Finite Group Databasebeta

← D3×#66165 #14482825

Subgroups — D3×#66165 #14482825

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×C5×D3×#41C211yesmaximal, characteristic, complemented
2C2×D3×Q8×D5C211yesmaximal, characteristic, complemented
3#11756590C211yesmaximal, characteristic, complemented
4C3×#66165C211yesmaximal, characteristic, complemented
5#11755244C211yesmaximal, characteristic, complemented
6D3×Q8×Dic5C211yesmaximal, characteristic, complemented
7#11755134C211yesmaximal, characteristic, complemented
8D3×#4084C213yesmaximal, complemented
9#11754951C213yesmaximal, complemented
10D3×#4082C213yesmaximal, complemented
11#11754802C213yesmaximal, complemented
12C4×D3×C22⋊D5C213yesmaximal, complemented
13#11754546C213yesmaximal, complemented
14D3×#4070C213yesmaximal, complemented
15#11754338C213yesmaximal, complemented
16C2×#66165—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C2×Q8×D15C2211yescharacteristic, complemented
19C5×D3×#41—28no—
20C2×C5×#239C2211yescharacteristic, complemented
21C2×C5×D3×Q8C2211yescharacteristic
22C2×C5×#237C2213yescomplemented
23C2×C5×D3×D4C2213yes—
24C2×C5×#235C2213yescomplemented
25C22×C4×C5×D3C2213yes—
26C2×C3×Q8×D5C2211yescharacteristic, complemented
27C2×D3×C22⋊D5C2213yes—
28D3×Q8×D5—28no—
29C2×C4×D3×D5C2213yes—
30C2×D15⋊Q8C2213yescomplemented
31C2×D3×Dic10C2213yes—
32C2×D5×Dic6C2213yescomplemented
33Q8×Dic15C2211yescharacteristic, complemented
34#91827C2213yescomplemented
35#91825C2213yescomplemented
36C4×#1220C2213yescomplemented
37#91813C2213yescomplemented
38C3×Q8×Dic5C2211yescharacteristic, complemented
39C3×#4084C2213yescomplemented
40C3×#4082C2213yescomplemented
41C3×C4×C22⋊D5C2213yescomplemented
42C3×#4070C2213yescomplemented
43#91575C2216yescomplemented
44#91557C2216yescomplemented
45#91556C2213yescomplemented
46D3×C22⋊Dic5C2216yes—
47D3×C22⋊Dic5C2213yes—
48Dic3×C22⋊D5C2213yescomplemented
49#91549C2216yescomplemented
50#91525C2216yescomplemented
51#91525C2216yescomplemented
52D3×#685C2211yescharacteristic
53#91466C2213yescomplemented
54#91449C2213yescomplemented
55#91446C2213yescomplemented
56C4×#1203C2213yescomplemented
57#91441C2213yescomplemented
58C4×#1201C2213yescomplemented
59D3×C4⋊Dic5C2213yes—
60D3×#683C2213yes—
61C4×D3×Dic5C2213yes—
62#91373C2213yescomplemented
63#91370C2213yescomplemented
64#91369C2213yescomplemented
65#91365C2213yescomplemented
66#91352C2216yescomplemented
67#91344C2213yescomplemented
68Dic5×Dic6C2213yescomplemented
69D3×#548—51nomaximal, Hall
70C22×C5×#41—31no—
71C22×Q8×D5—31no—
72#66165—31no—
73#66165—33no—
74#66165—33no—
75#66165—33no—
76#66165—33no—
77#66165—31no—
78#66165—31no—
79#66165D311yescharacteristic, direct product factor
80C2×Q8×Dic5—31no—
81C2×#4084—33no—
82C2×#4082—33no—
83C2×C4×C22⋊D5—33no—
84C2×#4070—33no—
85C23×C5×D3C2313yes—
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×#67C2316yes—
96C22×C5×Dic3C2313yes—
97C5×#239—24no—
98C5×D3×Q8D418yescomplemented
99C5×#237—212no—
100C5×D3×D4—212no—
101C5×#235—212no—
102C2×C5×D12C2313yes—
103C2×C4×C5×D3—212no—
104C2×C4×C5×D3C2311yescharacteristic
105C2×C4×C5×D3C2313yes—
106C2×C4×C5×D3C2313yes—
107C2×C4×C5×D3C2313yes—
108C2×C5×Dic6C2313yes—
109C2×C3×C22⋊D5C2313yes—
110C3×Q8×D5—24no—
111C2×C3×C4×D5C2313yes—
112C2×C3×Dic10C2313yes—
113D3×C22⋊D5—212no—
114C2×#1204C2316yes—
115C2×#1203C2313yes—
116C2×#1201C2313yes—
117C2×#1200C2313yes—
118C2×D3×Dic5C2311yescharacteristic
119C2×D3×Dic5C2313yes—
120C2×D3×Dic5C2313yes—
121C2×D5×Dic3C2313yes—
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—
132C3×C22⋊Dic5C2313yes—
133C3×C22⋊Dic5C2316yes—
134C3×#685C2311yescharacteristic
135C3×C4⋊Dic5C2313yes—
136C3×#683C2313yes—
137C3×C4×Dic5C2313yes—
138Dic3⋊Dic5C2316yes—
139#6669C2313yes—
140#6668C2313yes—
141#6667C2311yescharacteristic
142(C2×D3)⋊Dic5C2313yes—
143(C2×D3)⋊Dic5C2313yes—
144(C2×D3)⋊Dic5C2316yes—
145(C2×D3)⋊Dic5C2316yes—
146#6665C2311yescharacteristic
147Dic3×Dic5C2313yes—
148Dic3×Dic5C2313yes—
149C2×D3×#41D511yescharacteristic, complemented
150C22×D3×Q8—51no—
151C3×#548—51no—
152#5831—51no—
153#5817—51no—
154#5677—53no—
155D3×#124—53no—
156#5633—53no—
157D3×C22⋊Q8—53no—
158D3×#121—53no—
159#5598—53no—
160#5576—51no—
161C4×D3×Q8—51no—
162#5552—53no—
163C4×D3×D4—53no—
164C2×C5×#41—31no—
165C2×C5×#41—33no—
166C2×C5×#41—33no—
167C2×C5×#41—68no—
168C2×C5×#41C2×D311yescharacteristic, complemented
169C22×C5×Q8—31no—
170C22×C5×D4—33no—
171C23×C4×C5—33no—
172C22×C22⋊D5—33no—
173C2×Q8×D5—31no—
174C2×Q8×D5—33no—
175C2×Q8×D5—33no—
176C2×Q8×D5—68no—
177C2×Q8×D5C2×D311yescharacteristic, complemented
178C22×C4×D5—33no—
179C22×Dic10—33no—
180C2×C22⋊Dic5—36no—
181C2×C22⋊Dic5—33no—
182Q8×Dic5—31no—
183Q8×Dic5—33no—
184Q8×Dic5—33no—
185Q8×Dic5C2×D311yescharacteristic, complemented
186#4084—33no—
187#4084—36no—
188#4084—33no—
189#4084—36no—
190#4084—33no—
191#4084C2×D313yescomplemented
192#4082—33no—
193#4082—33no—
194#4082—36no—
195#4082—36no—
196#4082—33no—
197#4082C2×D313yescomplemented
198C4×C22⋊D5—33no—
199C4×C22⋊D5—33no—
200C4×C22⋊D5—33no—
201C4×C22⋊D5—33no—
202C4×C22⋊D5—33no—
203C4×C22⋊D5—33no—
204C4×C22⋊D5—33no—
205C4×C22⋊D5C2×D313yescomplemented
206C2×#685—31no—
207C2×C4⋊Dic5—33no—
208#4070—33no—
209#4070—33no—
210#4070—36no—
211#4070—33no—
212#4070—36no—
213#4070C2×D313yescomplemented
214C2×#683—33no—
215C2×C4×Dic5—33no—
216C2×#548—151noSylow
217C23×C3×C5C2413yes—
218C22×D15C2411yescharacteristic
219C22×C5×D3—26no—
220C22×C5×D3—26no—
221C22×C5×D3—26no—
222C22×C5×D3C2413yes—
223C22×C5×D3C2411yescharacteristic
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—212no—
240C2×C5×Dic3—26no—
241C2×C5×Dic3C2411yescharacteristic
242C2×C5×Dic3C2413yes—
243C5×D12—26no—
244C4×C5×D3—22no—
245C4×C5×D3—26no—
246C4×C5×D3—26no—
247C4×C5×D3C2×D4112yes—
248C5×Dic6C2×D4112yescomplemented
249C3×C22⋊D5—26no—
250C2×C3×Dic5C2411yescharacteristic
251C2×C3×Dic5C2413yes—
252C2×C3×Dic5C2413yes—
253C3×C4×D5—26no—
254C3×Dic10—26no—
255#1204—212no—
256#1203—26no—
257#1201—26no—
258#1200—26no—
259D3×Dic5—26no—
260D3×Dic5—26no—
261D3×Dic5—22no—
262D5×Dic3—26no—
263C2×C3×#41C2×D511yescharacteristic, complemented
264C22×C3×Q8—51no—
265D3×#41—28no—
266C2×#239C2×D511yescharacteristic, complemented
267C2×D3×Q8—51no—
268C2×D3×Q8—53no—
269C2×D3×Q8—53no—
270C2×D3×Q8—108no—
271C2×D3×Q8C2×D511yescharacteristic
272C2×#237C2×D513yescomplemented
273C2×D3×D4—53no—
274C2×D3×D4C2×D513yes—
275C2×#235C2×D513yescomplemented
276C22×C4×D3—53no—
277C22×C4×D3C2×D513yes—
278C22×Dic6—53no—
279C3×#124—53no—
280C3×C22⋊Q8—53no—
281C3×#121—53no—
282C3×C4×Q8—51no—
283C3×C4×D4—53no—
284#947—53no—
285#946—53no—
286Q8×Dic3—51no—
287#939—56no—
288#938—53no—
289#936—53no—
290D4×Dic3—53no—
291#930—53no—
292C4×#67—53no—
293C4×#67—53no—
294#924—53no—
295#897—53no—
296#896—56no—
297#895—53no—
298#893—53no—
299D3×C4⋊C4—53no—
300D3×C4⋊C4—53no—
301#887—53no—
302#885—56no—
303#885—56no—
304#884—56no—
305#67⋊C4—53no—
306#67⋊C4—53no—
307D3×C22⋊C4—53no—
308D3×C22⋊C4—56no—
309D3×C22⋊C4—51no—
310#878—56no—
311#875—53no—
312C4×D12—53no—
313C42×D3—53no—
314C4×Dic6—53no—
315C24×C5—33no—
316C23×D5—31no—
317C5×#41—24no—
318C5×#41—612no—
319C5×#41—612no—
320C5×#41—64no—
321C2×C5×Q8—38no—
322C2×C5×Q8—33no—
323C2×C5×Q8C22×D311yescharacteristic
324C2×C5×D4—36no—
325C2×C5×D4—33no—
326C2×C5×D4—612no—
327C2×C5×D4C22×D313yes—
328C22×C4×C5—33no—
329C22×C4×C5—33no—
330C22×C4×C5—31no—
331C22×C4×C5—33no—
332C22×C4×C5—33no—
333C22×C4×C5—612no—
334C22×C4×C5C22×D313yes—
335C2×C22⋊D5—33no—
336C2×C22⋊D5—33no—
337C2×C22⋊D5—33no—
338C2×C22⋊D5—612no—
339C2×C22⋊D5C22×D313yes—
340C22×Dic5—33no—
341C22×Dic5—31no—
342C22×Dic5—33no—
343Q8×D5—24no—
344Q8×D5—612no—
345Q8×D5—612no—
346Q8×D5—64no—
347C2×C4×D5—33no—
348C2×C4×D5—33no—
349C2×C4×D5—33no—
350C2×C4×D5—612no—
351C2×C4×D5C22×D313yes—
352C2×Dic10—33no—
353C2×Dic10—36no—
354C2×Dic10—612no—
355C2×Dic10C22×D313yes—
356C22⋊Dic5—36no—
357C22⋊Dic5—33no—
358C22⋊Dic5—36no—
359C22⋊Dic5—36no—
360C22⋊Dic5—33no—
361C22⋊Dic5—33no—
362C22⋊Dic5C22×D316yes—
363C22⋊Dic5C22×D313yes—
364#685—31no—
365#685—31no—
366#685—31no—
367#685C22×D311yescharacteristic
368C4⋊Dic5—33no—
369C4⋊Dic5—36no—
370C4⋊Dic5C22×D313yes—
371#683—33no—
372#683—33no—
373#683—33no—
374#683C22×D313yes—
375C4×Dic5—33no—
376C4×Dic5—33no—
377C4×Dic5—33no—
378C4×Dic5C22×D313yes—
379C22×#41—31no—
380C23×Q8—151no—
381#548—51no—
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—23no—
402C2×C5×D3—23no—
403C2×C5×D3—23no—
404C2×C5×D3—412no—
405C2×C5×D3C22×D412yes—
406C2×C5×D3C2×#4112yes—
407C2×C5×D32−1+412yes—
408C2×C3×D5—21no—
409C2×C3×D5—21no—
410C2×C3×D5C2×#4112yescomplemented
411D3×D5—28no—
412C3×C4×C5—21no—
413C3×C4×C5C22×D416yes—
414Dic15—23no—
415Dic15—23no—
416Dic15—21no—
417C3×Dic5—23no—
418C3×Dic5—23no—
419C3×Dic5—21no—
420C5×Dic3—21no—
421C5×Dic3C22×D416yes—
422C23×D3—51no—
423C23×D3C22×D513yes—
424C3×#41—24no—
425C2×C3×Q8—53no—
426C2×C3×Q8—104no—
427C2×C3×Q8C22×D511yescharacteristic
428C2×C3×D4—53no—
429C2×C3×D4C22×D513yes—
430C22×C3×C4—53no—
431C22×C3×C4C22×D513yes—
432C2×#67—53no—
433C2×#67—53no—
434C2×#67C22×D516yes—
435C22×Dic3—53no—
436C22×Dic3C22×D513yes—
437#239—24no—
438D3×Q8—104no—
439D3×Q8—1012no—
440D3×Q8—1012no—
441D3×Q8C22⋊D518yescomplemented
442#237—212no—
443D3×D4—212no—
444D3×D4—1012no—
445#235—212no—
446C2×D12—53no—
447C2×D12C22×D513yes—
448C2×C4×D3—212no—
449C2×C4×D3—51no—
450C2×C4×D3—53no—
451C2×C4×D3—53no—
452C2×C4×D3—53no—
453C2×C4×D3—53no—
454C2×C4×D3—1012no—
455C2×C4×D3C22×D513yes—
456C2×C4×D3C22×D511yescharacteristic
457C2×C4×D3C22×D513yes—
458C2×C4×D3C22×D513yes—
459C2×Dic6—53no—
460C2×Dic6—56no—
461C2×Dic6—1012no—
462C2×Dic6C22×D513yes—
463C3×C4⋊C4—53no—
464C3×C4⋊C4—53no—
465C3×C22⋊C4—56no—
466C3×C22⋊C4—53no—
467C3×C22⋊C4—51no—
468C3×C42—53no—
469#217—56no—
470#217—53no—
471#217—51no—
472(C2×D3)⋊C4—53no—
473(C2×D3)⋊C4—56no—
474(C2×D3)⋊C4—56no—
475(C2×D3)⋊C4—53no—
476(C2×D3)⋊C4—51no—
477(C2×D3)⋊C4—51no—
478C4⋊Dic3—53no—
479C4⋊Dic3—53no—
480Dic3⋊C4—53no—
481Dic3⋊C4—53no—
482Dic3⋊C4—56no—
483C4×Dic3—53no—
484C4×Dic3—53no—
485C4×Dic3—53no—
486C23×C5—31no—
487C23×C5—33no—
488C23×C5—66no—
489C23×C5—66no—
490C23×C5—66no—
491C23×C5C23×D313yes—
492C22×D5—31no—
493C22×D5—34no—
494C22×D5—62no—
495C22×D5—62no—
496C22×D5C23×D311yescharacteristic
497C5×Q8—312no—
498C5×Q8D3×D414yescomplemented
499C5×D4—26no—
500C5×D4—612no—
501C5×D4—66no—
502C2×C4×C5—26no—
503C2×C4×C5—33no—
504C2×C4×C5—312no—
505C2×C4×C5—31no—
506C2×C4×C5—66no—
507C2×C4×C5—62no—
508C2×C4×C5—66no—
509C2×C4×C5—66no—
510C2×C4×C5C23×D311yescharacteristic
511C2×C4×C5C23×D313yes—
512C22⋊D5—26no—
513C22⋊D5—66no—
514C22⋊D5—66no—
515C22⋊D5—66no—
516C2×Dic5—31no—
517C2×Dic5—33no—
518C2×Dic5—33no—
519C2×Dic5—66no—
520C2×Dic5—62no—
521C2×Dic5—66no—
522C2×Dic5C23×D311yescharacteristic
523C2×Dic5C23×D313yes—
524C2×Dic5C23×D313yes—
525C4×D5—26no—
526C4×D5—66no—
527C4×D5—66no—
528C4×D5—66no—
529Dic10—26no—
530Dic10—612no—
531Dic10—66no—
532C2×#41—31no—
533C2×#41—33no—
534C2×#41—33no—
535C2×#41—68no—
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—33no—
545C22×D4—153no—
546C23×C4—33no—
547C23×C4—153no—
548#124—53no—
549#124—153no—
550#124—156no—
551#124—156no—
552#124—153no—
553#124—153no—
554C22⋊Q8—53no—
555C22⋊Q8—156no—
556C22⋊Q8—156no—
557C22⋊Q8—153no—
558C22⋊Q8—153no—
559C22⋊Q8—153no—
560#121—53no—
561#121—156no—
562#121—153no—
563#121—153no—
564#121—156no—
565#121—153no—
566C4×Q8—51no—
567C4×Q8—153no—
568C4×Q8—153no—
569C4×Q8—151no—
570C4×D4—53no—
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—22no—
590C5×D3—43no—
591C5×D3#54814yescomplemented
592C23×C3—51no—
593C23×C3C23×D513yes—
594C22×D3—26no—
595C22×D3—26no—
596C22×D3—26no—
597C22×D3—51no—
598C22×D3—54no—
599C22×D3—102no—
600C22×D3—102no—
601C22×D3C23×D513yes—
602C22×D3C23×D511yescharacteristic
603C3×Q8—106no—
604C3×Q8C2×C22⋊D514yescomplemented
605C3×D4—26no—
606C3×D4—106no—
607C2×C3×C4—26no—
608C2×C3×C4—51no—
609C2×C3×C4—53no—
610C2×C3×C4—53no—
611C2×C3×C4—106no—
612C2×C3×C4C23×D511yescharacteristic
613C2×C3×C4C23×D513yes—
614#67—212no—
615#67—106no—
616#67—106no—
617C2×Dic3—26no—
618C2×Dic3—51no—
619C2×Dic3—53no—
620C2×Dic3—53no—
621C2×Dic3—106no—
622C2×Dic3C23×D511yescharacteristic
623C2×Dic3C23×D513yes—
624D12—26no—
625D12—106no—
626C4×D3—22no—
627C4×D3—26no—
628C4×D3—26no—
629C4×D3—106no—
630C4×D3—102no—
631C4×D3—106no—
632C4×D3—106no—
633C4×D3—106no—
634C4×D3C2×C22⋊D5112yes—
635Dic6—106no—
636Dic6—1012no—
637Dic6C2×C22⋊D5112yescomplemented
638C22×C5—23no—
639C22×C5—23no—
640C22×C5—23no—
641C22×C5—32no—
642C22×C5—32no—
643C22×C5—32no—
644C22×C5—63no—
645C22×C5—63no—
646C22×C5—63no—
647C22×C5—1212no—
648C22×C5C24×D311yescharacteristic
649C2×D5—21no—
650C2×D5—21no—
651C2×D5—32no—
652C2×D5—68no—
653C2×D5—61no—
654C2×D5—61no—
655C2×D5D3×#4112yescomplemented
656C4×C5—21no—
657C4×C5—36no—
658C4×C5—61no—
659C4×C5C2×D3×D416yes—
660Dic5—23no—
661Dic5—23no—
662Dic5—21no—
663Dic5—63no—
664Dic5—63no—
665Dic5—61no—
666C24—33no—
667C24—151no—
668#41—24no—
669#41—612no—
670#41—612no—
671#41—64no—
672C2×Q8—38no—
673C2×Q8—33no—
674C2×Q8—53no—
675C2×Q8—104no—
676C2×Q8—156no—
677C2×Q8—153no—
678C2×Q8—3012no—
679C2×Q8—3012no—
680C2×Q8—3012no—
681C2×Q8—304no—
682C2×Q8C2×D3×D511yescharacteristic
683C2×D4—36no—
684C2×D4—33no—
685C2×D4—53no—
686C2×D4—612no—
687C2×D4—153no—
688C2×D4—153no—
689C2×D4—153no—
690C2×D4—3012no—
691C2×D4C2×D3×D513yes—
692C22×C4—33no—
693C22×C4—33no—
694C22×C4—31no—
695C22×C4—33no—
696C22×C4—33no—
697C22×C4—53no—
698C22×C4—612no—
699C22×C4—153no—
700C22×C4—153no—
701C22×C4—151no—
702C22×C4—153no—
703C22×C4—153no—
704C22×C4—153no—
705C22×C4—3012no—
706C22×C4C2×D3×D513yes—
707C4⋊C4—53no—
708C4⋊C4—53no—
709C4⋊C4—153no—
710C4⋊C4—153no—
711C4⋊C4—156no—
712C4⋊C4—153no—
713C4⋊C4—153no—
714C22⋊C4—53no—
715C22⋊C4—56no—
716C22⋊C4—51no—
717C22⋊C4—151no—
718C22⋊C4—151no—
719C22⋊C4—153no—
720C22⋊C4—153no—
721C22⋊C4—156no—
722C22⋊C4—156no—
723C22⋊C4—153no—
724C22⋊C4—156no—
725C22⋊C4—151no—
726C42—53no—
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—101no—
736C22×C3—101no—
737C22×C3C24×D511yescharacteristic
738C2×D3—23no—
739C2×D3—23no—
740C2×D3—23no—
741C2×D3—412no—
742C2×D3—52no—
743C2×D3—101no—
744C2×D3—101no—
745C2×D3—108no—
746C2×D3D5×#4112yes—
747C2×D3#415012yes—
748C2×D3C22×C22⋊D512yes—
749C3×C4—21no—
750C3×C4—103no—
751C3×C4—101no—
752C3×C4—103no—
753C3×C4C22×C22⋊D516yes—
754Dic3—21no—
755Dic3—103no—
756Dic3—101no—
757Dic3—103no—
758Dic3C22×C22⋊D516yes—
759C2×C5—34no—
760C2×C5—43no—
761C2×C5—123no—
762C2×C5C22×D3×D411yescharacteristic
763C2×C5C2×D3×#4111yescharacteristic
764C2×C5D3×2−1+411yescharacteristic
765D5—22no—
766D5—62no—
767C23—31no—
768C23—33no—
769C23—51no—
770C23—66no—
771C23—66no—
772C23—66no—
773C23—154no—
774C23—151no—
775C23—302no—
776C23—302no—
777C23C22×D3×D513yes—
778Q8—312no—
779Q8—106no—
780Q8—3012no—
781Q8—306no—
782Q8D3×C22⋊D514yescomplemented
783D4—26no—
784D4—612no—
785D4—66no—
786D4—106no—
787D4—306no—
788D4—306no—
789D4—306no—
790C2×C4—26no—
791C2×C4—33no—
792C2×C4—312no—
793C2×C4—31no—
794C2×C4—51no—
795C2×C4—53no—
796C2×C4—53no—
797C2×C4—66no—
798C2×C4—62no—
799C2×C4—66no—
800C2×C4—66no—
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—102no—
815C2×C3C2×D5×#4111yescharacteristic
816C2×C3C2×#415011yescharacteristic
817C2×C3C23×C22⋊D511yescharacteristic
818D3—43no—
819D3—102no—
820D3#6616514yesdirect product factor
821C5D3×#54811yescharacteristic, complemented, Sylow
822C22—23no—
823C22—23no—
824C22—23no—
825C22—32no—
826C22—32no—
827C22—32no—
828C22—52no—
829C22—63no—
830C22—63no—
831C22—63no—
832C22—101no—
833C22—101no—
834C22—1212no—
835C22—152no—
836C22—308no—
837C22—301no—
838C22—301no—
839C22C23×D3×D511yescharacteristic
840C4—21no—
841C4—36no—
842C4—61no—
843C4—101no—
844C4—103no—
845C4—103no—
846C4—301no—
847C4—303no—
848C4—303no—
849C4C2×D3×C22⋊D516yes—
850C3C2×#6616511yescharacteristic, complemented, Sylow
851C2—34no—
852C2—43no—
853C2—102no—
854C2—123no—
855C2—302no—
856C2D3×D5×#4111yescharacteristic
857C2D3×#415011yescharacteristic
858C2C22×D3×C22⋊D511yescharacteristic
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×C5×D3×#41C2semidirect
2. C2×D3×Q8×D5C2semidirect
3. #11756590C2semidirect
4. C3×#66165C2semidirect
5. #11755244C2semidirect
6. D3×Q8×Dic5C2semidirect
7. #11755134C2semidirect
8. D3×#4084C2semidirect
9. #11754951C2semidirect
10. D3×#4082C2semidirect
11. #11754802C2semidirect
12. C4×D3×C22⋊D5C2semidirect
13. #11754546C2semidirect
14. D3×#4070C2semidirect
15. #11754338C2semidirect
17. C2×C3×C5×#41C22semidirect
18. C2×Q8×D15C22semidirect
20. C2×C5×#239C22semidirect
22. C2×C5×#237C22semidirect
24. C2×C5×#235C22semidirect
26. C2×C3×Q8×D5C22semidirect
30. C2×D15⋊Q8C22semidirect
32. C2×D5×Dic6C22semidirect
33. Q8×Dic15C22semidirect
34. #91827C22semidirect
35. #91825C22semidirect
36. C4×#1220C22semidirect
37. #91813C22semidirect
38. C3×Q8×Dic5C22semidirect
39. C3×#4084C22semidirect
40. C3×#4082C22semidirect
41. C3×C4×C22⋊D5C22semidirect
42. C3×#4070C22semidirect
43. #91575C22semidirect
44. #91557C22semidirect
45. #91556C22semidirect
48. Dic3×C22⋊D5C22semidirect
49. #91549C22semidirect
50. #91525C22semidirect
51. #91525C22semidirect
53. #91466C22semidirect
54. #91449C22semidirect
55. #91446C22semidirect
56. C4×#1203C22semidirect
57. #91441C22semidirect
58. C4×#1201C22semidirect
62. #91373C22semidirect
63. #91370C22semidirect
64. #91369C22semidirect
65. #91365C22semidirect
66. #91352C22semidirect
67. #91344C22semidirect
68. Dic5×Dic6C22semidirect
79. #66165D3direct (N × H)
98. C5×D3×Q8D4semidirect
149. C2×D3×#41D5semidirect
168. C2×C5×#41C2×D3semidirect
177. C2×Q8×D5C2×D3semidirect
185. Q8×Dic5C2×D3semidirect
191. #4084C2×D3semidirect
197. #4082C2×D3semidirect
205. C4×C22⋊D5C2×D3semidirect
213. #4070C2×D3semidirect
227. C2×D3×D5#41semidirect
228. C3×C5×Q8C2×D4semidirect
248. C5×Dic6C2×D4semidirect
263. C2×C3×#41C2×D5semidirect
266. C2×#239C2×D5semidirect
272. C2×#237C2×D5semidirect
275. C2×#235C2×D5semidirect
400. C2×D15C2×#41semidirect
410. C2×C3×D5C2×#41semidirect
441. D3×Q8C22⋊D5semidirect
498. C5×Q8D3×D4semidirect
536. C2×#41D3×D5semidirect
591. C5×D3#548semidirect
604. C3×Q8C2×C22⋊D5semidirect
637. Dic6C2×C22⋊D5semidirect
655. C2×D5D3×#41semidirect
730. C3×C5C2×#548semidirect
782. Q8D3×C22⋊D5semidirect
820. D3#66165direct (N × H)
821. C5D3×#548semidirect
850. C3C2×#66165semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×#412
C2×D3×Q8×D52
#117565902
C3×#661652
#117552442
D3×Q8×Dic52
#117551342
D3×#40842
#117549512
D3×#40822
#117548022
C4×D3×C22⋊D52
#117545462
D3×#40702
#117543382
C2×#661653
D3×#5485