Finite Group Databasebeta

← C53×#33555 #27241067

Subgroups — C53×#33555 #27241067

Order 13568.

1146 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3540C211yesmaximal, characteristic, complemented
2C53×#3027C211yesmaximal, characteristic, complemented
3C53×#3025C211yesmaximal, characteristic, complemented
4C53×#3022C211yesmaximal, characteristic, complemented
5C53×#2199C214yesmaximal, complemented
6C53×#2197C214yesmaximal, complemented
7C53×#2129C211yesmaximal, characteristic, complemented
8C53×#2122C211yesmaximal, characteristic, complemented
9C53×#2120C211yesmaximal, characteristic, complemented
10C53×#585C2211yescharacteristic
11C2×#137×C53—21no—
12C53×H(3,𝔽4)C2212yescomplemented
13C53×#560—21no—
14C53×#559—21no—
15C53×#556—21no—
16C53×#555—21no—
17C53×#551C2212yescomplemented
18C53×#548—21no—
19C53×#546—21no—
20C53×#542—22no—
21C53×#542—21no—
22C53×#538—22no—
23C53×#536C2211yescharacteristic
24C53×#535—21no—
25C53×#535C2211yescharacteristic
26C53×#525—21no—
27C53×#525—21no—
28C53×#525C2211yescharacteristic
29C53×#458—21no—
30C53×#458C2212yes—
31C53×B(4,𝔽2)—21no—
32C53×B(4,𝔽2)—22no—
33C53×B(4,𝔽2)C2214yes—
34C53×B(4,𝔽2)C2212yes—
35C53×#456—22no—
36C53×#455C2214yes—
37C53×#421—21no—
38C53×#413C2211yescharacteristic
39C53×#410—21no—
40C53×#410—21no—
41C53×#410C2211yescharacteristic
42C53×#410C2211yescharacteristic
43C53×#354C2214yescomplemented
44C53×#352C2212yescomplemented
45C53×AΣL(1,𝔽16)C2214yescomplemented
46C53×AΣL(1,𝔽16)C2212yescomplemented
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×C53C2311yescharacteristic
59C22×Q8×C53D411yescharacteristic, complemented
60C22×D4×C53D411yescharacteristic, complemented
61C23×C4×C53D411yescharacteristic, complemented
62#137×C53—24no—
63#137×C53—42no—
64C2×Q16×C53—41no—
65C2×SD16×C53—41no—
66C2×M16×C53—21no—
67C4⋊Q8×C53—21no—
68C4⋊Q8×C53D412yescomplemented
69#127×C53—21no—
70#127×C53—41no—
71#126×C53—22no—
72#126×C53—22no—
73#126×C53—22no—
74#124×C53—22no—
75#124×C53—21no—
76#124×C53—22no—
77#124×C53—22no—
78#124×C53—22no—
79#124×C53—21no—
80#124×C53—22no—
81#124×C53—41no—
82#124×C53C2312yes—
83#123×C53—22no—
84#123×C53—22no—
85#123×C53—22no—
86#123×C53—21no—
87#123×C53—21no—
88#123×C53—22no—
89#123×C53D411yescharacteristic, complemented
90#123×C53C2311yescharacteristic
91C22⋊Q8×C53—21no—
92C22⋊Q8×C53—22no—
93C22⋊Q8×C53—21no—
94C22⋊Q8×C53—22no—
95C22⋊Q8×C53—21no—
96C22⋊Q8×C53—21no—
97C22⋊Q8×C53—41no—
98#121×C53—21no—
99#121×C53—22no—
100#121×C53—22no—
101#121×C53—22no—
102#121×C53—21no—
103#121×C53—21no—
104#121×C53—21no—
105#121×C53—42no—
106#121×C53—41no—
107#120×C53—22no—
108#120×C53—22no—
109#120×C53—22no—
110#120×C53—24no—
111#120×C53D411yescharacteristic, complemented
112#120×C53D412yescomplemented
113#120×C53C2311yescharacteristic
114#120×C53C2312yes—
115C4×Q8×C53—21no—
116C4×Q8×C53—22no—
117C4×D4×C53—22no—
118C4×D4×C53—22no—
119C4×D4×C53—21no—
120C4×D4×C53—22no—
121C4×D4×C53—21no—
122C4×D4×C53—21no—
123C4×D4×C53—42no—
124#117×C53—21no—
125#117×C53—22no—
126#117×C53—21no—
127#117×C53—21no—
128#117×C53D411yescharacteristic, complemented
129#117×C53D411yescharacteristic, complemented
130#117×C53D411yescharacteristic, complemented
131C2×C22⋊C4×C53—22no—
132#104×C53—24no—
133#101×C53—21no—
134#100×C53C2312yes—
135#99×C53—24no—
136#99×C53—22no—
137#99×C53—22no—
138#99×C53—21no—
139#99×C53—21no—
140#99×C53C2312yes—
141#99×C53C2312yes—
142C24×C53C2×D412yes—
143C24×C53C2×D411yescharacteristic
144#41×C53—22no—
145#41×C53—22no—
146#41×C53—41no—
147#41×C53—41no—
148#41×C53—42no—
149#41×C53—41no—
150#41×C53—41no—
151#41×C53—41no—
152#41×C53—41no—
153#41×C53—41no—
154#41×C53—42no—
155#41×C53—42no—
156#41×C53—42no—
157#41×C53—41no—
158#41×C53—41no—
159#41×C53—41no—
160#41×C53—81no—
161#41×C53—81no—
162C2×Q8×C53—21no—
163C2×Q8×C53—21no—
164C2×Q8×C53—22no—
165C2×Q8×C53—21no—
166C2×Q8×C53—21no—
167C2×Q8×C53—41no—
168C2×Q8×C53—41no—
169C2×Q8×C53—42no—
170C2×Q8×C53C2×D412yes—
171C2×Q8×C53C2×D411yescharacteristic
172C2×D4×C53—21no—
173C2×D4×C53—21no—
174C2×D4×C53—21no—
175C2×D4×C53—22no—
176C2×D4×C53—22no—
177C2×D4×C53—22no—
178C2×D4×C53—22no—
179C2×D4×C53—21no—
180C2×D4×C53—22no—
181C2×D4×C53—21no—
182C2×D4×C53—22no—
183C2×D4×C53—21no—
184C2×D4×C53—21no—
185C2×D4×C53—41no—
186C2×D4×C53—41no—
187C2×D4×C53—42no—
188C2×D4×C53—42no—
189C2×D4×C53—42no—
190C2×D4×C53—41no—
191C2×D4×C53—42no—
192C2×D4×C53—44no—
193C2×D4×C53C2×D411yescharacteristic
194C2×D4×C53C2×D411yescharacteristic
195C2×D4×C53C2411yescharacteristic
196C22×C4×C53—22no—
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
209C22×C4×C53C2×D411yescharacteristic
210Q16×C53—44no—
211SD16×C53—44no—
212M16×C53—22no—
213M16×C53—41no—
214C2×C8×C53—41no—
215C4⋊C4×C53—22no—
216C4⋊C4×C53—22no—
217C4⋊C4×C53—22no—
218C4⋊C4×C53—21no—
219C4⋊C4×C53—21no—
220C4⋊C4×C53—22no—
221C4⋊C4×C53—22no—
222C4⋊C4×C53—21no—
223C4⋊C4×C53—21no—
224C4⋊C4×C53—21no—
225C4⋊C4×C53—41no—
226C4⋊C4×C53—41no—
227C4⋊C4×C53—42no—
228C22⋊C4×C53—22no—
229C22⋊C4×C53—22no—
230C22⋊C4×C53—22no—
231C22⋊C4×C53—22no—
232C22⋊C4×C53—22no—
233C22⋊C4×C53—22no—
234C22⋊C4×C53—21no—
235C22⋊C4×C53—21no—
236C22⋊C4×C53—21no—
237C22⋊C4×C53—22no—
238C22⋊C4×C53—22no—
239C22⋊C4×C53—21no—
240C22⋊C4×C53—22no—
241C22⋊C4×C53—22no—
242C22⋊C4×C53—21no—
243C22⋊C4×C53—22no—
244C22⋊C4×C53—22no—
245C22⋊C4×C53—42no—
246C22⋊C4×C53—44no—
247C22⋊C4×C53—42no—
248C22⋊C4×C53C2×D412yes—
249C22⋊C4×C53C2×D411yescharacteristic
250C22⋊C4×C53C2×D411yescharacteristic
251C42×C53—22no—
252C42×C53—22no—
253C42×C53—21no—
254C42×C53—21no—
255C42×C53—41no—
256C42×C53—41no—
257C42×C53C2×D412yes—
258C23×C53—22no—
259C23×C53—22no—
260C23×C53—22no—
261C23×C53—21no—
262C23×C53—41no—
263C23×C53—41no—
264C23×C53—42no—
265C23×C53—81no—
266C23×C53—82no—
267C23×C53#12011yescharacteristic
268C23×C53C22×D411yescharacteristic
269C23×C53C22×D411yescharacteristic
270Q8×C53—22no—
271Q8×C53—41no—
272Q8×C53—41no—
273Q8×C53—41no—
274Q8×C53—42no—
275Q8×C53—41no—
276Q8×C53—41no—
277Q8×C53—41no—
278Q8×C53—82no—
279D4×C53—22no—
280D4×C53—41no—
281D4×C53—41no—
282D4×C53—41no—
283D4×C53—41no—
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—81no—
294D4×C53—82no—
295D4×C53—82no—
296D4×C53—82no—
297D4×C53—81no—
298D4×C53—82no—
299D4×C53—84no—
300D4×C53—164no—
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—21no—
310C2×C4×C53—22no—
311C2×C4×C53—21no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—21no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
317C2×C4×C53—42no—
318C2×C4×C53—41no—
319C2×C4×C53—42no—
320C2×C4×C53—41no—
321C2×C4×C53—41no—
322C2×C4×C53—41no—
323C2×C4×C53—42no—
324C2×C4×C53—42no—
325C2×C4×C53—81no—
326C2×C4×C53—81no—
327C2×C4×C53—82no—
328C2×C4×C53—82no—
329C2×C4×C53#12011yescharacteristic
330C2×C4×C53#12011yescharacteristic
331C2×C4×C53#12011yescharacteristic
332C2×C4×C53C22×D411yescharacteristic
333C8×C53—42no—
334#33555C5311yesmaximal, characteristic, direct product factor, Sylow
335C22×C53—21no—
336C22×C53—21no—
337C22×C53—21no—
338C22×C53—41no—
339C22×C53—41no—
340C22×C53—41no—
341C22×C53—42no—
342C22×C53—41no—
343C22×C53—41no—
344C22×C53—42no—
345C22×C53—42no—
346C22×C53—42no—
347C22×C53—41no—
348C22×C53—42no—
349C22×C53—82no—
350C22×C53—82no—
351C22×C53—84no—
352C22×C53—81no—
353C22×C53—161no—
354C22×C53C2×#12011yescharacteristic
355C4×C53—21no—
356C4×C53—21no—
357C4×C53—21no—
358C4×C53—41no—
359C4×C53—42no—
360C4×C53—42no—
361C4×C53—41no—
362C4×C53—42no—
363C4×C53—41no—
364C4×C53—42no—
365C4×C53—82no—
366C4×C53—82no—
367C4×C53B(4,𝔽2)11yescharacteristic
368C4×C53B(4,𝔽2)11yescharacteristic
369#3540C2×C5311yescharacteristic, complemented
370#3027C2×C5311yescharacteristic, complemented
371#3025C2×C5311yescharacteristic, complemented
372#3022C2×C5311yescharacteristic, complemented
373#2199C2×C5314yescomplemented
374#2197C2×C5314yescomplemented
375#2129C2×C5311yescharacteristic, complemented
376#2122C2×C5311yescharacteristic, complemented
377#2120C2×C5311yescharacteristic, complemented
378C2×C53—21no—
379C2×C53—41no—
380C2×C53—41no—
381C2×C53—41no—
382C2×C53—81no—
383C2×C53—82no—
384C2×C53—82no—
385C2×C53C2×B(4,𝔽2)11yescharacteristic
386#585C22×C5311yescharacteristic
387C2×#137—21no—
388H(3,𝔽4)C22×C5312yescomplemented
389#560—21no—
390#559—21no—
391#556—21no—
392#555—21no—
393#551C22×C5312yescomplemented
394#548—21no—
395#546—21no—
396#542—22no—
397#542—21no—
398#538—22no—
399#536C22×C5311yescharacteristic
400#535—21no—
401#535C22×C5311yescharacteristic
402#525—21no—
403#525—21no—
404#525C22×C5311yescharacteristic
405#458—21no—
406#458C22×C5312yes—
407B(4,𝔽2)—21no—
408B(4,𝔽2)—22no—
409B(4,𝔽2)C22×C5314yes—
410B(4,𝔽2)C22×C5312yes—
411#456—22no—
412#455C22×C5314yes—
413#421—21no—
414#413C22×C5311yescharacteristic
415#410—21no—
416#410—21no—
417#410C22×C5311yescharacteristic
418#410C22×C5311yescharacteristic
419#354C22×C5314yescomplemented
420#352C22×C5312yescomplemented
421AΣL(1,𝔽16)C22×C5312yescomplemented
422AΣL(1,𝔽16)C22×C5314yescomplemented
423C53#3355511yescharacteristic, direct product factor, Sylow
4242−1+4—21no—
4252−1+4—41no—
426H(5,𝔽2)—21no—
427H(5,𝔽2)—21no—
428H(5,𝔽2)—41no—
429H(5,𝔽2)C23×C5312yes—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—42no—
435C2×#41C23×C5311yescharacteristic
436C22×Q8D4×C5311yescharacteristic, complemented
437C22×D4D4×C5311yescharacteristic, complemented
438C23×C4D4×C5311yescharacteristic, complemented
439#137—24no—
440#137—42no—
441C2×Q16—41no—
442C2×SD16—41no—
443C2×M16—21no—
444C4⋊Q8—21no—
445C4⋊Q8D4×C5312yescomplemented
446#127—21no—
447#127—41no—
448#126—22no—
449#126—22no—
450#126—22no—
451#124—22no—
452#124—21no—
453#124—21no—
454#124—22no—
455#124—22no—
456#124—22no—
457#124—22no—
458#124—41no—
459#124C23×C5312yes—
460#123—22no—
461#123—22no—
462#123—21no—
463#123—21no—
464#123—22no—
465#123—22no—
466#123D4×C5311yescharacteristic, complemented
467#123C23×C5311yescharacteristic
468C22⋊Q8—21no—
469C22⋊Q8—22no—
470C22⋊Q8—21no—
471C22⋊Q8—22no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—41no—
475#121—21no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—42no—
483#121—41no—
484#120—22no—
485#120—22no—
486#120—22no—
487#120—24no—
488#120D4×C5311yescharacteristic, complemented
489#120D4×C5312yescomplemented
490#120C23×C5311yescharacteristic
491#120C23×C5312yes—
492C4×Q8—21no—
493C4×Q8—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—21no—
497C4×D4—22no—
498C4×D4—21no—
499C4×D4—21no—
500C4×D4—42no—
501#117—21no—
502#117—22no—
503#117—21no—
504#117—21no—
505#117D4×C5311yescharacteristic, complemented
506#117D4×C5311yescharacteristic, complemented
507#117D4×C5311yescharacteristic, complemented
508C2×C22⋊C4—22no—
509#104—24no—
510#101—21no—
511#100C23×C5312yes—
512#99—21no—
513#99—21no—
514#99—24no—
515#99—22no—
516#99—22no—
517#99C23×C5312yes—
518#99C23×C5312yes—
519C24C2×D4×C5312yes—
520C24C2×D4×C5311yescharacteristic
521#41—22no—
522#41—22no—
523#41—41no—
524#41—41no—
525#41—42no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—41no—
531#41—42no—
532#41—42no—
533#41—42no—
534#41—41no—
535#41—41no—
536#41—41no—
537#41—81no—
538#41—81no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—22no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—42no—
547C2×Q8C2×D4×C5312yes—
548C2×Q8C2×D4×C5311yescharacteristic
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—41no—
568C2×D4—42no—
569C2×D4—44no—
570C2×D4C2×D4×C5311yescharacteristic
571C2×D4C2×D4×C5311yescharacteristic
572C2×D4C24×C5311yescharacteristic
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4C2×D4×C5311yescharacteristic
584C22×C4C2×D4×C5311yescharacteristic
585C22×C4C2×D4×C5311yescharacteristic
586C22×C4C2×D4×C5311yescharacteristic
587Q16—44no—
588SD16—44no—
589M16—22no—
590M16—41no—
591C2×C8—41no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—42no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—21no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—42no—
623C22⋊C4—44no—
624C22⋊C4—42no—
625C22⋊C4C2×D4×C5312yes—
626C22⋊C4C2×D4×C5311yescharacteristic
627C22⋊C4C2×D4×C5311yescharacteristic
628C42—22no—
629C42—22no—
630C42—21no—
631C42—21no—
632C42—41no—
633C42—41no—
634C42C2×D4×C5312yes—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—21no—
639C23—41no—
640C23—41no—
641C23—42no—
642C23—81no—
643C23—82no—
644C23#120×C5311yescharacteristic
645C23C22×D4×C5311yescharacteristic
646C23C22×D4×C5311yescharacteristic
647Q8—22no—
648Q8—41no—
649Q8—42no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653Q8—41no—
654Q8—41no—
655Q8—82no—
656D4—22no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—41no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—81no—
670D4—81no—
671D4—82no—
672D4—82no—
673D4—82no—
674D4—81no—
675D4—82no—
676D4—84no—
677D4—164no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4#120×C5311yescharacteristic
707C2×C4#120×C5311yescharacteristic
708C2×C4#120×C5311yescharacteristic
709C2×C4C22×D4×C5311yescharacteristic
710C8—42no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—42no—
718C22—41no—
719C22—41no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—82no—
726C22—82no—
727C22—84no—
728C22—81no—
729C22—161no—
730C22C2×#120×C5311yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—41no—
735C4—42no—
736C4—42no—
737C4—41no—
738C4—42no—
739C4—41no—
740C4—42no—
741C4—82no—
742C4—82no—
743C4C53×B(4,𝔽2)11yescharacteristic
744C4C53×B(4,𝔽2)11yescharacteristic
745C2—21no—
746C2—41no—
747C2—41no—
748C2—41no—
749C2—81no—
750C2—82no—
751C2—82no—
752C2C2×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×#3540C2semidirect
2. C53×#3027C2semidirect
3. C53×#3025C2semidirect
4. C53×#3022C2semidirect
5. C53×#2199C2semidirect
6. C53×#2197C2semidirect
7. C53×#2129C2semidirect
8. C53×#2122C2semidirect
9. C53×#2120C2semidirect
12. C53×H(3,𝔽4)C22semidirect
17. C53×#551C22semidirect
43. C53×#354C22semidirect
44. C53×#352C22semidirect
45. C53×AΣL(1,𝔽16)C22semidirect
46. C53×AΣL(1,𝔽16)C22semidirect
59. C22×Q8×C53D4semidirect
60. C22×D4×C53D4semidirect
61. C23×C4×C53D4semidirect
68. C4⋊Q8×C53D4semidirect
89. #123×C53D4semidirect
111. #120×C53D4semidirect
112. #120×C53D4semidirect
128. #117×C53D4semidirect
129. #117×C53D4semidirect
130. #117×C53D4semidirect
334. #33555C53direct (N × H)
369. #3540C2×C53semidirect
370. #3027C2×C53semidirect
371. #3025C2×C53semidirect
372. #3022C2×C53semidirect
373. #2199C2×C53semidirect
374. #2197C2×C53semidirect
375. #2129C2×C53semidirect
376. #2122C2×C53semidirect
377. #2120C2×C53semidirect
388. H(3,𝔽4)C22×C53semidirect
393. #551C22×C53semidirect
419. #354C22×C53semidirect
420. #352C22×C53semidirect
421. AΣL(1,𝔽16)C22×C53semidirect
422. AΣL(1,𝔽16)C22×C53semidirect
423. C53#33555direct (N × H)
436. C22×Q8D4×C53semidirect
437. C22×D4D4×C53semidirect
438. C23×C4D4×C53semidirect
445. C4⋊Q8D4×C53semidirect
466. #123D4×C53semidirect
488. #120D4×C53semidirect
489. #120D4×C53semidirect
505. #117D4×C53semidirect
506. #117D4×C53semidirect
507. #117D4×C53semidirect

Maximal subgroups

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

subgroupindex
C53×#35402
C53×#30272
C53×#30252
C53×#30222
C53×#21992
C53×#21972
C53×#21292
C53×#21222
C53×#21202
#3355553