Finite Group Databasebeta

← C53×#33560 #27241072

Subgroups — C53×#33560 #27241072

Order 13568.

1132 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3551C211yesmaximal, characteristic, complemented
2C53×#3028C211yesmaximal, characteristic, complemented
3C53×#3027C211yesmaximal, characteristic, complemented
4C53×#3018C211yesmaximal, characteristic, complemented
5C53×#2200C214yesmaximal, complemented
6C53×#2197C214yesmaximal, complemented
7C53×#2126C211yesmaximal, characteristic, complemented
8C53×#2123C211yesmaximal, characteristic, complemented
9C53×#2122C211yesmaximal, characteristic, complemented
10C53×#585C2211yescharacteristic
11C53×#575—21no—
12C53×#563—21no—
13C53×#560C2212yescomplemented
14C53×#555—21no—
15C53×#553—21no—
16C53×#552—21no—
17C53×#551C2212yescomplemented
18C53×#548—21no—
19C53×#546—21no—
20C53×#540—22no—
21C53×#538—22no—
22C53×#537—21no—
23C53×#536—21no—
24C53×#536C2211yescharacteristic
25C53×#535—21no—
26C53×#535C2211yescharacteristic
27C53×#532C2211yescharacteristic
28C53×#529—21no—
29C53×#458—22no—
30C53×#458C2214yes—
31C53×B(4,𝔽2)—22no—
32C53×B(4,𝔽2)C2214yes—
33C53×#456—21no—
34C53×#455C2212yes—
35C53×#454—21no—
36C53×#453C2212yes—
37C2×#104×C53—21no—
38C53×#413C2211yescharacteristic
39C53×#410—21no—
40C53×#410—21no—
41C53×#410C2211yescharacteristic
42C53×#410C2211yescharacteristic
43C53×#354C2212yescomplemented
44C53×#353C2212yescomplemented
45C53×#352C2214yescomplemented
46C53×AΣL(1,𝔽16)C2214yescomplemented
472−1+4×C53—21no—
482−1+4×C53—41no—
49H(5,𝔽2)×C53—21no—
50H(5,𝔽2)×C53—21no—
51H(5,𝔽2)×C53—41no—
52H(5,𝔽2)×C53C2312yes—
53C2×#41×C53—21no—
54C2×#41×C53—21no—
55C2×#41×C53—21no—
56C2×#41×C53—21no—
57C2×#41×C53—42no—
58C2×#41×C53D411yescharacteristic, complemented
59C2×#41×C53C2311yescharacteristic
60C22×Q8×C53D411yescharacteristic, complemented
61C22×D4×C53D411yescharacteristic
62#137×C53—22no—
63#137×C53—41no—
64AGL(1,ℤ/8)×C53—22no—
65AGL(1,ℤ/8)×C53—41no—
66#135×C53—42no—
67C2×M16×C53—21no—
68C4⋊Q8×C53—21no—
69C4⋊Q8×C53—41no—
70C4⋊Q8×C53D411yescharacteristic, complemented
71#127×C53—21no—
72#127×C53—41no—
73#127×C53C2311yescharacteristic
74#126×C53—22no—
75#126×C53—22no—
76#126×C53—22no—
77#125×C53—21no—
78#125×C53—22no—
79#124×C53—21no—
80#124×C53—22no—
81#124×C53—21no—
82#124×C53—21no—
83#124×C53—41no—
84#124×C53—41no—
85#124×C53D411yescharacteristic, complemented
86#124×C53C2311yescharacteristic
87#123×C53—22no—
88#123×C53—22no—
89#123×C53—22no—
90#123×C53—22no—
91#123×C53—24no—
92#123×C53D412yescomplemented
93#123×C53C2312yes—
94C22⋊Q8×C53—21no—
95C22⋊Q8×C53—22no—
96C22⋊Q8×C53—22no—
97C22⋊Q8×C53—21no—
98C22⋊Q8×C53—21no—
99C22⋊Q8×C53—42no—
100#121×C53—22no—
101#121×C53—22no—
102#121×C53—21no—
103#121×C53—22no—
104#121×C53—22no—
105#121×C53—21no—
106#121×C53—21no—
107#121×C53—22no—
108#121×C53—21no—
109#121×C53—21no—
110#121×C53—22no—
111#121×C53—42no—
112#120×C53—22no—
113#120×C53—24no—
114#120×C53D412yes—
115#120×C53C2312yes—
116C4×Q8×C53—21no—
117C4×D4×C53—22no—
118C4×D4×C53—21no—
119C4×D4×C53—22no—
120C4×D4×C53—21no—
121C4×D4×C53—21no—
122C4×D4×C53—22no—
123#117×C53—22no—
124#117×C53—22no—
125#117×C53—21no—
126#117×C53—21no—
127#117×C53D411yescharacteristic
128#117×C53D411yescharacteristic, complemented
129C2×C4⋊C4×C53—21no—
130C2×C22⋊C4×C53—22no—
131C2×C42×C53D411yescharacteristic, complemented
132#104×C53—22no—
133#104×C53—22no—
134#101×C53—21no—
135#100×C53C2312yes—
136#99×C53—24no—
137#99×C53—24no—
138#99×C53—21no—
139#99×C53—21no—
140#99×C53C2312yes—
141#99×C53C2312yes—
142C24×C53C2×D412yes—
143#41×C53—22no—
144#41×C53—22no—
145#41×C53—41no—
146#41×C53—41no—
147#41×C53—42no—
148#41×C53—41no—
149#41×C53—41no—
150#41×C53—41no—
151#41×C53—41no—
152#41×C53—41no—
153#41×C53—42no—
154#41×C53—42no—
155#41×C53—41no—
156#41×C53—41no—
157#41×C53—42no—
158#41×C53—41no—
159#41×C53—41no—
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—21no—
168C2×Q8×C53—41no—
169C2×Q8×C53—41no—
170C2×Q8×C53—42no—
171C2×Q8×C53C2×D411yescharacteristic
172C2×Q8×C53C2×D411yescharacteristic
173C2×D4×C53—21no—
174C2×D4×C53—21no—
175C2×D4×C53—21no—
176C2×D4×C53—22no—
177C2×D4×C53—22no—
178C2×D4×C53—22no—
179C2×D4×C53—22no—
180C2×D4×C53—22no—
181C2×D4×C53—21no—
182C2×D4×C53—21no—
183C2×D4×C53—22no—
184C2×D4×C53—21no—
185C2×D4×C53—21no—
186C2×D4×C53—21no—
187C2×D4×C53—41no—
188C2×D4×C53—41no—
189C2×D4×C53—42no—
190C2×D4×C53—42no—
191C2×D4×C53—42no—
192C2×D4×C53—41no—
193C2×D4×C53—44no—
194C2×D4×C53C2×D411yescharacteristic
195C2×D4×C53C2×D411yescharacteristic
196C2×D4×C53C2×D411yescharacteristic
197C2×D4×C53C2411yescharacteristic
198C22×C4×C53—22no—
199C22×C4×C53—22no—
200C22×C4×C53—22no—
201C22×C4×C53—22no—
202C22×C4×C53—22no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—41no—
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D411yescharacteristic
209C22×C4×C53C2×D412yes—
210Q16×C53—42no—
211SD16×C53—42no—
212SD16×C53—42no—
213D8×C53—42no—
214M16×C53—22no—
215M16×C53—41no—
216C2×C8×C53—41no—
217C4⋊C4×C53—22no—
218C4⋊C4×C53—22no—
219C4⋊C4×C53—22no—
220C4⋊C4×C53—22no—
221C4⋊C4×C53—22no—
222C4⋊C4×C53—22no—
223C4⋊C4×C53—21no—
224C4⋊C4×C53—21no—
225C4⋊C4×C53—21no—
226C4⋊C4×C53—21no—
227C4⋊C4×C53—22no—
228C4⋊C4×C53—41no—
229C4⋊C4×C53—41no—
230C4⋊C4×C53—44no—
231C22⋊C4×C53—22no—
232C22⋊C4×C53—22no—
233C22⋊C4×C53—22no—
234C22⋊C4×C53—22no—
235C22⋊C4×C53—22no—
236C22⋊C4×C53—22no—
237C22⋊C4×C53—21no—
238C22⋊C4×C53—22no—
239C22⋊C4×C53—21no—
240C22⋊C4×C53—21no—
241C22⋊C4×C53—21no—
242C22⋊C4×C53—22no—
243C22⋊C4×C53—22no—
244C22⋊C4×C53—22no—
245C22⋊C4×C53—22no—
246C22⋊C4×C53—44no—
247C22⋊C4×C53—44no—
248C22⋊C4×C53C2×D412yes—
249C22⋊C4×C53C2×D412yes—
250C42×C53—22no—
251C42×C53—21no—
252C42×C53—21no—
253C42×C53—21no—
254C42×C53—41no—
255C42×C53—41no—
256C42×C53C2×D411yescharacteristic
257C42×C53C2×D411yescharacteristic
258C23×C53—22no—
259C23×C53—22no—
260C23×C53—21no—
261C23×C53—22no—
262C23×C53—41no—
263C23×C53—42no—
264C23×C53—82no—
265C23×C53#12011yescharacteristic
266C23×C53C22×D411yescharacteristic
267C23×C53C22×D411yescharacteristic
268Q8×C53—22no—
269Q8×C53—41no—
270Q8×C53—41no—
271Q8×C53—41no—
272Q8×C53—41no—
273Q8×C53—41no—
274Q8×C53—41no—
275Q8×C53—41no—
276Q8×C53—81no—
277D4×C53—22no—
278D4×C53—41no—
279D4×C53—41no—
280D4×C53—41no—
281D4×C53—41no—
282D4×C53—41no—
283D4×C53—41no—
284D4×C53—42no—
285D4×C53—42no—
286D4×C53—42no—
287D4×C53—42no—
288D4×C53—41no—
289D4×C53—41no—
290D4×C53—41no—
291D4×C53—81no—
292D4×C53—81no—
293D4×C53—82no—
294D4×C53—82no—
295D4×C53—82no—
296D4×C53—81no—
297D4×C53—81no—
298D4×C53—82no—
299D4×C53—164no—
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—22no—
307C2×C4×C53—22no—
308C2×C4×C53—21no—
309C2×C4×C53—21no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—21no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
317C2×C4×C53—41no—
318C2×C4×C53—42no—
319C2×C4×C53—41no—
320C2×C4×C53—41no—
321C2×C4×C53—42no—
322C2×C4×C53—42no—
323C2×C4×C53—42no—
324C2×C4×C53—82no—
325C2×C4×C53—81no—
326C2×C4×C53—82no—
327C2×C4×C53—82no—
328C2×C4×C53#12011yescharacteristic
329C2×C4×C53#12011yescharacteristic
330C2×C4×C53#12011yescharacteristic
331C2×C4×C53C22×D411yescharacteristic
332C8×C53—42no—
333#33560C5311yesmaximal, characteristic, direct product factor, Sylow
334C22×C53—21no—
335C22×C53—21no—
336C22×C53—21no—
337C22×C53—41no—
338C22×C53—41no—
339C22×C53—41no—
340C22×C53—41no—
341C22×C53—42no—
342C22×C53—41no—
343C22×C53—42no—
344C22×C53—42no—
345C22×C53—41no—
346C22×C53—42no—
347C22×C53—82no—
348C22×C53—84no—
349C22×C53—82no—
350C22×C53—161no—
351C22×C53C2×#12011yescharacteristic
352C4×C53—21no—
353C4×C53—21no—
354C4×C53—21no—
355C4×C53—41no—
356C4×C53—42no—
357C4×C53—42no—
358C4×C53—41no—
359C4×C53—42no—
360C4×C53—41no—
361C4×C53—42no—
362C4×C53—82no—
363C4×C53—82no—
364C4×C53B(4,𝔽2)11yescharacteristic
365C4×C53B(4,𝔽2)11yescharacteristic
366#3551C2×C5311yescharacteristic, complemented
367#3028C2×C5311yescharacteristic, complemented
368#3027C2×C5311yescharacteristic, complemented
369#3018C2×C5311yescharacteristic, complemented
370#2200C2×C5314yescomplemented
371#2197C2×C5314yescomplemented
372#2126C2×C5311yescharacteristic, complemented
373#2123C2×C5311yescharacteristic, complemented
374#2122C2×C5311yescharacteristic, complemented
375C2×C53—21no—
376C2×C53—41no—
377C2×C53—41no—
378C2×C53—41no—
379C2×C53—81no—
380C2×C53—82no—
381C2×C53—82no—
382C2×C53C2×B(4,𝔽2)11yescharacteristic
383#585C22×C5311yescharacteristic
384#575—21no—
385#563—21no—
386#560C22×C5312yescomplemented
387#555—21no—
388#553—21no—
389#552—21no—
390#551C22×C5312yescomplemented
391#548—21no—
392#546—21no—
393#540—22no—
394#538—22no—
395#537—21no—
396#536—21no—
397#536C22×C5311yescharacteristic
398#535—21no—
399#535C22×C5311yescharacteristic
400#532C22×C5311yescharacteristic
401#529—21no—
402#458—22no—
403#458C22×C5314yes—
404B(4,𝔽2)—22no—
405B(4,𝔽2)C22×C5314yes—
406#456—21no—
407#455C22×C5312yes—
408#454—21no—
409#453C22×C5312yes—
410C2×#104—21no—
411#413C22×C5311yescharacteristic
412#410—21no—
413#410—21no—
414#410C22×C5311yescharacteristic
415#410C22×C5311yescharacteristic
416#354C22×C5312yescomplemented
417#353C22×C5312yescomplemented
418#352C22×C5314yescomplemented
419AΣL(1,𝔽16)C22×C5314yescomplemented
420C53#3356011yescharacteristic, direct product factor, Sylow
4212−1+4—21no—
4222−1+4—41no—
423H(5,𝔽2)—21no—
424H(5,𝔽2)—21no—
425H(5,𝔽2)—41no—
426H(5,𝔽2)C23×C5312yes—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—42no—
432C2×#41D4×C5311yescharacteristic, complemented
433C2×#41C23×C5311yescharacteristic
434C22×Q8D4×C5311yescharacteristic, complemented
435C22×D4D4×C5311yescharacteristic
436#137—22no—
437#137—41no—
438AGL(1,ℤ/8)—22no—
439AGL(1,ℤ/8)—41no—
440#135—42no—
441C2×M16—21no—
442C4⋊Q8—21no—
443C4⋊Q8—41no—
444C4⋊Q8D4×C5311yescharacteristic, complemented
445#127—21no—
446#127—41no—
447#127C23×C5311yescharacteristic
448#126—22no—
449#126—22no—
450#126—22no—
451#125—21no—
452#125—22no—
453#124—21no—
454#124—22no—
455#124—21no—
456#124—21no—
457#124—41no—
458#124—41no—
459#124D4×C5311yescharacteristic, complemented
460#124C23×C5311yescharacteristic
461#123—22no—
462#123—22no—
463#123—22no—
464#123—22no—
465#123—24no—
466#123D4×C5312yescomplemented
467#123C23×C5312yes—
468C22⋊Q8—21no—
469C22⋊Q8—22no—
470C22⋊Q8—22no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—42no—
474#121—22no—
475#121—22no—
476#121—21no—
477#121—22no—
478#121—21no—
479#121—21no—
480#121—22no—
481#121—21no—
482#121—21no—
483#121—22no—
484#121—22no—
485#121—42no—
486#120—22no—
487#120—24no—
488#120D4×C5312yes—
489#120C23×C5312yes—
490C4×Q8—21no—
491C4×D4—22no—
492C4×D4—21no—
493C4×D4—22no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—22no—
497#117—22no—
498#117—22no—
499#117—21no—
500#117—21no—
501#117D4×C5311yescharacteristic
502#117D4×C5311yescharacteristic, complemented
503C2×C4⋊C4—21no—
504C2×C22⋊C4—22no—
505C2×C42D4×C5311yescharacteristic, complemented
506#104—22no—
507#104—22no—
508#101—21no—
509#100C23×C5312yes—
510#99—21no—
511#99—21no—
512#99—24no—
513#99—24no—
514#99C23×C5312yes—
515#99C23×C5312yes—
516C24C2×D4×C5312yes—
517#41—22no—
518#41—22no—
519#41—41no—
520#41—41no—
521#41—42no—
522#41—41no—
523#41—41no—
524#41—41no—
525#41—41no—
526#41—41no—
527#41—42no—
528#41—42no—
529#41—41no—
530#41—41no—
531#41—42no—
532#41—41no—
533#41—41no—
534#41—41no—
535#41—81no—
536#41—81no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—41no—
543C2×Q8—41no—
544C2×Q8—42no—
545C2×Q8C2×D4×C5311yescharacteristic
546C2×Q8C2×D4×C5311yescharacteristic
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—41no—
567C2×D4—44no—
568C2×D4C2×D4×C5311yescharacteristic
569C2×D4C2×D4×C5311yescharacteristic
570C2×D4C2×D4×C5311yescharacteristic
571C2×D4C24×C5311yescharacteristic
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—41no—
580C22×C4C2×D4×C5311yescharacteristic
581C22×C4C2×D4×C5311yescharacteristic
582C22×C4C2×D4×C5311yescharacteristic
583C22×C4C2×D4×C5312yes—
584Q16—42no—
585SD16—42no—
586SD16—42no—
587D8—42no—
588M16—22no—
589M16—41no—
590C2×C8—41no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—22no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—22no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—44no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—21no—
612C22⋊C4—22no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4C2×D4×C5312yes—
623C22⋊C4C2×D4×C5312yes—
624C42—22no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—41no—
629C42—41no—
630C42C2×D4×C5311yescharacteristic
631C42C2×D4×C5311yescharacteristic
632C23—22no—
633C23—22no—
634C23—22no—
635C23—21no—
636C23—41no—
637C23—42no—
638C23—82no—
639C23#120×C5311yescharacteristic
640C23C22×D4×C5311yescharacteristic
641C23C22×D4×C5311yescharacteristic
642Q8—22no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—81no—
651D4—22no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—42no—
659D4—42no—
660D4—42no—
661D4—42no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—81no—
666D4—81no—
667D4—82no—
668D4—82no—
669D4—82no—
670D4—81no—
671D4—81no—
672D4—82no—
673D4—164no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—82no—
699C2×C4—81no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4#120×C5311yescharacteristic
703C2×C4#120×C5311yescharacteristic
704C2×C4#120×C5311yescharacteristic
705C2×C4C22×D4×C5311yescharacteristic
706C8—42no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—42no—
715C22—41no—
716C22—42no—
717C22—42no—
718C22—41no—
719C22—42no—
720C22—82no—
721C22—84no—
722C22—82no—
723C22—161no—
724C22C2×#120×C5311yescharacteristic
725C4—21no—
726C4—21no—
727C4—21no—
728C4—41no—
729C4—42no—
730C4—42no—
731C4—41no—
732C4—42no—
733C4—41no—
734C4—42no—
735C4—82no—
736C4—82no—
737C4C53×B(4,𝔽2)11yescharacteristic
738C4C53×B(4,𝔽2)11yescharacteristic
739C2—21no—
740C2—41no—
741C2—41no—
742C2—41no—
743C2—82no—
744C2—81no—
745C2—82no—
746C2C2×C53×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C53C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C53
LCSG ▷ C2×D4 ▷ 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×#3028C2semidirect
3. C53×#3027C2semidirect
4. C53×#3018C2semidirect
5. C53×#2200C2semidirect
6. C53×#2197C2semidirect
7. C53×#2126C2semidirect
8. C53×#2123C2semidirect
9. C53×#2122C2semidirect
13. C53×#560C22semidirect
17. C53×#551C22semidirect
43. C53×#354C22semidirect
44. C53×#353C22semidirect
45. C53×#352C22semidirect
46. C53×AΣL(1,𝔽16)C22semidirect
58. C2×#41×C53D4semidirect
60. C22×Q8×C53D4semidirect
70. C4⋊Q8×C53D4semidirect
85. #124×C53D4semidirect
92. #123×C53D4semidirect
128. #117×C53D4semidirect
131. C2×C42×C53D4semidirect
333. #33560C53direct (N × H)
366. #3551C2×C53semidirect
367. #3028C2×C53semidirect
368. #3027C2×C53semidirect
369. #3018C2×C53semidirect
370. #2200C2×C53semidirect
371. #2197C2×C53semidirect
372. #2126C2×C53semidirect
373. #2123C2×C53semidirect
374. #2122C2×C53semidirect
386. #560C22×C53semidirect
390. #551C22×C53semidirect
416. #354C22×C53semidirect
417. #353C22×C53semidirect
418. #352C22×C53semidirect
419. AΣL(1,𝔽16)C22×C53semidirect
420. C53#33560direct (N × H)
432. C2×#41D4×C53semidirect
434. C22×Q8D4×C53semidirect
444. C4⋊Q8D4×C53semidirect
459. #124D4×C53semidirect
466. #123D4×C53semidirect
502. #117D4×C53semidirect
505. C2×C42D4×C53semidirect

Maximal subgroups

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

subgroupindex
C53×#35512
C53×#30282
C53×#30272
C53×#30182
C53×#22002
C53×#21972
C53×#21262
C53×#21232
C53×#21222
#3356053