Finite Group Databasebeta

← D5×#5831 #14482823

Subgroups — D5×#5831 #14482823

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
1C2×C3×D5×#41C211yesmaximal, characteristic, complemented
2C2×D3×Q8×D5C211yesmaximal, characteristic, complemented
3#11756590C211yesmaximal, characteristic, complemented
4C5×#5831C211yesmaximal, characteristic, complemented
5#11755257C211yesmaximal, characteristic, complemented
6#11755247C211yesmaximal, characteristic, complemented
7Q8×D5×Dic3C211yesmaximal, characteristic, complemented
8D5×#938C213yesmaximal, complemented
9#11754939C213yesmaximal, complemented
10#11754798C213yesmaximal, complemented
11D5×#936C213yesmaximal, complemented
12C4×D5×#67C213yesmaximal, complemented
13#11754528C213yesmaximal, complemented
14D5×#924C213yesmaximal, complemented
15#11754215C213yesmaximal, complemented
16D5×#548—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C2×Q8×D15C2211yescharacteristic, complemented
19C2×C5×D3×Q8C2211yescharacteristic, complemented
20C3×D5×#41—28no—
21C2×C3×#713C2211yescharacteristic, complemented
22C2×C3×Q8×D5C2211yescharacteristic
23C2×C3×#711C2213yescomplemented
24C2×C3×D4×D5C2213yes—
25C2×C3×#709C2213yescomplemented
26C22×C3×C4×D5C2213yes—
27C2×D5×#67C2213yes—
28D3×Q8×D5—28no—
29C2×C4×D3×D5C2213yes—
30C2×D15⋊Q8C2213yescomplemented
31C2×D3×Dic10C2213yescomplemented
32C2×D5×Dic6C2213yes—
33Q8×Dic15C2211yescharacteristic, complemented
34#91827C2213yescomplemented
35#91825C2213yescomplemented
36C4×#1220C2213yescomplemented
37#91813C2213yescomplemented
38C5×Q8×Dic3C2211yescharacteristic, complemented
39C5×#938C2213yescomplemented
40C5×#936C2213yescomplemented
41C4×C5×#67C2213yescomplemented
42C5×#924C2213yescomplemented
43#91574C2216yescomplemented
44#91565C2216yescomplemented
45#91552C2213yescomplemented
46Dic5×#67C2213yescomplemented
47D5×#217C2216yes—
48D5×#217C2213yes—
49#91534C2216yescomplemented
50#91534C2216yescomplemented
51#91533C2216yescomplemented
52D5×(C2×D3)⋊C4C2211yescharacteristic
53#91465C2213yescomplemented
54#91456C2213yescomplemented
55#91444C2213yescomplemented
56C4×#1202C2213yescomplemented
57#91440C2213yescomplemented
58C4×#1201C2213yescomplemented
59D5×C4⋊Dic3C2213yes—
60D5×Dic3⋊C4C2213yes—
61C4×D5×Dic3C2213yes—
62#91368C2213yescomplemented
63#91364C2213yescomplemented
64#91360C2213yescomplemented
65#91359C2213yescomplemented
66#91349C2216yescomplemented
67#91331C2213yescomplemented
68Dic3×Dic10C2213yescomplemented
69C2×#5831—51nomaximal, Hall
70C2×D5×#41D311yescharacteristic, complemented
71C22×Q8×D5—31no—
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×D5C2313yes—
86C22×D3×D5C2311yescharacteristic
87C3×C5×#41—24no—
88C2×C3×C5×Q8C2311yescharacteristic
89C2×C3×C5×D4C2313yes—
90C22×C3×C4×C5C2313yes—
91C2×#1220C2313yes—
92Q8×D15—24no—
93C2×C4×D15C2313yes—
94C2×Dic30C2313yes—
95C2×C5×#67C2313yes—
96C5×D3×Q8—24no—
97C2×C4×C5×D3C2313yes—
98C2×C5×Dic6C2313yes—
99C2×C3×C22⋊D5C2316yes—
100C22×C3×Dic5C2313yes—
101C3×#713—24no—
102C3×Q8×D5D418yescomplemented
103C3×#711—212no—
104C3×D4×D5—212no—
105C3×#709—212no—
106C2×C3×D20C2313yes—
107C2×C3×C4×D5—212no—
108C2×C3×C4×D5C2311yescharacteristic
109C2×C3×C4×D5C2313yes—
110C2×C3×C4×D5C2313yes—
111C2×C3×C4×D5C2313yes—
112C2×C3×Dic10C2313yes—
113D5×#67—212no—
114C2×#1204C2316yes—
115C2×#1202C2313yes—
116C2×#1201C2313yes—
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#6719C2316yes—
128#6714C2311yescharacteristic
129C4⋊Dic15C2313yes—
130#6712C2313yes—
131C4×Dic15C2313yes—
132C5×#217C2316yes—
133C5×#217C2313yes—
134C5×(C2×D3)⋊C4C2311yescharacteristic
135C5×C4⋊Dic3C2313yes—
136C5×Dic3⋊C4C2313yes—
137C4×C5×Dic3C2313yes—
138Dic3⋊Dic5C2313yes—
139#6669C2313yes—
140#6668C2316yes—
141#6667C2311yescharacteristic
142(C2×D3)⋊Dic5C2311yescharacteristic
143#6665C2313yes—
144#6665C2313yes—
145#6665C2316yes—
146#6665C2316yes—
147Dic3×Dic5C2313yes—
148Dic3×Dic5C2313yes—
149C22×C3×#41—51no—
150C22×D3×Q8—51no—
151#5831—51no—
152#5831—51no—
153#5831—51no—
154#5831—53no—
155#5831—53no—
156#5831—53no—
157#5831—53no—
158#5831D511yescharacteristic, direct product factor
159C2×Q8×Dic3—51no—
160C2×#938—53no—
161C2×#936—53no—
162C2×C4×#67—53no—
163C2×#924—53no—
164C2×C5×#41C2×D311yescharacteristic, complemented
165C22×C5×Q8—31no—
166D5×#41—28no—
167C2×#713C2×D311yescharacteristic, complemented
168C2×Q8×D5—31no—
169C2×Q8×D5—33no—
170C2×Q8×D5—33no—
171C2×Q8×D5—68no—
172C2×Q8×D5C2×D311yescharacteristic
173C2×#711C2×D313yescomplemented
174C2×D4×D5—33no—
175C2×D4×D5C2×D313yes—
176C2×#709C2×D313yescomplemented
177C22×C4×D5—33no—
178C22×C4×D5C2×D313yes—
179C22×Dic10—33no—
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—33no—
209D5×C22⋊C4—36no—
210D5×C22⋊C4—31no—
211#4024—36no—
212#4021—33no—
213C4×D20—33no—
214C42×D5—33no—
215C4×Dic10—33no—
216C2×#548—151noSylow
217C23×C3×C5C2413yes—
218C22×D15C2411yescharacteristic
219C22×C5×D3C2411yescharacteristic
220C22×C3×D5—26no—
221C22×C3×D5—26no—
222C22×C3×D5—26no—
223C22×C3×D5C2413yes—
224C22×C3×D5C2411yescharacteristic
225C2×D3×D5—22no—
226C2×D3×D5—22no—
227C2×D3×D5#4114yescomplemented
228C3×C5×Q8C2×D414yescomplemented
229C3×C5×D4—26no—
230C2×C3×C4×C5—26no—
231C2×C3×C4×C5C2411yescharacteristic
232C2×C3×C4×C5C2413yes—
233#1220—26no—
234C2×Dic15C2411yescharacteristic
235C2×Dic15C2413yes—
236C2×Dic15C2413yes—
237C4×D15—26no—
238Dic30—26no—
239C5×#67—26no—
240C2×C5×Dic3C2411yescharacteristic
241C2×C5×Dic3C2413yes—
242C2×C5×Dic3C2413yes—
243C4×C5×D3—26no—
244C5×Dic6—26no—
245C3×C22⋊D5—212no—
246C2×C3×Dic5—26no—
247C2×C3×Dic5C2411yescharacteristic
248C2×C3×Dic5C2413yes—
249C3×D20—26no—
250C3×C4×D5—22no—
251C3×C4×D5—26no—
252C3×C4×D5—26no—
253C3×C4×D5C2×D4112yes—
254C3×Dic10C2×D4112yescomplemented
255#1204—212no—
256#1202—26no—
257#1201—26no—
258#1200—26no—
259D3×Dic5—26no—
260D5×Dic3—26no—
261D5×Dic3—26no—
262D5×Dic3—22no—
263C2×C3×#41—51no—
264C2×C3×#41—53no—
265C2×C3×#41—53no—
266C2×C3×#41—108no—
267C2×C3×#41C2×D511yescharacteristic, complemented
268C22×C3×Q8—51no—
269C22×C3×D4—53no—
270C23×C3×C4—53no—
271C22×#67—53no—
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—56no—
280C2×#217—53no—
281Q8×Dic3—51no—
282Q8×Dic3—53no—
283Q8×Dic3—53no—
284Q8×Dic3C2×D511yescharacteristic, complemented
285#938—53no—
286#938—56no—
287#938—53no—
288#938—56no—
289#938—53no—
290#938C2×D513yescomplemented
291#936—53no—
292#936—53no—
293#936—56no—
294#936—56no—
295#936—53no—
296#936C2×D513yescomplemented
297C4×#67—53no—
298C4×#67—53no—
299C4×#67—53no—
300C4×#67—53no—
301C4×#67—53no—
302C4×#67—53no—
303C4×#67—53no—
304C4×#67C2×D513yescomplemented
305C2×(C2×D3)⋊C4—51no—
306C2×C4⋊Dic3—53no—
307#924—53no—
308#924—53no—
309#924—56no—
310#924—53no—
311#924—56no—
312#924C2×D513yescomplemented
313C2×Dic3⋊C4—53no—
314C2×C4×Dic3—53no—
315C23×D5—31no—
316C23×D5C22×D313yes—
317C5×#41—24no—
318C2×C5×Q8—33no—
319C2×C5×Q8—64no—
320C2×C5×Q8C22×D311yescharacteristic
321C2×C5×D4—33no—
322C2×C5×D4C22×D313yes—
323C22×C4×C5—33no—
324C22×C4×C5C22×D313yes—
325C2×C22⋊D5—33no—
326C2×C22⋊D5—33no—
327C2×C22⋊D5C22×D316yes—
328C22×Dic5—33no—
329C22×Dic5C22×D313yes—
330#713—24no—
331Q8×D5—64no—
332Q8×D5—612no—
333Q8×D5—612no—
334Q8×D5#6718yescomplemented
335#711—212no—
336D4×D5—212no—
337D4×D5—612no—
338#709—212no—
339C2×D20—33no—
340C2×D20C22×D313yes—
341C2×C4×D5—212no—
342C2×C4×D5—33no—
343C2×C4×D5—33no—
344C2×C4×D5—31no—
345C2×C4×D5—33no—
346C2×C4×D5—33no—
347C2×C4×D5—612no—
348C2×C4×D5C22×D311yescharacteristic
349C2×C4×D5C22×D313yes—
350C2×C4×D5C22×D313yes—
351C2×C4×D5C22×D313yes—
352C2×Dic10—33no—
353C2×Dic10—36no—
354C2×Dic10—612no—
355C2×Dic10C22×D313yes—
356C5×C4⋊C4—33no—
357C5×C4⋊C4—33no—
358C5×C22⋊C4—33no—
359C5×C22⋊C4—36no—
360C5×C22⋊C4—31no—
361C42×C5—33no—
362C22⋊Dic5—36no—
363C22⋊Dic5—33no—
364C22⋊Dic5—31no—
365#685—33no—
366#685—36no—
367#685—36no—
368#685—33no—
369#685—31no—
370#685—31no—
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—51no—
380C23×Q8—151no—
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—23no—
395C22×C3×C5—23no—
396C22×C3×C5—23no—
397C22×C3×C5C2511yescharacteristic
398C2×D15—21no—
399C2×D15—21no—
400C2×D15C2×#4112yescomplemented
401C2×C5×D3—21no—
402C2×C5×D3—21no—
403C2×C5×D3C2×#4112yescomplemented
404C2×C3×D5—23no—
405C2×C3×D5—23no—
406C2×C3×D5—23no—
407C2×C3×D5—412no—
408C2×C3×D5C22×D412yes—
409C2×C3×D5C2×#4112yes—
410C2×C3×D52−1+412yes—
411D3×D5—28no—
412C3×C4×C5—21no—
413C3×C4×C5C22×D416yes—
414Dic15—23no—
415Dic15—23no—
416Dic15—21no—
417C3×Dic5—21no—
418C3×Dic5C22×D416yes—
419C5×Dic3—23no—
420C5×Dic3—23no—
421C5×Dic3—21no—
422C24×C3—53no—
423C23×D3—51no—
424C3×#41—24no—
425C3×#41—1012no—
426C3×#41—1012no—
427C3×#41—104no—
428C2×C3×Q8—58no—
429C2×C3×Q8—53no—
430C2×C3×Q8C22×D511yescharacteristic
431C2×C3×D4—56no—
432C2×C3×D4—53no—
433C2×C3×D4—1012no—
434C2×C3×D4C22×D513yes—
435C22×C3×C4—53no—
436C22×C3×C4—53no—
437C22×C3×C4—51no—
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—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—56no—
464#217—53no—
465#217—56no—
466#217—56no—
467#217—53no—
468#217—53no—
469#217C22×D516yes—
470#217C22×D513yes—
471(C2×D3)⋊C4—51no—
472(C2×D3)⋊C4—51no—
473(C2×D3)⋊C4—51no—
474(C2×D3)⋊C4C22×D511yescharacteristic
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—31no—
487C23×C5C23×D313yes—
488C22×D5—26no—
489C22×D5—26no—
490C22×D5—26no—
491C22×D5—31no—
492C22×D5—34no—
493C22×D5—62no—
494C22×D5—62no—
495C22×D5C23×D313yes—
496C22×D5C23×D311yescharacteristic
497C5×Q8—66no—
498C5×Q8C2×#6714yescomplemented
499C5×D4—26no—
500C5×D4—66no—
501C2×C4×C5—26no—
502C2×C4×C5—31no—
503C2×C4×C5—33no—
504C2×C4×C5—33no—
505C2×C4×C5—66no—
506C2×C4×C5C23×D311yescharacteristic
507C2×C4×C5C23×D313yes—
508C22⋊D5—212no—
509C22⋊D5—66no—
510C22⋊D5—66no—
511C2×Dic5—26no—
512C2×Dic5—31no—
513C2×Dic5—33no—
514C2×Dic5—33no—
515C2×Dic5—66no—
516C2×Dic5C23×D311yescharacteristic
517C2×Dic5C23×D313yes—
518D20—26no—
519D20—66no—
520C4×D5—22no—
521C4×D5—26no—
522C4×D5—26no—
523C4×D5—66no—
524C4×D5—62no—
525C4×D5—66no—
526C4×D5—66no—
527C4×D5—66no—
528C4×D5C2×#67112yes—
529Dic10—66no—
530Dic10—612no—
531Dic10C2×#67112yescomplemented
532C2×#41—51no—
533C2×#41—53no—
534C2×#41—53no—
535C2×#41—108no—
536C2×#41D3×D511yescharacteristic, complemented
537C22×Q8—31no—
538C22×Q8—51no—
539C22×Q8—153no—
540C22×Q8—153no—
541C22×Q8—153no—
542C22×Q8—151no—
543C22×Q8—308no—
544C22×D4—53no—
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—151no—
581C2×C22⋊C4—153no—
582C2×C22⋊C4—156no—
583C2×C42—153no—
584C2×C3×C5—43no—
585C2×C3×C5C23×D411yescharacteristic
586C2×C3×C5C22×#4111yescharacteristic
587C2×C3×C5C2×2−1+411yescharacteristic
588D15—22no—
589C3×D5—43no—
590C3×D5#54814yescomplemented
591C5×D3—22no—
592C23×C3—51no—
593C23×C3—53no—
594C23×C3—106no—
595C23×C3—106no—
596C23×C3—106no—
597C23×C3C23×D513yes—
598C22×D3—51no—
599C22×D3—54no—
600C22×D3—102no—
601C22×D3—102no—
602C22×D3C23×D511yescharacteristic
603C3×Q8—512no—
604C3×Q8D4×D514yescomplemented
605C3×D4—26no—
606C3×D4—1012no—
607C3×D4—106no—
608C2×C3×C4—26no—
609C2×C3×C4—53no—
610C2×C3×C4—512no—
611C2×C3×C4—51no—
612C2×C3×C4—106no—
613C2×C3×C4—102no—
614C2×C3×C4—106no—
615C2×C3×C4—106no—
616C2×C3×C4C23×D511yescharacteristic
617C2×C3×C4C23×D513yes—
618#67—26no—
619#67—106no—
620#67—106no—
621#67—106no—
622C2×Dic3—51no—
623C2×Dic3—53no—
624C2×Dic3—53no—
625C2×Dic3—106no—
626C2×Dic3—102no—
627C2×Dic3—106no—
628C2×Dic3C23×D511yescharacteristic
629C2×Dic3C23×D513yes—
630C2×Dic3C23×D513yes—
631C4×D3—26no—
632C4×D3—106no—
633C4×D3—106no—
634C4×D3—106no—
635Dic6—26no—
636Dic6—1012no—
637Dic6—106no—
638C22×C5—23no—
639C22×C5—23no—
640C22×C5—23no—
641C22×C5—32no—
642C22×C5—61no—
643C22×C5—61no—
644C22×C5C24×D311yescharacteristic
645C2×D5—23no—
646C2×D5—23no—
647C2×D5—23no—
648C2×D5—32no—
649C2×D5—412no—
650C2×D5—61no—
651C2×D5—61no—
652C2×D5—68no—
653C2×D5D3×#4112yes—
654C2×D5#101012yes—
655C2×D5C22×#6712yes—
656C4×C5—21no—
657C4×C5—63no—
658C4×C5—61no—
659C4×C5—63no—
660C4×C5C22×#6716yes—
661Dic5—21no—
662Dic5—63no—
663Dic5—61no—
664Dic5—63no—
665Dic5C22×#6716yes—
666C24—53no—
667C24—151no—
668#41—24no—
669#41—1012no—
670#41—1012no—
671#41—104no—
672C2×Q8—33no—
673C2×Q8—58no—
674C2×Q8—53no—
675C2×Q8—64no—
676C2×Q8—156no—
677C2×Q8—153no—
678C2×Q8—3012no—
679C2×Q8—3012no—
680C2×Q8—3012no—
681C2×Q8—304no—
682C2×Q8C2×D3×D511yescharacteristic
683C2×D4—33no—
684C2×D4—56no—
685C2×D4—53no—
686C2×D4—1012no—
687C2×D4—153no—
688C2×D4—153no—
689C2×D4—153no—
690C2×D4—3012no—
691C2×D4C2×D3×D513yes—
692C22×C4—33no—
693C22×C4—53no—
694C22×C4—53no—
695C22×C4—51no—
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—153no—
710C4⋊C4—153no—
711C4⋊C4—156no—
712C4⋊C4—153no—
713C4⋊C4—153no—
714C22⋊C4—33no—
715C22⋊C4—36no—
716C22⋊C4—31no—
717C22⋊C4—151no—
718C22⋊C4—153no—
719C22⋊C4—153no—
720C22⋊C4—156no—
721C22⋊C4—156no—
722C22⋊C4—151no—
723C22⋊C4—153no—
724C22⋊C4—156no—
725C22⋊C4—151no—
726C42—33no—
727C42—153no—
728C42—153no—
729C42—153no—
730C3×C5C2×#54811yescharacteristic, complemented, Hall
731C22×C3—23no—
732C22×C3—23no—
733C22×C3—23no—
734C22×C3—52no—
735C22×C3—52no—
736C22×C3—52no—
737C22×C3—103no—
738C22×C3—103no—
739C22×C3—103no—
740C22×C3—2012no—
741C22×C3C24×D511yescharacteristic
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—52no—
745C2×D3—108no—
746C2×D3—101no—
747C2×D3—101no—
748C2×D3D5×#4112yescomplemented
749C3×C4—21no—
750C3×C4—56no—
751C3×C4—101no—
752C3×C4C2×D4×D516yes—
753Dic3—23no—
754Dic3—23no—
755Dic3—21no—
756Dic3—103no—
757Dic3—103no—
758Dic3—101no—
759C2×C5—43no—
760C2×C5—62no—
761C2×C5C2×D3×#4111yescharacteristic
762C2×C5C2×#101011yescharacteristic
763C2×C5C23×#6711yescharacteristic
764D5—43no—
765D5—62no—
766D5#583114yesdirect product factor
767C23—31no—
768C23—51no—
769C23—53no—
770C23—106no—
771C23—106no—
772C23—106no—
773C23—154no—
774C23—151no—
775C23—302no—
776C23—302no—
777C23C22×D3×D513yes—
778Q8—512no—
779Q8—66no—
780Q8—3012no—
781Q8—306no—
782Q8D5×#6714yescomplemented
783D4—26no—
784D4—66no—
785D4—1012no—
786D4—106no—
787D4—306no—
788D4—306no—
789D4—306no—
790C2×C4—26no—
791C2×C4—31no—
792C2×C4—33no—
793C2×C4—33no—
794C2×C4—53no—
795C2×C4—512no—
796C2×C4—51no—
797C2×C4—66no—
798C2×C4—106no—
799C2×C4—102no—
800C2×C4—106no—
801C2×C4—106no—
802C2×C4—151no—
803C2×C4—153no—
804C2×C4—153no—
805C2×C4—306no—
806C2×C4—306no—
807C2×C4—306no—
808C2×C4—306no—
809C2×C4—302no—
810C2×C4—306no—
811C2×C4C22×D3×D511yescharacteristic
812C2×C4C22×D3×D513yes—
813C2×C3—43no—
814C2×C3—54no—
815C2×C3—203no—
816C2×C3C22×D4×D511yescharacteristic
817C2×C3C2×D5×#4111yescharacteristic
818C2×C3D5×2−1+411yescharacteristic
819D3—22no—
820D3—102no—
821C5C2×#583111yescharacteristic, complemented, Sylow
822C22—23no—
823C22—23no—
824C22—23no—
825C22—32no—
826C22—52no—
827C22—52no—
828C22—52no—
829C22—61no—
830C22—61no—
831C22—103no—
832C22—103no—
833C22—103no—
834C22—152no—
835C22—2012no—
836C22—308no—
837C22—301no—
838C22—301no—
839C22C23×D3×D511yescharacteristic
840C4—21no—
841C4—56no—
842C4—63no—
843C4—63no—
844C4—61no—
845C4—101no—
846C4—303no—
847C4—303no—
848C4—301no—
849C4C2×D5×#6716yes—
850C3D5×#54811yescharacteristic, complemented, Sylow
851C2—43no—
852C2—54no—
853C2—62no—
854C2—203no—
855C2—302no—
856C2D3×D5×#4111yescharacteristic
857C2D5×#101011yescharacteristic
858C2C22×D5×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC2×C3×C5×#41C22
hypercenterC2×#41D3×D5
hypocenterC3×C5C2×#548
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×D5×#41C2semidirect
2. C2×D3×Q8×D5C2semidirect
3. #11756590C2semidirect
4. C5×#5831C2semidirect
5. #11755257C2semidirect
6. #11755247C2semidirect
7. Q8×D5×Dic3C2semidirect
8. D5×#938C2semidirect
9. #11754939C2semidirect
10. #11754798C2semidirect
11. D5×#936C2semidirect
12. C4×D5×#67C2semidirect
13. #11754528C2semidirect
14. D5×#924C2semidirect
15. #11754215C2semidirect
17. C2×C3×C5×#41C22semidirect
18. C2×Q8×D15C22semidirect
19. C2×C5×D3×Q8C22semidirect
21. C2×C3×#713C22semidirect
23. C2×C3×#711C22semidirect
25. C2×C3×#709C22semidirect
30. C2×D15⋊Q8C22semidirect
31. C2×D3×Dic10C22semidirect
33. Q8×Dic15C22semidirect
34. #91827C22semidirect
35. #91825C22semidirect
36. C4×#1220C22semidirect
37. #91813C22semidirect
38. C5×Q8×Dic3C22semidirect
39. C5×#938C22semidirect
40. C5×#936C22semidirect
41. C4×C5×#67C22semidirect
42. C5×#924C22semidirect
43. #91574C22semidirect
44. #91565C22semidirect
45. #91552C22semidirect
46. Dic5×#67C22semidirect
49. #91534C22semidirect
50. #91534C22semidirect
51. #91533C22semidirect
53. #91465C22semidirect
54. #91456C22semidirect
55. #91444C22semidirect
56. C4×#1202C22semidirect
57. #91440C22semidirect
58. C4×#1201C22semidirect
62. #91368C22semidirect
63. #91364C22semidirect
64. #91360C22semidirect
65. #91359C22semidirect
66. #91349C22semidirect
67. #91331C22semidirect
68. Dic3×Dic10C22semidirect
70. C2×D5×#41D3semidirect
102. C3×Q8×D5D4semidirect
158. #5831D5direct (N × H)
164. C2×C5×#41C2×D3semidirect
167. C2×#713C2×D3semidirect
173. C2×#711C2×D3semidirect
176. C2×#709C2×D3semidirect
227. C2×D3×D5#41semidirect
228. C3×C5×Q8C2×D4semidirect
254. C3×Dic10C2×D4semidirect
267. C2×C3×#41C2×D5semidirect
276. C2×D3×Q8C2×D5semidirect
284. Q8×Dic3C2×D5semidirect
290. #938C2×D5semidirect
296. #936C2×D5semidirect
304. C4×#67C2×D5semidirect
312. #924C2×D5semidirect
334. Q8×D5#67semidirect
400. C2×D15C2×#41semidirect
403. C2×C5×D3C2×#41semidirect
498. C5×Q8C2×#67semidirect
531. Dic10C2×#67semidirect
536. C2×#41D3×D5semidirect
590. C3×D5#548semidirect
604. C3×Q8D4×D5semidirect
730. C3×C5C2×#548semidirect
748. C2×D3D5×#41semidirect
766. D5#5831direct (N × H)
782. Q8D5×#67semidirect
821. C5C2×#5831semidirect
850. C3D5×#548semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×#412
C2×D3×Q8×D52
#117565902
C5×#58312
#117552572
#117552472
Q8×D5×Dic32
D5×#9382
#117549392
#117547982
D5×#9362
C4×D5×#672
#117545282
D5×#9242
#117542152
D5×#5483
C2×#58315