidirect
740. C22×C3D5×#41semidirect
766. D5#5817direct (N × H)
782. Q8D5×#67semidirect
821. C5C2×#5817semidirect
838. C22D5×#239semidirect
850. C3D5×#548semidirect

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×D5×#2392
#117565762
C5×#58172
D5×#9472
D5×#9462
#117552442
#117552272
#117552262
Q8×D5×Dic32
#117551282
D5×#9302
C4×D5×#672
#117543212
#117543192
D5×#5483
C2×#58175