Finite Group Databasebeta

← C2×C53×#2200 #27241060

Subgroups — C2×C53×#2200 #27241060

Order 13568.

1328 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
1C2×C53×#560C211yesmaximal, characteristic, complemented
2C2×C53×#458C211yesmaximal, characteristic, complemented
3C2×C53×B(4,𝔽2)C211yesmaximal, characteristic, complemented
4C2×C53×#453C211yesmaximal, characteristic, complemented
5C53×#2200C218yesmaximal, direct product factor
6C2×C53×#353C211yesmaximal, characteristic, complemented
7C2×C53×#352C211yesmaximal, characteristic, complemented
8C2×C53×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C53C2211yescharacteristic
10C2×AGL(1,ℤ/8)×C53—21no—
11C53×#560—22no—
12C53×#560—22no—
13C53×#560—22no—
14C53×#560C2214yescomplemented
15C2×#127×C53C2211yescharacteristic
16C2×#126×C53—21no—
17C2×#123×C53—21no—
18C2×#123×C53—21no—
19C2×#123×C53C2211yescharacteristic
20C2×#121×C53—21no—
21C2×#121×C53—21no—
22C2×#121×C53—21no—
23C2×#120×C53—21no—
24C2×#120×C53—21no—
25C2×#120×C53C2211yescharacteristic
26C53×#458—22no—
27C53×#458C2214yescomplemented
28C53×B(4,𝔽2)—22no—
29C53×B(4,𝔽2)C2214yescomplemented
30C53×#453—22no—
31C53×#453C2214yescomplemented
32C2×#104×C53—21no—
33C2×#100×C53C2211yescharacteristic
34C2×#99×C53—21no—
35C2×#99×C53—21no—
36C2×#99×C53C2211yescharacteristic
37C2×#99×C53C2211yescharacteristic
38C53×#353C2214yescomplemented
39C53×#352C2214yescomplemented
40C53×AΣL(1,𝔽16)C2214yescomplemented
41C25×C53D411yescharacteristic
42H(5,𝔽2)×C53—21no—
43H(5,𝔽2)×C53—21no—
44H(5,𝔽2)×C53—21no—
45H(5,𝔽2)×C53—42no—
46H(5,𝔽2)×C53C2312yes—
47C2×#41×C53—21no—
48C2×#41×C53—41no—
49C22×D4×C53—21no—
50C22×D4×C53—21no—
51C22×D4×C53—21no—
52C22×D4×C53—21no—
53C22×D4×C53—21no—
54C22×D4×C53—21no—
55C22×D4×C53—21no—
56C22×D4×C53—41no—
57C22×D4×C53—41no—
58C22×D4×C53D411yescharacteristic, complemented
59C22×D4×C53C2311yescharacteristic
60C23×C4×C53—21no—
61C23×C4×C53D411yescharacteristic, complemented
62AGL(1,ℤ/8)×C53—24no—
63AGL(1,ℤ/8)×C53—42no—
64C2×SD16×C53—41no—
65C2×D8×C53—41no—
66C2×M16×C53—21no—
67#127×C53—21no—
68#127×C53—21no—
69#127×C53D412yescomplemented
70#127×C53C2312yes—
71#126×C53—24no—
72#126×C53—24no—
73#123×C53—24no—
74#123×C53—24no—
75#123×C53—21no—
76#123×C53—21no—
77#123×C53—24no—
78#123×C53—42no—
79#123×C53D412yescomplemented
80#123×C53C2312yes—
81#121×C53—24no—
82#121×C53—24no—
83#121×C53—24no—
84#121×C53—24no—
85#121×C53—24no—
86#121×C53—24no—
87#120×C53—24no—
88#120×C53—24no—
89#120×C53—21no—
90#120×C53—21no—
91#120×C53—24no—
92#120×C53—42no—
93#120×C53D412yes—
94#120×C53C2312yes—
95C2×C4⋊C4×C53—21no—
96C2×C4⋊C4×C53—21no—
97C2×C4⋊C4×C53—21no—
98C2×C4⋊C4×C53—41no—
99C2×C22⋊C4×C53—21no—
100C2×C22⋊C4×C53—21no—
101C2×C22⋊C4×C53—21no—
102C2×C22⋊C4×C53—21no—
103C2×C22⋊C4×C53—21no—
104C2×C22⋊C4×C53—21no—
105C2×C22⋊C4×C53—21no—
106C2×C22⋊C4×C53—41no—
107C2×C22⋊C4×C53—41no—
108C2×C22⋊C4×C53D411yescharacteristic
109C2×C22⋊C4×C53D411yescharacteristic, complemented
110C2×C42×C53D411yescharacteristic, complemented
111#104×C53—24no—
112#100×C53—21no—
113#100×C53C2312yes—
114#99×C53—24no—
115#99×C53—24no—
116#99×C53—21no—
117#99×C53—21no—
118#99×C53C2312yes—
119#99×C53C2312yes—
120C24×C53—21no—
121C24×C53—21no—
122C24×C53—21no—
123C24×C53—21no—
124C24×C53—21no—
125C24×C53—41no—
126C24×C53—41no—
127C24×C53—82no—
128C24×C53C2×D411yescharacteristic
129C24×C53C2×D411yescharacteristic
130C24×C53C2×D412yes—
131#41×C53—22no—
132#41×C53—22no—
133#41×C53—42no—
134#41×C53—41no—
135#41×C53—42no—
136#41×C53—42no—
137#41×C53—42no—
138#41×C53—41no—
139C2×Q8×C53—21no—
140C2×D4×C53—21no—
141C2×D4×C53—22no—
142C2×D4×C53—22no—
143C2×D4×C53—22no—
144C2×D4×C53—22no—
145C2×D4×C53—24no—
146C2×D4×C53—24no—
147C2×D4×C53—22no—
148C2×D4×C53—22no—
149C2×D4×C53—22no—
150C2×D4×C53—22no—
151C2×D4×C53—22no—
152C2×D4×C53—22no—
153C2×D4×C53—21no—
154C2×D4×C53—41no—
155C2×D4×C53—41no—
156C2×D4×C53—41no—
157C2×D4×C53—41no—
158C2×D4×C53—42no—
159C2×D4×C53—42no—
160C2×D4×C53—41no—
161C2×D4×C53—41no—
162C2×D4×C53—41no—
163C2×D4×C53—41no—
164C2×D4×C53—42no—
165C2×D4×C53—42no—
166C2×D4×C53—41no—
167C2×D4×C53—41no—
168C2×D4×C53—41no—
169C2×D4×C53—44no—
170C2×D4×C53—82no—
171C2×D4×C53—82no—
172C2×D4×C53—82no—
173C2×D4×C53—82no—
174C2×D4×C53—81no—
175C2×D4×C53—81no—
176C2×D4×C53—84no—
177C2×D4×C53C2×D411yescharacteristic
178C2×D4×C53C2×D411yescharacteristic
179C2×D4×C53C2×D411yescharacteristic
180C2×D4×C53C2×D412yescomplemented
181C2×D4×C53C2411yescharacteristic
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—24no—
189C22×C4×C53—21no—
190C22×C4×C53—41no—
191C22×C4×C53—41no—
192C22×C4×C53—41no—
193C22×C4×C53—41no—
194C22×C4×C53—41no—
195C22×C4×C53—82no—
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D412yescomplemented
198SD16×C53—44no—
199D8×C53—44no—
200M16×C53—22no—
201M16×C53—41no—
202C2×C8×C53—41no—
203C4⋊C4×C53—24no—
204C4⋊C4×C53—24no—
205C4⋊C4×C53—22no—
206C4⋊C4×C53—22no—
207C4⋊C4×C53—44no—
208C22⋊C4×C53—24no—
209C22⋊C4×C53—24no—
210C22⋊C4×C53—24no—
211C22⋊C4×C53—22no—
212C22⋊C4×C53—21no—
213C22⋊C4×C53—21no—
214C22⋊C4×C53—22no—
215C22⋊C4×C53—22no—
216C22⋊C4×C53—22no—
217C22⋊C4×C53—22no—
218C22⋊C4×C53—22no—
219C22⋊C4×C53—44no—
220C22⋊C4×C53—41no—
221C22⋊C4×C53—41no—
222C22⋊C4×C53—44no—
223C22⋊C4×C53C2×D412yes—
224C22⋊C4×C53C2×D412yescomplemented
225C42×C53—21no—
226C42×C53C2×D412yescomplemented
227C23×C53—21no—
228C23×C53—21no—
229C23×C53—21no—
230C23×C53—21no—
231C23×C53—22no—
232C23×C53—22no—
233C23×C53—22no—
234C23×C53—22no—
235C23×C53—42no—
236C23×C53—42no—
237C23×C53—42no—
238C23×C53—42no—
239C23×C53—42no—
240C23×C53—42no—
241C23×C53—42no—
242C23×C53—41no—
243C23×C53—41no—
244C23×C53—44no—
245C23×C53—41no—
246C23×C53—41no—
247C23×C53—41no—
248C23×C53—41no—
249C23×C53—41no—
250C23×C53—81no—
251C23×C53—82no—
252C23×C53—82no—
253C23×C53—82no—
254C23×C53—84no—
255C23×C53—82no—
256C23×C53—82no—
257C23×C53#12011yescharacteristic
258C23×C53#12011yescharacteristic
259C23×C53#12011yescharacteristic
260C23×C53C22×D411yescharacteristic
261C23×C53C22×D411yescharacteristic
262Q8×C53—22no—
263Q8×C53—41no—
264D4×C53—22no—
265D4×C53—41no—
266D4×C53—41no—
267D4×C53—41no—
268D4×C53—41no—
269D4×C53—42no—
270D4×C53—41no—
271D4×C53—42no—
272D4×C53—42no—
273D4×C53—42no—
274D4×C53—42no—
275D4×C53—42no—
276D4×C53—42no—
277D4×C53—81no—
278D4×C53—82no—
279D4×C53—82no—
280D4×C53—84no—
281D4×C53—82no—
282D4×C53—82no—
283D4×C53—82no—
284D4×C53—82no—
285D4×C53—84no—
286D4×C53—88no—
287C2×C4×C53—21no—
288C2×C4×C53—21no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—42no—
296C2×C4×C53—42no—
297C2×C4×C53—42no—
298C2×C4×C53—42no—
299C2×C4×C53—41no—
300C2×C4×C53—41no—
301C2×C4×C53—42no—
302C2×C4×C53—41no—
303C2×C4×C53—41no—
304C2×C4×C53—41no—
305C2×C4×C53—42no—
306C2×C4×C53—42no—
307C2×C4×C53—42no—
308C2×C4×C53—81no—
309C2×C4×C53—84no—
310C2×C4×C53—82no—
311C2×C4×C53—82no—
312C2×C4×C53#12011yescharacteristic
313C2×C4×C53C22×D411yescharacteristic
314C8×C53—42no—
315C2×#2200C5311yesmaximal, characteristic, direct product factor, Sylow
316C22×C53—22no—
317C22×C53—21no—
318C22×C53—21no—
319C22×C53—21no—
320C22×C53—21no—
321C22×C53—41no—
322C22×C53—41no—
323C22×C53—41no—
324C22×C53—41no—
325C22×C53—42no—
326C22×C53—42no—
327C22×C53—42no—
328C22×C53—42no—
329C22×C53—42no—
330C22×C53—42no—
331C22×C53—44no—
332C22×C53—42no—
333C22×C53—42no—
334C22×C53—42no—
335C22×C53—81no—
336C22×C53—81no—
337C22×C53—82no—
338C22×C53—82no—
339C22×C53—82no—
340C22×C53—82no—
341C22×C53—82no—
342C22×C53—84no—
343C22×C53—82no—
344C22×C53—82no—
345C22×C53—82no—
346C22×C53—161no—
347C22×C53—161no—
348C22×C53B(4,𝔽2)11yescharacteristic
349C22×C53B(4,𝔽2)11yescharacteristic
350C22×C53C2×#12011yescharacteristic
351C4×C53—21no—
352C4×C53—21no—
353C4×C53—42no—
354C4×C53—42no—
355C4×C53—42no—
356C4×C53—42no—
357C4×C53—42no—
358C4×C53—82no—
359C4×C53—82no—
360C2×#560C2×C5311yescharacteristic, complemented
361C2×#458C2×C5311yescharacteristic, complemented
362C2×B(4,𝔽2)C2×C5311yescharacteristic, complemented
363C2×#453C2×C5311yescharacteristic, complemented
364#2200C2×C5318yesdirect product factor
365C2×#353C2×C5311yescharacteristic, complemented
366C2×#352C2×C5311yescharacteristic, complemented
367C2×AΣL(1,𝔽16)C2×C5311yescharacteristic, complemented
368C2×C53—21no—
369C2×C53—21no—
370C2×C53—41no—
371C2×C53—41no—
372C2×C53—41no—
373C2×C53—41no—
374C2×C53—82no—
375C2×C53—82no—
376C2×C53—82no—
377C2×C53#220012yesdirect product factor
378C2×C53C2×B(4,𝔽2)11yescharacteristic
379C2×H(5,𝔽2)C22×C5311yescharacteristic
380C2×AGL(1,ℤ/8)—21no—
381#560—22no—
382#560—22no—
383#560—22no—
384#560C22×C5314yescomplemented
385C2×#127C22×C5311yescharacteristic
386C2×#126—21no—
387C2×#123—21no—
388C2×#123—21no—
389C2×#123C22×C5311yescharacteristic
390C2×#121—21no—
391C2×#121—21no—
392C2×#121—21no—
393C2×#120—21no—
394C2×#120—21no—
395C2×#120C22×C5311yescharacteristic
396#458—22no—
397#458C22×C5314yescomplemented
398B(4,𝔽2)—22no—
399B(4,𝔽2)C22×C5314yescomplemented
400#453—22no—
401#453C22×C5314yescomplemented
402C2×#104—21no—
403C2×#100C22×C5311yescharacteristic
404C2×#99—21no—
405C2×#99—21no—
406C2×#99C22×C5311yescharacteristic
407C2×#99C22×C5311yescharacteristic
408#353C22×C5314yescomplemented
409#352C22×C5314yescomplemented
410AΣL(1,𝔽16)C22×C5314yescomplemented
411C53C2×#220011yescharacteristic, direct product factor, Sylow
412C25D4×C5311yescharacteristic
413H(5,𝔽2)—21no—
414H(5,𝔽2)—21no—
415H(5,𝔽2)—21no—
416H(5,𝔽2)—42no—
417H(5,𝔽2)C23×C5312yes—
418C2×#41—21no—
419C2×#41—41no—
420C22×D4—21no—
421C22×D4—21no—
422C22×D4—21no—
423C22×D4—21no—
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—21no—
427C22×D4—41no—
428C22×D4—41no—
429C22×D4D4×C5311yescharacteristic, complemented
430C22×D4C23×C5311yescharacteristic
431C23×C4—21no—
432C23×C4D4×C5311yescharacteristic, complemented
433AGL(1,ℤ/8)—24no—
434AGL(1,ℤ/8)—42no—
435C2×SD16—41no—
436C2×D8—41no—
437C2×M16—21no—
438#127—21no—
439#127—21no—
440#127D4×C5312yescomplemented
441#127C23×C5312yes—
442#126—24no—
443#126—24no—
444#123—24no—
445#123—21no—
446#123—21no—
447#123—24no—
448#123—24no—
449#123—42no—
450#123D4×C5312yescomplemented
451#123C23×C5312yes—
452#121—24no—
453#121—24no—
454#121—24no—
455#121—24no—
456#121—24no—
457#121—24no—
458#120—24no—
459#120—24no—
460#120—21no—
461#120—21no—
462#120—24no—
463#120—42no—
464#120D4×C5312yes—
465#120C23×C5312yes—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—41no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—41no—
478C2×C22⋊C4—41no—
479C2×C22⋊C4D4×C5311yescharacteristic
480C2×C22⋊C4D4×C5311yescharacteristic, complemented
481C2×C42D4×C5311yescharacteristic, complemented
482#104—24no—
483#100—21no—
484#100C23×C5312yes—
485#99—21no—
486#99—21no—
487#99—24no—
488#99—24no—
489#99C23×C5312yes—
490#99C23×C5312yes—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—41no—
497C24—41no—
498C24—82no—
499C24C2×D4×C5311yescharacteristic
500C24C2×D4×C5311yescharacteristic
501C24C2×D4×C5312yes—
502#41—22no—
503#41—22no—
504#41—42no—
505#41—41no—
506#41—42no—
507#41—42no—
508#41—42no—
509#41—41no—
510C2×Q8—21no—
511C2×D4—21no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—21no—
525C2×D4—41no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—41no—
532C2×D4—41no—
533C2×D4—41no—
534C2×D4—41no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—41no—
538C2×D4—41no—
539C2×D4—41no—
540C2×D4—44no—
541C2×D4—82no—
542C2×D4—82no—
543C2×D4—82no—
544C2×D4—82no—
545C2×D4—81no—
546C2×D4—81no—
547C2×D4—84no—
548C2×D4C2×D4×C5311yescharacteristic
549C2×D4C2×D4×C5311yescharacteristic
550C2×D4C2×D4×C5311yescharacteristic
551C2×D4C2×D4×C5312yescomplemented
552C2×D4C24×C5311yescharacteristic
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—24no—
560C22×C4—21no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—82no—
567C22×C4C2×D4×C5311yescharacteristic
568C22×C4C2×D4×C5312yescomplemented
569SD16—44no—
570D8—44no—
571M16—22no—
572M16—41no—
573C2×C8—41no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—44no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C22⋊C4—24no—
582C22⋊C4—22no—
583C22⋊C4—21no—
584C22⋊C4—21no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—44no—
591C22⋊C4—41no—
592C22⋊C4—41no—
593C22⋊C4—44no—
594C22⋊C4C2×D4×C5312yes—
595C22⋊C4C2×D4×C5312yescomplemented
596C42—21no—
597C42C2×D4×C5312yescomplemented
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—41no—
614C23—41no—
615C23—44no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—81no—
622C23—82no—
623C23—82no—
624C23—82no—
625C23—84no—
626C23—82no—
627C23—82no—
628C23#120×C5311yescharacteristic
629C23#120×C5311yescharacteristic
630C23#120×C5311yescharacteristic
631C23C22×D4×C5311yescharacteristic
632C23C22×D4×C5311yescharacteristic
633Q8—22no—
634Q8—41no—
635D4—22no—
636D4—41no—
637D4—41no—
638D4—41no—
639D4—41no—
640D4—42no—
641D4—41no—
642D4—42no—
643D4—42no—
644D4—42no—
645D4—42no—
646D4—42no—
647D4—42no—
648D4—81no—
649D4—82no—
650D4—82no—
651D4—84no—
652D4—82no—
653D4—82no—
654D4—82no—
655D4—82no—
656D4—84no—
657D4—88no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—81no—
680C2×C4—84no—
681C2×C4—82no—
682C2×C4—82no—
683C2×C4#120×C5311yescharacteristic
684C2×C4C22×D4×C5311yescharacteristic
685C8—42no—
686C22—22no—
687C22—21no—
688C22—21no—
689C22—21no—
690C22—21no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—44no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—81no—
706C22—81no—
707C22—82no—
708C22—82no—
709C22—82no—
710C22—82no—
711C22—82no—
712C22—84no—
713C22—82no—
714C22—82no—
715C22—82no—
716C22—161no—
717C22—161no—
718C22C53×B(4,𝔽2)11yescharacteristic
719C22C53×B(4,𝔽2)11yescharacteristic
720C22C2×#120×C5311yescharacteristic
721C4—21no—
722C4—21no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—82no—
729C4—82no—
730C2—21no—
731C2—21no—
732C2—41no—
733C2—41no—
734C2—41no—
735C2—41no—
736C2—82no—
737C2—82no—
738C2—82no—
739C2C53×#220012yesdirect product factor
740C2C2×C53×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C53B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C53
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C53 ◁ C23×C53 ◁ C22×D4×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C53×#560C2semidirect
2. C2×C53×#458C2semidirect
3. C2×C53×B(4,𝔽2)C2semidirect
4. C2×C53×#453C2semidirect
5. C53×#2200C2direct (N × H)
6. C2×C53×#353C2semidirect
7. C2×C53×#352C2semidirect
8. C2×C53×AΣL(1,𝔽16)C2semidirect
14. C53×#560C22semidirect
27. C53×#458C22semidirect
29. C53×B(4,𝔽2)C22semidirect
31. C53×#453C22semidirect
38. C53×#353C22semidirect
39. C53×#352C22semidirect
40. C53×AΣL(1,𝔽16)C22semidirect
58. C22×D4×C53D4semidirect
61. C23×C4×C53D4semidirect
69. #127×C53D4semidirect
79. #123×C53D4semidirect
109. C2×C22⋊C4×C53D4semidirect
110. C2×C42×C53D4semidirect
180. C2×D4×C53C2×D4semidirect
197. C22×C4×C53C2×D4semidirect
224. C22⋊C4×C53C2×D4semidirect
226. C42×C53C2×D4semidirect
315. C2×#2200C53direct (N × H)
360. C2×#560C2×C53semidirect
361. C2×#458C2×C53semidirect
362. C2×B(4,𝔽2)C2×C53semidirect
363. C2×#453C2×C53semidirect
364. #2200C2×C53direct (N × H)
365. C2×#353C2×C53semidirect
366. C2×#352C2×C53semidirect
367. C2×AΣL(1,𝔽16)C2×C53semidirect
377. C2×C53#2200direct (N × H)
384. #560C22×C53semidirect
397. #458C22×C53semidirect
399. B(4,𝔽2)C22×C53semidirect
401. #453C22×C53semidirect
408. #353C22×C53semidirect
409. #352C22×C53semidirect
410. AΣL(1,𝔽16)C22×C53semidirect
411. C53C2×#2200direct (N × H)
429. C22×D4D4×C53semidirect
432. C23×C4D4×C53semidirect
440. #127D4×C53semidirect
450. #123D4×C53semidirect
480. C2×C22⋊C4D4×C53semidirect
481. C2×C42D4×C53semidirect
551. C2×D4C2×D4×C53semidirect
568. C22×C4C2×D4×C53semidirect
595. C22⋊C4C2×D4×C53semidirect
597. C42C2×D4×C53semidirect
739. C2C53×#2200direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C53×#5602
C2×C53×#4582
C2×C53×B(4,𝔽2)2
C2×C53×#4532
C53×#22002
C2×C53×#3532
C2×C53×#3522
C2×C53×AΣL(1,𝔽16)2
C2×#220053