Finite Group Databasebeta

← C2×#385×D53 #27542395

Subgroups — C2×#385×D53 #27542395

Order 13568.

8670 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C4×D53C211yesmaximal, characteristic
2C22×C4⋊C4×D53C212yesmaximal, complemented
3C22×C22⋊C4×D53C211yesmaximal, characteristic
4C22×C22⋊C4×D53C211yesmaximal, characteristic
5C2×#16810498C211yesmaximal, characteristic, complemented
6C2×#16810497C212yesmaximal, complemented
7C2×#16810496C211yesmaximal, characteristic, complemented
8C2×#16810495C211yesmaximal, characteristic, complemented
9C2×#16810494C212yesmaximal, complemented
10#385×D53C2116yesmaximal, direct product factor
11C2×#95×D53C212yesmaximal, complemented
12C2×C53×#385C211yesmaximal, characteristic, complemented
13C25×D53C2211yescharacteristic
14C24×Dic53C2211yescharacteristic
15C23×C4×D53—28no—
16C23×C4×D53—216no—
17C23×C4×D53C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C23×C4×D53C2218yes—
20C23×C4×D53C2212yes—
21C23×C4×D53C2212yes—
22C23×C4×D53C2212yes—
23C22×C4⋊Dic53C2212yescomplemented
24C22×#11719919C2212yescomplemented
25C22×#11719919C2212yescomplemented
26C2×C4⋊C4×D53—216no—
27C2×C4⋊C4×D53C22116yescomplemented
28C22×C22⋊Dic53C2211yescharacteristic
29C22×C22⋊Dic53C2211yescharacteristic
30C22×#11719921C2211yescharacteristic
31C22×#11719921C2211yescharacteristic
32C22×#11719921C2212yes—
33C2×C22⋊C4×D53—28no—
34C2×C22⋊C4×D53C4116yescomplemented
35C2×C22⋊C4×D53C2218yes—
36C2×C22⋊C4×D53C2218yes—
37#16810498C2218yescomplemented
38#16810497C22116yescomplemented
39#16810496C2218yescomplemented
40#16810495C2218yescomplemented
41#16810494C22116yescomplemented
42C2×#13133124C2212yescomplemented
43C2×#13133124C2212yescomplemented
44C2×#13133124C2212yescomplemented
45#95×D53C22116yescomplemented
46C24×C4×C53C2211yescharacteristic
47C22×C4⋊C4×C53C2212yescomplemented
48C22×C22⋊C4×C53C2211yescharacteristic
49C22×C22⋊C4×C53C2211yescharacteristic
50C53×#385C2218yescomplemented
51C2×#95×C53C2212yescomplemented
52C24×D53—28no—
53C24×D53—28no—
54C24×D53C2×C418yes—
55C24×D53D418yes—
56C24×D53Q818yes—
57C24×D53C2314yes—
58C24×D53C2311yescharacteristic
59C24×D53C2311yescharacteristic
60C23×Dic53—24no—
61C23×Dic53—28no—
62C23×Dic53C2314yes—
63C23×Dic53C2311yescharacteristic
64C23×Dic53C2311yescharacteristic
65C23×Dic53C2312yes—
66C23×Dic53C2312yes—
67C22×C4×D53—2128no—
68C22×C4×D53—28no—
69C22×C4×D53—232no—
70C22×C4×D53—28no—
71C22×C4×D53—28no—
72C22×C4×D53—28no—
73C22×C4×D53—28no—
74C22×C4×D53—28no—
75C22×C4×D53—28no—
76C22×C4×D53—264no—
77C22×C4×D53—24no—
78C22×C4×D53—24no—
79C22×C4×D53—28no—
80C22×C4×D53—28no—
81C22×C4×D53C2×C4116yescomplemented
82C22×C4×D53D4116yes—
83C22×C4×D53C2318yes—
84C22×C4×D53C2314yes—
85C22×C4×D53C2314yes—
86C22×C4×D53C2318yes—
87C22×C4×D53C2318yes—
88C2×C4⋊Dic53—28no—
89C2×C4⋊Dic53C2318yescomplemented
90C2×#11719919—28no—
91C2×#11719919—28no—
92C2×#11719919C2318yescomplemented
93C2×#11719919C2318yescomplemented
94C4⋊C4×D53—264no—
95C2×C22⋊Dic53—24no—
96C2×C22⋊Dic53C2×C418yescomplemented
97C2×C22⋊Dic53C2314yes—
98C2×C22⋊Dic53C2314yes—
99C2×#11719921—24no—
100C2×#11719921—24no—
101C2×#11719921C2×C4116yescomplemented
102C2×#11719921C2314yes—
103C2×#11719921C2314yes—
104C2×#11719921C2318yes—
105C22⋊C4×D53—232no—
106C22⋊C4×D53C2×C4164yescomplemented
107#13133124C2318yescomplemented
108#13133124C2318yescomplemented
109#13133124C2318yescomplemented
110C25×C53C2311yescharacteristic
111C23×C4×C53—24no—
112C23×C4×C53—28no—
113C23×C4×C53C2314yes—
114C23×C4×C53C2311yescharacteristic
115C23×C4×C53C2311yescharacteristic
116C23×C4×C53C2312yes—
117C23×C4×C53C2312yes—
118C2×C4⋊C4×C53—28no—
119C2×C4⋊C4×C53C2318yescomplemented
120C2×C22⋊C4×C53—24no—
121C2×C22⋊C4×C53C2×C418yescomplemented
122C2×C22⋊C4×C53C2314yes—
123C2×C22⋊C4×C53C2314yes—
124#95×C53C2318yescomplemented
125C24×C53—24no—
126C24×C53—24no—
127C24×C53C22×C414yes—
128C24×C53C2×D414yes—
129C24×C53C2×Q814yes—
130C24×C53C2412yes—
131C24×C53C2411yescharacteristic
132C23×D53—24no—
133C23×D53—24no—
134C23×D53—264no—
135C23×D53—232no—
136C23×D53—264no—
137C23×D53—232no—
138C23×D53—216no—
139C23×D53—216no—
140C23×D53C4⋊C4164yescomplemented
141C23×D53C22×C4116yes—
142C23×D53C22×C414yes—
143C23×D53C22×C414yes—
144C23×D53C2×D4116yes—
145C23×D53C2×D414yes—
146C23×D53C2×D414yes—
147C23×D53C2×D418yes—
148C23×D53C2×Q814yes—
149C23×D53C2×Q8116yes—
150C23×D53C2×Q814yes—
151C23×D53#4118yes—
152C23×D53C2412yes—
153C23×D53C2412yes—
154C22×C4×C53—232no—
155C22×C4×C53—24no—
156C22×C4×C53—28no—
157C22×C4×C53—24no—
158C22×C4×C53—24no—
159C22×C4×C53—24no—
160C22×C4×C53—216no—
161C22×C4×C53—22no—
162C22×C4×C53—22no—
163C22×C4×C53—24no—
164C22×C4×C53—24no—
165C22×C4×C53C22×C418yescomplemented
166C22×C4×C53C2×D418yes—
167C22×C4×C53C2412yes—
168C22×C4×C53C2412yes—
169C22×C4×C53C2414yes—
170C22×C4×C53C2414yes—
171C22×Dic53—232no—
172C22×Dic53—24no—
173C22×Dic53—28no—
174C22×Dic53—24no—
175C22×Dic53—24no—
176C22×Dic53—24no—
177C22×Dic53—216no—
178C22×Dic53—22no—
179C22×Dic53—22no—
180C22×Dic53—24no—
181C22×Dic53—24no—
182C22×Dic53C22×C418yescomplemented
183C22×Dic53C2×D418yes—
184C22×Dic53C2412yes—
185C22×Dic53C2412yes—
186C22×Dic53C2414yes—
187C22×Dic53C2414yes—
188C2×C4×D53—264no—
189C2×C4×D53—2256no—
190C2×C4×D53—264no—
191C2×C4×D53—264no—
192C2×C4×D53—216no—
193C2×C4×D53—216no—
194C2×C4×D53—216no—
195C2×C4×D53—216no—
196C2×C4×D53—216no—
197C2×C4×D53—216no—
198C2×C4×D53—216no—
199C2×C4×D53—28no—
200C2×C4×D53—28no—
201C2×C4×D53—216no—
202C2×C4×D53—216no—
203C2×C4×D53—416no—
204C2×C4×D53—416no—
205C2×C4×D53C22×C4132yescomplemented
206C2×C4×D53C2×D4132yes—
207C4⋊C4×C53—216no—
208C22⋊C4×C53—28no—
209C22⋊C4×C53C22×C4116yescomplemented
210C22⋊Dic53—28no—
211C22⋊Dic53C22×C4116yescomplemented
212#11719921—28no—
213#11719921—28no—
214#11719921C22×C4132yescomplemented
215C4⋊Dic53—216no—
216#11719919—216no—
217#11719919—216no—
218C23×C53—216no—
219C23×C53—28no—
220C23×C53—216no—
221C23×C53—28no—
222C23×C53—24no—
223C23×C53—24no—
224C23×C53C2×C4⋊C4116yescomplemented
225C23×C53C23×C414yes—
226C23×C53C23×C412yes—
227C23×C53C22×D414yes—
228C23×C53C22×D412yes—
229C23×C53C22×D414yes—
230C23×C53C22×Q814yes—
231C23×C53C22×Q812yes—
232C23×C53C2×#4114yes—
233C23×C53C2511yescharacteristic
234C22×D53—216no—
235C22×D53—28no—
236C22×D53—216no—
237C22×D53—28no—
238C22×D53—24no—
239C22×D53—24no—
240C22×D53—264no—
241C22×D53—232no—
242C22×D53—264no—
243C22×D53—232no—
244C22×D53—2256no—
245C22×D53C2×C4⋊C4116yes—
246C22×D53C2×C4⋊C4164yescomplemented
247C22×D53C2×C4⋊C4116yescomplemented
248C22×D53C4×D4132yes—
249C22×D53#120116yes—
250C22×D53C22⋊Q8132yes—
251C22×D53#123116yes—
252C22×D53C23×C414yes—
253C22×D53C23×C414yes—
254C22×D53C22×D414yes—
255C22×D53C22×D414yes—
256C22×D53C22×D418yes—
257C22×D53C22×Q814yes—
258C22×D53C22×Q814yes—
259C22×D53C2×#4118yes—
260C2×C4×C53—232no—
261C2×C4×C53—216no—
262C2×C4×C53—216no—
263C2×C4×C53—24no—
264C2×C4×C53—24no—
265C2×C4×C53—24no—
266C2×C4×C53—24no—
267C2×C4×C53—24no—
268C2×C4×C53—22no—
269C2×C4×C53—22no—
270C2×C4×C53—24no—
271C2×C4×C53—44no—
272C2×C4×C53—44no—
273C2×C4×C53C23×C418yescomplemented
274C2×C4×C53C22×D418yes—
275C2×Dic53—232no—
276C2×Dic53—216no—
277C2×Dic53—216no—
278C2×Dic53—24no—
279C2×Dic53—24no—
280C2×Dic53—24no—
281C2×Dic53—24no—
282C2×Dic53—24no—
283C2×Dic53—22no—
284C2×Dic53—22no—
285C2×Dic53—24no—
286C2×Dic53—44no—
287C2×Dic53—44no—
288C2×Dic53C23×C418yescomplemented
289C2×Dic53C22×D418yes—
290C4×D53—264no—
291C4×D53—264no—
292C4×D53—264no—
293C4×D53—416no—
294C4×D53—416no—
295C22×#385—531nomaximal, Sylow
296C22×C53—28no—
297C22×C53—24no—
298C22×C53—28no—
299C22×C53—24no—
300C22×C53—232no—
301C22×C53C22×C4⋊C414yes—
302C22×C53C22×C4⋊C418yescomplemented
303C22×C53C2×C4×D418yes—
304C22×C53C2×#12014yes—
305C22×C53C2×C22⋊Q818yes—
306C22×C53C2×#12314yes—
307C22×C53C24×C411yescharacteristic
308C22×C53C23×D411yescharacteristic
309C22×C53C23×D412yes—
310C22×C53C23×Q811yescharacteristic
311C22×C53C22×#4112yes—
312C2×D53—28no—
313C2×D53—24no—
314C2×D53—28no—
315C2×D53—24no—
316C2×D53—232no—
317C2×D53—2128no—
318C2×D53#385164yesdirect product factor
319C2×D53C22×C4⋊C418yes—
320C2×D53C22×C4⋊C418yescomplemented
321C2×D53C2×C4×D4116yes—
322C2×D53C2×#12018yes—
323C2×D53C2×C22⋊Q8116yes—
324C2×D53C2×#12318yes—
325C4×C53—28no—
326C4×C53—28no—
327C4×C53—42no—
328C4×C53—42no—
329Dic53—28no—
330Dic53—28no—
331Dic53—42no—
332Dic53—42no—
333C25×C4—531no—
334C23×C4⋊C4—532no—
335C23×C22⋊C4—531no—
336C23×C22⋊C4—531no—
337C2×#385—5316no—
338C2×#385—532no—
339C2×#385—531no—
340C2×#385—532no—
341C2×#385—531no—
342C2×#385—531no—
343C2×#385D5311yescharacteristic, direct product factor
344C22×#95—532no—
345C2×C53—28no—
346C2×C53C2×#38518yescomplemented
347C2×C53C23×C4⋊C411yescharacteristic
348C2×C53C22×C4×D412yes—
349C2×C53C22×#12011yescharacteristic
350C2×C53C22×C22⋊Q812yes—
351C2×C53C22×#12311yescharacteristic
352D53—28no—
353D53C2×#385116yesdirect product factor
354C26—531no—
355C24×C4—532no—
356C24×C4—532no—
357C24×C4—531no—
358C24×C4—532no—
359C24×C4—538no—
360C24×C4—531no—
361C24×C4—531no—
362C24×C4—10616no—
363C24×C4—1068no—
364C24×C4C2×D5311yescharacteristic
365C22×C4⋊C4—532no—
366C22×C4⋊C4—532no—
367C22×C4⋊C4—532no—
368C22×C4⋊C4—5316no—
369C22×C4⋊C4—10616no—
370C22×C4⋊C4C2×D5312yescomplemented
371C22×C22⋊C4—531no—
372C22×C22⋊C4—532no—
373C22×C22⋊C4—5316no—
374C22×C22⋊C4—538no—
375C22×C22⋊C4—531no—
376C22×C22⋊C4—531no—
377C22×C22⋊C4—531no—
378C22×C22⋊C4—538no—
379C22×C22⋊C4—1068no—
380C22×C22⋊C4C2×D5311yescharacteristic
381C22×C22⋊C4C2×D5311yescharacteristic
382#385—538no—
383#385—5316no—
384#385—538no—
385#385—538no—
386#385—5316no—
387#385C2×D5318yesdirect product factor
388C2×#95—532no—
389C2×#95—532no—
390C2×#95—532no—
391C2×#95—5316no—
392C2×#95C2×D5312yescomplemented
393C53C22×#38511yescharacteristic, complemented, Sylow
394C25—531no—
395C25—538no—
396C25—538no—
397C25—538no—
398C25—534no—
399C25—531no—
400C25—1068no—
401C25—1068no—
402C25C22×D5311yescharacteristic
403C23×C4—24no—
404C23×C4—28no—
405C23×C4—532no—
406C23×C4—532no—
407C23×C4—5316no—
408C23×C4—5316no—
409C23×C4—538no—
410C23×C4—538no—
411C23×C4—534no—
412C23×C4—531no—
413C23×C4—531no—
414C23×C4—534no—
415C23×C4—534no—
416C23×C4—538no—
417C23×C4—1068no—
418C23×C4—10664no—
419C23×C4—1068no—
420C23×C4—1068no—
421C23×C4—1068no—
422C23×C4—10632no—
423C23×C4—1068no—
424C23×C4—1068no—
425C23×C4—106128no—
426C23×C4—1064no—
427C23×C4—1064no—
428C23×C4—1068no—
429C23×C4—1068no—
430C23×C4—1068no—
431C23×C4—1064no—
432C23×C4—1068no—
433C23×C4C22×D5314yes—
434C23×C4C22×D5311yescharacteristic
435C23×C4C22×D5311yescharacteristic
436C23×C4C22×D5312yes—
437C23×C4C22×D5312yes—
438C2×C4⋊C4—28no—
439C2×C4⋊C4—538no—
440C2×C4⋊C4—538no—
441C2×C4⋊C4—538no—
442C2×C4⋊C4—10664no—
443C2×C4⋊C4—1068no—
444C2×C4⋊C4—1068no—
445C2×C4⋊C4—1068no—
446C2×C4⋊C4C22×D5318yescomplemented
447C2×C22⋊C4—24no—
448C2×C22⋊C4—538no—
449C2×C22⋊C4—534no—
450C2×C22⋊C4—5316no—
451C2×C22⋊C4—538no—
452C2×C22⋊C4—5364no—
453C2×C22⋊C4—534no—
454C2×C22⋊C4—534no—
455C2×C22⋊C4—534no—
456C2×C22⋊C4—10632no—
457C2×C22⋊C4—1064no—
458C2×C22⋊C4—1064no—
459C2×C22⋊C4—1064no—
460C2×C22⋊C4C4×D5318yescomplemented
461C2×C22⋊C4C22×D5314yes—
462C2×C22⋊C4C22×D5314yes—
463#95—538no—
464#95—538no—
465#95—538no—
466#95C22×D5318yescomplemented
467C24—24no—
468C24—24no—
469C24—534no—
470C24—538no—
471C24—534no—
472C24—534no—
473C24—538no—
474C24—532no—
475C24—5364no—
476C24—5316no—
477C24—534no—
478C24—5316no—
479C24—534no—
480C24—5316no—
481C24—534no—
482C24—532no—
483C24—10632no—
484C24—10616no—
485C24—10664no—
486C24—10664no—
487C24—10632no—
488C24—10616no—
489C24—1064no—
490C24—1064no—
491C24C2×C4×D5314yes—
492C24D4×D5314yes—
493C24Q8×D5314yes—
494C24C23×D5312yes—
495C24C23×D5311yescharacteristic
496C22×C4—232no—
497C22×C4—24no—
498C22×C4—28no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—216no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—538no—
508C22×C4—538no—
509C22×C4—534no—
510C22×C4—534no—
511C22×C4—5332no—
512C22×C4—5332no—
513C22×C4—532no—
514C22×C4—532no—
515C22×C4—10616no—
516C22×C4—10616no—
517C22×C4—10664no—
518C22×C4—10616no—
519C22×C4—10664no—
520C22×C4—10616no—
521C22×C4—10616no—
522C22×C4—10616no—
523C22×C4—106256no—
524C22×C4—10664no—
525C22×C4—1068no—
526C22×C4—1068no—
527C22×C4—10616no—
528C22×C4—10616no—
529C22×C4—10616no—
530C22×C4—10632no—
531C22×C4—1064no—
532C22×C4—1068no—
533C22×C4—1064no—
534C22×C4—1064no—
535C22×C4—1064no—
536C22×C4—10616no—
537C22×C4—1062no—
538C22×C4—1062no—
539C22×C4—1064no—
540C22×C4—1064no—
541C22×C4—21216no—
542C22×C4—21216no—
543C22×C4C2×C4×D5318yescomplemented
544C22×C4D4×D5318yes—
545C22×C4C23×D5312yes—
546C22×C4C23×D5312yes—
547C22×C4C23×D5314yes—
548C22×C4C23×D5314yes—
549C4⋊C4—216no—
550C4⋊C4—10616no—
551C4⋊C4—10616no—
552C4⋊C4—10616no—
553C22⋊C4—28no—
554C22⋊C4—5316no—
555C22⋊C4—5332no—
556C22⋊C4—1068no—
557C22⋊C4—1068no—
558C22⋊C4—1068no—
559C22⋊C4C2×C4×D53116yescomplemented
560C23—216no—
561C23—28no—
562C23—216no—
563C23—28no—
564C23—24no—
565C23—24no—
566C23—5316no—
567C23—5332no—
568C23—5316no—
569C23—5332no—
570C23—5316no—
571C23—534no—
572C23—538no—
573C23—534no—
574C23—534no—
575C23—538no—
576C23—5316no—
577C23—5364no—
578C23—534no—
579C23—534no—
580C23—534no—
581C23—10632no—
582C23—106256no—
583C23—10664no—
584C23—10664no—
585C23—10632no—
586C23—10616no—
587C23—1068no—
588C23—10616no—
589C23—1068no—
590C23—1064no—
591C23—1064no—
592C23C4⋊C4×D53116yescomplemented
593C23C22×C4×D5314yes—
594C23C22×C4×D5312yes—
595C23C2×D4×D5314yes—
596C23C2×D4×D5312yes—
597C23C2×D4×D5314yes—
598C23C2×Q8×D5314yes—
599C23C2×Q8×D5312yes—
600C23#41×D5314yes—
601C23C24×D5311yescharacteristic
602C2×C4—232no—
603C2×C4—216no—
604C2×C4—216no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—44no—
614C2×C4—44no—
615C2×C4—538no—
616C2×C4—538no—
617C2×C4—10664no—
618C2×C4—10664no—
619C2×C4—10664no—
620C2×C4—10632no—
621C2×C4—10616no—
622C2×C4—10616no—
623C2×C4—1064no—
624C2×C4—1064no—
625C2×C4—1064no—
626C2×C4—1064no—
627C2×C4—1062no—
628C2×C4—1062no—
629C2×C4—1064no—
630C2×C4—1064no—
631C2×C4—21216no—
632C2×C4—21216no—
633C2×C4—2124no—
634C2×C4—2124no—
635C2×C4C22×C4×D5318yescomplemented
636C2×C4C2×D4×D5318yes—
637C22—232no—
638C22—28no—
639C22—24no—
640C22—28no—
641C22—24no—
642C22—538no—
643C22—5364no—
644C22—5316no—
645C22—538no—
646C22—5316no—
647C22—538no—
648C22—538no—
649C22—106128no—
650C22—10632no—
651C22—1068no—
652C22—1064no—
653C22—1068no—
654C22—1064no—
655C22C2×C4⋊C4×D5314yes—
656C22C2×C4⋊C4×D5318yescomplemented
657C22C4×D4×D5318yes—
658C22#120×D5314yes—
659C22C22⋊Q8×D5318yes—
660C22#123×D5314yes—
661C22C23×C4×D5311yescharacteristic
662C22C22×D4×D5311yescharacteristic
663C22C22×D4×D5312yes—
664C22C22×Q8×D5311yescharacteristic
665C22C2×#41×D5312yes—
666C4—28no—
667C4—28no—
668C4—42no—
669C4—42no—
670C4—1068no—
671C4—1068no—
672C4—2122no—
673C4—2122no—
674C2—28no—
675C2—5316no—
676C2—1068no—
677C2#385×D5318yesdirect product factor
678C2C22×C4⋊C4×D5311yescharacteristic
679C2C2×C4×D4×D5312yes—
680C2C2×#120×D5311yescharacteristic
681C2C2×C22⋊Q8×D5312yes—
682C2C2×#123×D5311yescharacteristic
subgroupG/H
centerC24C23×D53
commutatorC22×C53C24×C4
FrattiniC23C24×D53
FittingC2×C53×#385C2
socleC24×C53C24
prime radicalC25×D53C22
cosocleC23×C53C25
hypercenterC2×#385D53
hypocenterC53C22×#385
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D53C2semidirect
5. C2×#16810498C2semidirect
6. C2×#16810497C2semidirect
7. C2×#16810496C2semidirect
8. C2×#16810495C2semidirect
9. C2×#16810494C2semidirect
10. #385×D53C2direct (N × H)
11. C2×#95×D53C2semidirect
12. C2×C53×#385C2semidirect
23. C22×C4⋊Dic53C22semidirect
24. C22×#11719919C22semidirect
25. C22×#11719919C22semidirect
27. C2×C4⋊C4×D53C22semidirect
34. C2×C22⋊C4×D53C4semidirect
37. #16810498C22semidirect
38. #16810497C22semidirect
39. #16810496C22semidirect
40. #16810495C22semidirect
41. #16810494C22semidirect
42. C2×#13133124C22semidirect
43. C2×#13133124C22semidirect
44. C2×#13133124C22semidirect
45. #95×D53C22semidirect
47. C22×C4⋊C4×C53C22semidirect
50. C53×#385C22semidirect
51. C2×#95×C53C22semidirect
81. C22×C4×D53C2×C4semidirect
89. C2×C4⋊Dic53C23semidirect
92. C2×#11719919C23semidirect
93. C2×#11719919C23semidirect
96. C2×C22⋊Dic53C2×C4semidirect
101. C2×#11719921C2×C4semidirect
106. C22⋊C4×D53C2×C4semidirect
107. #13133124C23semidirect
108. #13133124C23semidirect
109. #13133124C23semidirect
119. C2×C4⋊C4×C53C23semidirect
121. C2×C22⋊C4×C53C2×C4semidirect
124. #95×C53C23semidirect
140. C23×D53C4⋊C4semidirect
165. C22×C4×C53C22×C4semidirect
182. C22×Dic53C22×C4semidirect
205. C2×C4×D53C22×C4semidirect
209. C22⋊C4×C53C22×C4semidirect
211. C22⋊Dic53C22×C4semidirect
214. #11719921C22×C4semidirect
224. C23×C53C2×C4⋊C4semidirect
246. C22×D53C2×C4⋊C4semidirect
247. C22×D53C2×C4⋊C4semidirect
273. C2×C4×C53C23×C4semidirect
288. C2×Dic53C23×C4semidirect
302. C22×C53C22×C4⋊C4semidirect
318. C2×D53#385direct (N × H)
320. C2×D53C22×C4⋊C4semidirect
343. C2×#385D53direct (N × H)
346. C2×C53C2×#385semidirect
353. D53C2×#385direct (N × H)
370. C22×C4⋊C4C2×D53semidirect
387. #385C2×D53direct (N × H)
392. C2×#95C2×D53semidirect
393. C53C22×#385semidirect
446. C2×C4⋊C4C22×D53semidirect
460. C2×C22⋊C4C4×D53semidirect
466. #95C22×D53semidirect
543. C22×C4C2×C4×D53semidirect
559. C22⋊C4C2×C4×D53semidirect
592. C23C4⋊C4×D53semidirect
635. C2×C4C22×C4×D53semidirect
656. C22C2×C4⋊C4×D53semidirect
677. C2#385×D53direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C4×D532
C22×C4⋊C4×D532
C22×C22⋊C4×D532
C2×#168104982
C2×#168104972
C2×#168104962
C2×#168104952
C2×#168104942
#385×D532
C2×#95×D532
C2×C53×#3852
C22×#38553