Finite Group Databasebeta

← C53×#33572 #27241084

Subgroups — C53×#33572 #27241084

Order 13568.

1108 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3551C211yesmaximal, characteristic, complemented
2C53×#3022C211yesmaximal, characteristic, complemented
3C53×#3021C211yesmaximal, characteristic, complemented
4C53×#3018C211yesmaximal, characteristic, complemented
5C53×#2204C214yesmaximal, complemented
6C53×#2203C214yesmaximal, complemented
7C53×#2135C211yesmaximal, characteristic, complemented
8C53×#2134C211yesmaximal, characteristic, complemented
9C53×#2132C211yesmaximal, characteristic, complemented
10C53×#585C2211yescharacteristic
11C53×#575—21no—
12C2×#137×C53—21no—
13C2×AGL(1,ℤ/8)×C53—21no—
14C53×#563C2212yescomplemented
15C53×#560—21no—
16C53×#555C2212yescomplemented
17C53×#553—21no—
18C53×#552—21no—
19C53×#551—21no—
20C53×#548—21no—
21C53×#546—21no—
22C53×#540—22no—
23C53×#538—22no—
24C53×#537—21no—
25C53×#536C2211yescharacteristic
26C53×#535C2211yescharacteristic
27C53×#532C2211yescharacteristic
28C53×#529—21no—
29C53×#456C2212yescomplemented
30C53×#456C2214yescomplemented
31C53×#455—21no—
32C53×#455—22no—
33C53×#454C2214yes—
34C53×#454C2212yescomplemented
35C53×#453—21no—
36C53×#453—22no—
37C53×#421—21no—
38C53×#421—21no—
39C2×#104×C53—21no—
40C53×#413C2211yescharacteristic
41C53×#413C2211yescharacteristic
42C53×#413C2211yescharacteristic
43C53×#356C2212yescomplemented
44C53×#356C2214yescomplemented
45C53×#355C2214yescomplemented
46C53×#355C2212yescomplemented
472−1+4×C53—41no—
482−1+4×C53C2312yes—
49H(5,𝔽2)×C53—21no—
50H(5,𝔽2)×C53—21no—
51H(5,𝔽2)×C53—21no—
52H(5,𝔽2)×C53—41no—
53C2×#41×C53—21no—
54C2×#41×C53—21no—
55C2×#41×C53—21no—
56C2×#41×C53—21no—
57C2×#41×C53—42no—
58C2×#41×C53D411yescharacteristic
59C2×#41×C53C2311yescharacteristic
60C22×Q8×C53D411yescharacteristic
61C22×D4×C53D411yescharacteristic
62#137×C53—24no—
63#137×C53—22no—
64#137×C53—41no—
65#137×C53—42no—
66AGL(1,ℤ/8)×C53—24no—
67AGL(1,ℤ/8)×C53—22no—
68AGL(1,ℤ/8)×C53—41no—
69AGL(1,ℤ/8)×C53—42no—
70#135×C53—42no—
71C2×Q16×C53—41no—
72C2×SD16×C53—41no—
73C2×SD16×C53—41no—
74C2×D8×C53—41no—
75C2×M16×C53—21no—
76C2×M16×C53—21no—
77C2×M16×C53—21no—
78C4⋊Q8×C53C2311yescharacteristic
79C4⋊Q8×C53C2312yes—
80#127×C53D411yescharacteristic
81#127×C53D412yes—
82#126×C53—22no—
83#126×C53—22no—
84#126×C53—22no—
85#125×C53—21no—
86#125×C53—22no—
87#124×C53—21no—
88#124×C53—22no—
89#124×C53D411yescharacteristic
90#124×C53D412yes—
91#124×C53C2311yescharacteristic
92#124×C53C2312yes—
93#123×C53—22no—
94#123×C53—22no—
95#123×C53—22no—
96#123×C53—21no—
97#123×C53—21no—
98#123×C53—22no—
99C22⋊Q8×C53—21no—
100C22⋊Q8×C53—22no—
101C22⋊Q8×C53—22no—
102C22⋊Q8×C53—21no—
103C22⋊Q8×C53—21no—
104#121×C53—22no—
105#121×C53—22no—
106#121×C53—21no—
107#121×C53—22no—
108#121×C53—22no—
109#121×C53—21no—
110#121×C53—21no—
111#121×C53—22no—
112#121×C53—22no—
113#121×C53—21no—
114#121×C53—21no—
115#120×C53—22no—
116#120×C53—21no—
117#120×C53—21no—
118C4×Q8×C53—21no—
119C4×D4×C53—22no—
120C4×D4×C53—21no—
121C4×D4×C53—22no—
122C4×D4×C53—22no—
123C4×D4×C53—21no—
124C4×D4×C53—21no—
125#117×C53—22no—
126#117×C53—22no—
127#117×C53D411yescharacteristic
128#117×C53D411yescharacteristic
129C2×C4⋊C4×C53—21no—
130C2×C22⋊C4×C53—22no—
131C2×C42×C53D411yescharacteristic
132#104×C53—22no—
133#104×C53—22no—
134#104×C53—24no—
135#104×C53—24no—
136#101×C53C2312yes—
137#101×C53C2312yes—
138#101×C53C2312yes—
139#100×C53—21no—
140#100×C53—21no—
141#100×C53—21no—
142C24×C53—21no—
143#41×C53—22no—
144#41×C53—22no—
145#41×C53—22no—
146#41×C53—22no—
147#41×C53—22no—
148#41×C53—22no—
149#41×C53—41no—
150#41×C53—41no—
151#41×C53—41no—
152#41×C53—41no—
153#41×C53—41no—
154#41×C53—41no—
155#41×C53—41no—
156#41×C53—42no—
157#41×C53—42no—
158#41×C53—42no—
159#41×C53—42no—
160#41×C53—41no—
161#41×C53—81no—
162#41×C53—81no—
163C2×Q8×C53—21no—
164C2×Q8×C53—21no—
165C2×Q8×C53—21no—
166C2×Q8×C53—21no—
167C2×Q8×C53—41no—
168C2×Q8×C53—41no—
169C2×Q8×C53—42no—
170C2×Q8×C53C2×D411yescharacteristic
171C2×Q8×C53C2×D412yes—
172C2×Q8×C53C2411yescharacteristic
173C2×D4×C53—21no—
174C2×D4×C53—21no—
175C2×D4×C53—21no—
176C2×D4×C53—22no—
177C2×D4×C53—22no—
178C2×D4×C53—21no—
179C2×D4×C53—22no—
180C2×D4×C53—22no—
181C2×D4×C53—21no—
182C2×D4×C53—21no—
183C2×D4×C53—21no—
184C2×D4×C53—41no—
185C2×D4×C53—41no—
186C2×D4×C53—42no—
187C2×D4×C53—42no—
188C2×D4×C53—42no—
189C2×D4×C53—41no—
190C2×D4×C53—41no—
191C2×D4×C53—41no—
192C2×D4×C53C2×D411yescharacteristic
193C2×D4×C53C2×D412yes—
194C2×D4×C53C2×D411yescharacteristic
195C2×D4×C53C2×D411yescharacteristic
196C2×D4×C53C2×D411yescharacteristic
197C22×C4×C53—22no—
198C22×C4×C53—22no—
199C22×C4×C53—22no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—41no—
204C22×C4×C53—41no—
205C22×C4×C53—41no—
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D411yescharacteristic
209Q16×C53—44no—
210Q16×C53—42no—
211SD16×C53—44no—
212SD16×C53—42no—
213SD16×C53—44no—
214SD16×C53—42no—
215D8×C53—44no—
216D8×C53—42no—
217M16×C53—22no—
218M16×C53—22no—
219M16×C53—22no—
220M16×C53—41no—
221M16×C53—41no—
222M16×C53—41no—
223C2×C8×C53—41no—
224C2×C8×C53—41no—
225C2×C8×C53—41no—
226C4⋊C4×C53—22no—
227C4⋊C4×C53—22no—
228C4⋊C4×C53—22no—
229C4⋊C4×C53—22no—
230C4⋊C4×C53—22no—
231C4⋊C4×C53—21no—
232C4⋊C4×C53—21no—
233C4⋊C4×C53—22no—
234C4⋊C4×C53—22no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53—21no—
237C22⋊C4×C53—22no—
238C22⋊C4×C53—22no—
239C22⋊C4×C53—22no—
240C22⋊C4×C53—22no—
241C22⋊C4×C53—22no—
242C22⋊C4×C53—21no—
243C22⋊C4×C53—22no—
244C22⋊C4×C53—21no—
245C22⋊C4×C53—21no—
246C22⋊C4×C53—21no—
247C22⋊C4×C53—22no—
248C22⋊C4×C53—21no—
249C22⋊C4×C53—22no—
250C22⋊C4×C53—21no—
251C22⋊C4×C53—22no—
252C42×C53—22no—
253C42×C53—21no—
254C42×C53C2×D411yescharacteristic
255C42×C53C2×D411yescharacteristic
256C42×C53C2×D412yes—
257C42×C53C2×D412yes—
258C23×C53—21no—
259C23×C53—22no—
260C23×C53—41no—
261C23×C53—41no—
262C23×C53—41no—
263C23×C53—81no—
264C23×C53—82no—
265C23×C53#12011yescharacteristic
266C23×C53#12011yescharacteristic
267C23×C53#12011yescharacteristic
268Q8×C53—22no—
269Q8×C53—22no—
270Q8×C53—22no—
271Q8×C53—41no—
272Q8×C53—42no—
273Q8×C53—41no—
274Q8×C53—41no—
275Q8×C53—41no—
276Q8×C53—41no—
277D4×C53—22no—
278D4×C53—22no—
279D4×C53—22no—
280D4×C53—41no—
281D4×C53—41no—
282D4×C53—41no—
283D4×C53—42no—
284D4×C53—41no—
285D4×C53—42no—
286D4×C53—42no—
287D4×C53—42no—
288D4×C53—42no—
289D4×C53—41no—
290D4×C53—41no—
291D4×C53—41no—
292D4×C53—81no—
293D4×C53—82no—
294D4×C53—82no—
295D4×C53—82no—
296D4×C53—81no—
297D4×C53—81no—
298D4×C53—82no—
299C2×C4×C53—21no—
300C2×C4×C53—21no—
301C2×C4×C53—21no—
302C2×C4×C53—21no—
303C2×C4×C53—21no—
304C2×C4×C53—21no—
305C2×C4×C53—21no—
306C2×C4×C53—21no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—21no—
311C2×C4×C53—42no—
312C2×C4×C53—42no—
313C2×C4×C53—42no—
314C2×C4×C53—41no—
315C2×C4×C53—41no—
316C2×C4×C53—41no—
317C2×C4×C53—41no—
318C2×C4×C53—41no—
319C2×C4×C53—42no—
320C2×C4×C53—81no—
321C2×C4×C53—82no—
322C2×C4×C53—81no—
323C2×C4×C53—82no—
324C2×C4×C53—82no—
325C2×C4×C53#12011yescharacteristic
326C2×C4×C53C22×D411yescharacteristic
327C2×C4×C53C22×D411yescharacteristic
328C2×C4×C53C22×D411yescharacteristic
329C8×C53—42no—
330C8×C53—42no—
331C8×C53—42no—
332#33572C5311yesmaximal, characteristic, direct product factor, Sylow
333C22×C53—21no—
334C22×C53—21no—
335C22×C53—21no—
336C22×C53—41no—
337C22×C53—41no—
338C22×C53—41no—
339C22×C53—41no—
340C22×C53—42no—
341C22×C53—41no—
342C22×C53—42no—
343C22×C53—42no—
344C22×C53—41no—
345C22×C53—42no—
346C22×C53—161no—
347C22×C53—161no—
348C22×C53—161no—
349C22×C53—162no—
350C22×C53C2×#12011yescharacteristic
351C4×C53—21no—
352C4×C53—21no—
353C4×C53—21no—
354C4×C53—41no—
355C4×C53—42no—
356C4×C53—42no—
357C4×C53—41no—
358C4×C53—41no—
359C4×C53—42no—
360C4×C53—42no—
361C4×C53B(4,𝔽2)11yescharacteristic
362C4×C53B(4,𝔽2)11yescharacteristic
363#3551C2×C5311yescharacteristic, complemented
364#3022C2×C5311yescharacteristic, complemented
365#3021C2×C5311yescharacteristic, complemented
366#3018C2×C5311yescharacteristic, complemented
367#2204C2×C5314yescomplemented
368#2203C2×C5314yescomplemented
369#2135C2×C5311yescharacteristic, complemented
370#2134C2×C5311yescharacteristic, complemented
371#2132C2×C5311yescharacteristic, complemented
372C2×C53—21no—
373C2×C53—41no—
374C2×C53—41no—
375C2×C53—41no—
376C2×C53—81no—
377C2×C53—82no—
378C2×C53—82no—
379C2×C53C2×B(4,𝔽2)11yescharacteristic
380#585C22×C5311yescharacteristic
381#575—21no—
382C2×#137—21no—
383C2×AGL(1,ℤ/8)—21no—
384#563C22×C5312yescomplemented
385#560—21no—
386#555C22×C5312yescomplemented
387#553—21no—
388#552—21no—
389#551—21no—
390#548—21no—
391#546—21no—
392#540—22no—
393#538—22no—
394#537—21no—
395#536C22×C5311yescharacteristic
396#535C22×C5311yescharacteristic
397#532C22×C5311yescharacteristic
398#529—21no—
399#456C22×C5312yescomplemented
400#456C22×C5314yescomplemented
401#455—21no—
402#455—22no—
403#454C22×C5314yes—
404#454C22×C5312yescomplemented
405#453—21no—
406#453—22no—
407#421—21no—
408#421—21no—
409C2×#104—21no—
410#413C22×C5311yescharacteristic
411#413C22×C5311yescharacteristic
412#413C22×C5311yescharacteristic
413#356C22×C5312yescomplemented
414#356C22×C5314yescomplemented
415#355C22×C5312yescomplemented
416#355C22×C5314yescomplemented
417C53#3357211yescharacteristic, direct product factor, Sylow
4182−1+4—41no—
4192−1+4C23×C5312yes—
420H(5,𝔽2)—21no—
421H(5,𝔽2)—21no—
422H(5,𝔽2)—21no—
423H(5,𝔽2)—41no—
424C2×#41—21no—
425C2×#41—21no—
426C2×#41—21no—
427C2×#41—21no—
428C2×#41—42no—
429C2×#41D4×C5311yescharacteristic
430C2×#41C23×C5311yescharacteristic
431C22×Q8D4×C5311yescharacteristic
432C22×D4D4×C5311yescharacteristic
433#137—24no—
434#137—22no—
435#137—41no—
436#137—42no—
437AGL(1,ℤ/8)—24no—
438AGL(1,ℤ/8)—22no—
439AGL(1,ℤ/8)—41no—
440AGL(1,ℤ/8)—42no—
441#135—42no—
442C2×Q16—41no—
443C2×SD16—41no—
444C2×SD16—41no—
445C2×D8—41no—
446C2×M16—21no—
447C2×M16—21no—
448C2×M16—21no—
449C4⋊Q8C23×C5311yescharacteristic
450C4⋊Q8C23×C5312yes—
451#127D4×C5311yescharacteristic
452#127D4×C5312yes—
453#126—22no—
454#126—22no—
455#126—22no—
456#125—21no—
457#125—22no—
458#124—21no—
459#124—22no—
460#124D4×C5311yescharacteristic
461#124D4×C5312yes—
462#124C23×C5311yescharacteristic
463#124C23×C5312yes—
464#123—22no—
465#123—22no—
466#123—22no—
467#123—21no—
468#123—21no—
469#123—22no—
470C22⋊Q8—21no—
471C22⋊Q8—22no—
472C22⋊Q8—22no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475#121—22no—
476#121—22no—
477#121—21no—
478#121—22no—
479#121—22no—
480#121—21no—
481#121—21no—
482#121—22no—
483#121—22no—
484#121—21no—
485#121—21no—
486#120—22no—
487#120—21no—
488#120—21no—
489C4×Q8—21no—
490C4×D4—22no—
491C4×D4—21no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—22no—
496#117—22no—
497#117—22no—
498#117D4×C5311yescharacteristic
499#117D4×C5311yescharacteristic
500C2×C4⋊C4—21no—
501C2×C22⋊C4—22no—
502C2×C42D4×C5311yescharacteristic
503#104—22no—
504#104—22no—
505#104—24no—
506#104—24no—
507#101C23×C5312yes—
508#101C23×C5312yes—
509#101C23×C5312yes—
510#100—21no—
511#100—21no—
512#100—21no—
513C24—21no—
514#41—22no—
515#41—22no—
516#41—22no—
517#41—22no—
518#41—22no—
519#41—22no—
520#41—41no—
521#41—41no—
522#41—41no—
523#41—41no—
524#41—41no—
525#41—41no—
526#41—41no—
527#41—42no—
528#41—42no—
529#41—42no—
530#41—42no—
531#41—41no—
532#41—81no—
533#41—81no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—41no—
539C2×Q8—41no—
540C2×Q8—42no—
541C2×Q8C2×D4×C5311yescharacteristic
542C2×Q8C2×D4×C5312yes—
543C2×Q8C24×C5311yescharacteristic
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4C2×D4×C5311yescharacteristic
564C2×D4C2×D4×C5312yes—
565C2×D4C2×D4×C5311yescharacteristic
566C2×D4C2×D4×C5311yescharacteristic
567C2×D4C2×D4×C5311yescharacteristic
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4C2×D4×C5311yescharacteristic
578C22×C4C2×D4×C5311yescharacteristic
579C22×C4C2×D4×C5311yescharacteristic
580Q16—44no—
581Q16—42no—
582SD16—44no—
583SD16—42no—
584SD16—44no—
585SD16—42no—
586D8—44no—
587D8—42no—
588M16—22no—
589M16—22no—
590M16—22no—
591M16—41no—
592M16—41no—
593M16—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—22no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—22no—
623C42—22no—
624C42—21no—
625C42C2×D4×C5311yescharacteristic
626C42C2×D4×C5311yescharacteristic
627C42C2×D4×C5312yes—
628C42C2×D4×C5312yes—
629C23—22no—
630C23—21no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—81no—
635C23—82no—
636C23#120×C5311yescharacteristic
637C23#120×C5311yescharacteristic
638C23#120×C5311yescharacteristic
639Q8—22no—
640Q8—22no—
641Q8—22no—
642Q8—41no—
643Q8—42no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648D4—22no—
649D4—22no—
650D4—22no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—42no—
655D4—41no—
656D4—42no—
657D4—42no—
658D4—42no—
659D4—42no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—81no—
664D4—82no—
665D4—82no—
666D4—82no—
667D4—81no—
668D4—81no—
669D4—82no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—81no—
692C2×C4—82no—
693C2×C4—81no—
694C2×C4—82no—
695C2×C4—82no—
696C2×C4#120×C5311yescharacteristic
697C2×C4C22×D4×C5311yescharacteristic
698C2×C4C22×D4×C5311yescharacteristic
699C2×C4C22×D4×C5311yescharacteristic
700C8—42no—
701C8—42no—
702C8—42no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—42no—
711C22—41no—
712C22—42no—
713C22—42no—
714C22—41no—
715C22—42no—
716C22—161no—
717C22—161no—
718C22—161no—
719C22—162no—
720C22C2×#120×C5311yescharacteristic
721C4—21no—
722C4—21no—
723C4—21no—
724C4—41no—
725C4—42no—
726C4—42no—
727C4—41no—
728C4—41no—
729C4—42no—
730C4—42no—
731C4C53×B(4,𝔽2)11yescharacteristic
732C4C53×B(4,𝔽2)11yescharacteristic
733C2—21no—
734C2—41no—
735C2—41no—
736C2—41no—
737C2—82no—
738C2—81no—
739C2—82no—
740C2C2×C53×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C53C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×Q8C24×C53
LCSG ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C53 ◁ C2×C4×C53 ◁ C2×#41×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C53×#3551C2semidirect
2. C53×#3022C2semidirect
3. C53×#3021C2semidirect
4. C53×#3018C2semidirect
5. C53×#2204C2semidirect
6. C53×#2203C2semidirect
7. C53×#2135C2semidirect
8. C53×#2134C2semidirect
9. C53×#2132C2semidirect
14. C53×#563C22semidirect
16. C53×#555C22semidirect
29. C53×#456C22semidirect
30. C53×#456C22semidirect
34. C53×#454C22semidirect
43. C53×#356C22semidirect
44. C53×#356C22semidirect
45. C53×#355C22semidirect
46. C53×#355C22semidirect
332. #33572C53direct (N × H)
363. #3551C2×C53semidirect
364. #3022C2×C53semidirect
365. #3021C2×C53semidirect
366. #3018C2×C53semidirect
367. #2204C2×C53semidirect
368. #2203C2×C53semidirect
369. #2135C2×C53semidirect
370. #2134C2×C53semidirect
371. #2132C2×C53semidirect
384. #563C22×C53semidirect
386. #555C22×C53semidirect
399. #456C22×C53semidirect
400. #456C22×C53semidirect
404. #454C22×C53semidirect
413. #356C22×C53semidirect
414. #356C22×C53semidirect
415. #355C22×C53semidirect
416. #355C22×C53semidirect
417. C53#33572direct (N × H)

Maximal subgroups

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

subgroupindex
C53×#35512
C53×#30222
C53×#30212
C53×#30182
C53×#22042
C53×#22032
C53×#21352
C53×#21342
C53×#21322
#3357253