Finite Group Databasebeta

← C53×#33556 #27241068

Subgroups — C53×#33556 #27241068

Order 13568.

1134 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3540C211yesmaximal, characteristic, complemented
2C53×#3028C211yesmaximal, characteristic, complemented
3C53×#3025C211yesmaximal, characteristic, complemented
4C53×#3021C211yesmaximal, characteristic, complemented
5C53×#2200C214yesmaximal, complemented
6C53×#2198C214yesmaximal, complemented
7C53×#2128C211yesmaximal, characteristic, complemented
8C53×#2123C211yesmaximal, characteristic, complemented
9C53×#2120C211yesmaximal, characteristic, complemented
10C53×#585C2211yescharacteristic
11C2×AGL(1,ℤ/8)×C53—21no—
12C53×H(3,𝔽4)—21no—
13C53×#560C2212yescomplemented
14C53×#559C2212yescomplemented
15C53×#556—21no—
16C53×#555—21no—
17C53×#551—21no—
18C53×#548—21no—
19C53×#546—21no—
20C53×#542—22no—
21C53×#542—21no—
22C53×#538—22no—
23C53×#536—21no—
24C53×#536C2211yescharacteristic
25C53×#535C2211yescharacteristic
26C53×#525—21no—
27C53×#525—21no—
28C53×#525C2211yescharacteristic
29C53×#458—21no—
30C53×#458—22no—
31C53×#458C2212yescomplemented
32C53×#458C2214yescomplemented
33C53×B(4,𝔽2)—21no—
34C53×B(4,𝔽2)C2212yescomplemented
35C53×#454—22no—
36C53×#453C2214yes—
37C53×#421—21no—
38C53×#413C2211yescharacteristic
39C53×#410—21no—
40C53×#410—21no—
41C53×#410C2211yescharacteristic
42C53×#410C2211yescharacteristic
43C53×#353C2214yescomplemented
44C53×#352C2212yescomplemented
45C53×#352C2214yescomplemented
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
62AGL(1,ℤ/8)×C53—24no—
63AGL(1,ℤ/8)×C53—42no—
64C2×SD16×C53—41no—
65C2×D8×C53—41no—
66C2×M16×C53—21no—
67C4⋊Q8×C53—21no—
68C4⋊Q8×C53—21no—
69C4⋊Q8×C53—41no—
70#127×C53C2312yes—
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—22no—
80#124×C53—21no—
81#124×C53—41no—
82#124×C53D412yescomplemented
83#123×C53—22no—
84#123×C53—22no—
85#123×C53—22no—
86#123×C53—22no—
87#123×C53—24no—
88#123×C53D411yescharacteristic
89#123×C53D412yescomplemented
90#123×C53C2311yescharacteristic
91#123×C53C2312yes—
92C22⋊Q8×C53—21no—
93C22⋊Q8×C53—22no—
94C22⋊Q8×C53—22no—
95C22⋊Q8×C53—21no—
96C22⋊Q8×C53—21no—
97C22⋊Q8×C53—21no—
98C22⋊Q8×C53—42no—
99C22⋊Q8×C53—41no—
100#121×C53—21no—
101#121×C53—22no—
102#121×C53—21no—
103#121×C53—22no—
104#121×C53—21no—
105#121×C53—21no—
106#121×C53—22no—
107#121×C53—41no—
108#120×C53—22no—
109#120×C53—22no—
110#120×C53—21no—
111#120×C53—21no—
112#120×C53—22no—
113#120×C53D411yescharacteristic
114#120×C53C2311yescharacteristic
115C4×Q8×C53—21no—
116C4×Q8×C53—22no—
117C4×D4×C53—22no—
118C4×D4×C53—21no—
119C4×D4×C53—22no—
120C4×D4×C53—21no—
121C4×D4×C53—21no—
122C4×D4×C53—22no—
123C4×D4×C53—42no—
124#117×C53—21no—
125#117×C53—22no—
126#117×C53—21no—
127#117×C53—21no—
128#117×C53D411yescharacteristic
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—22no—
136#99×C53—22no—
137#99×C53—24no—
138#99×C53—21no—
139#99×C53—21no—
140#99×C53C2312yes—
141#99×C53C2312yes—
142C24×C53—21no—
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—21no—
168C2×Q8×C53—41no—
169C2×Q8×C53—41no—
170C2×Q8×C53—42no—
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—22no—
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—42no—
191C2×D4×C53C2×D411yescharacteristic
192C2×D4×C53C2×D411yescharacteristic
193C2×D4×C53C2×D412yes—
194C2×D4×C53C2411yescharacteristic
195C22×C4×C53—22no—
196C22×C4×C53—22no—
197C22×C4×C53—22no—
198C22×C4×C53—22no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—41no—
202C22×C4×C53—41no—
203C22×C4×C53—41no—
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D412yes—
209SD16×C53—44no—
210D8×C53—44no—
211M16×C53—22no—
212M16×C53—41no—
213C2×C8×C53—41no—
214C4⋊C4×C53—22no—
215C4⋊C4×C53—22no—
216C4⋊C4×C53—22no—
217C4⋊C4×C53—21no—
218C4⋊C4×C53—21no—
219C4⋊C4×C53—22no—
220C4⋊C4×C53—21no—
221C4⋊C4×C53—21no—
222C4⋊C4×C53—21no—
223C4⋊C4×C53—22no—
224C4⋊C4×C53—41no—
225C4⋊C4×C53—41no—
226C4⋊C4×C53—42no—
227C4⋊C4×C53—44no—
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—22no—
236C22⋊C4×C53—21no—
237C22⋊C4×C53—21no—
238C22⋊C4×C53—22no—
239C22⋊C4×C53—22no—
240C22⋊C4×C53—22no—
241C22⋊C4×C53—21no—
242C22⋊C4×C53—21no—
243C22⋊C4×C53—22no—
244C22⋊C4×C53—22no—
245C22⋊C4×C53—42no—
246C22⋊C4×C53—42no—
247C22⋊C4×C53—44no—
248C22⋊C4×C53C2×D411yescharacteristic
249C22⋊C4×C53C2×D411yescharacteristic
250C22⋊C4×C53C2×D412yes—
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—21no—
261C23×C53—22no—
262C23×C53—41no—
263C23×C53—41no—
264C23×C53—81no—
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—41no—
275Q8×C53—41no—
276Q8×C53—41no—
277Q8×C53—81no—
278Q8×C53—82no—
279D4×C53—22no—
280D4×C53—41no—
281D4×C53—41no—
282D4×C53—41no—
283D4×C53—42no—
284D4×C53—41no—
285D4×C53—41no—
286D4×C53—42no—
287D4×C53—42no—
288D4×C53—42no—
289D4×C53—42no—
290D4×C53—41no—
291D4×C53—41no—
292D4×C53—41no—
293D4×C53—81no—
294D4×C53—82no—
295D4×C53—82no—
296D4×C53—82no—
297D4×C53—81no—
298D4×C53—82no—
299D4×C53—84no—
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—41no—
322C2×C4×C53—42no—
323C2×C4×C53—42no—
324C2×C4×C53—42no—
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#33556C5311yesmaximal, 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—42no—
341C22×C53—41no—
342C22×C53—41no—
343C22×C53—42no—
344C22×C53—42no—
345C22×C53—42no—
346C22×C53—41no—
347C22×C53—42no—
348C22×C53—82no—
349C22×C53—82no—
350C22×C53—81no—
351C22×C53—161no—
352C22×C53—162no—
353C22×C53C2×#12011yescharacteristic
354C4×C53—21no—
355C4×C53—21no—
356C4×C53—21no—
357C4×C53—41no—
358C4×C53—42no—
359C4×C53—42no—
360C4×C53—41no—
361C4×C53—42no—
362C4×C53—41no—
363C4×C53—42no—
364C4×C53—82no—
365C4×C53—82no—
366C4×C53B(4,𝔽2)11yescharacteristic
367C4×C53B(4,𝔽2)11yescharacteristic
368#3540C2×C5311yescharacteristic, complemented
369#3028C2×C5311yescharacteristic, complemented
370#3025C2×C5311yescharacteristic, complemented
371#3021C2×C5311yescharacteristic, complemented
372#2200C2×C5314yescomplemented
373#2198C2×C5314yescomplemented
374#2128C2×C5311yescharacteristic, complemented
375#2123C2×C5311yescharacteristic, complemented
376#2120C2×C5311yescharacteristic, complemented
377C2×C53—21no—
378C2×C53—41no—
379C2×C53—41no—
380C2×C53—41no—
381C2×C53—81no—
382C2×C53—82no—
383C2×C53—82no—
384C2×C53C2×B(4,𝔽2)11yescharacteristic
385#585C22×C5311yescharacteristic
386C2×AGL(1,ℤ/8)—21no—
387H(3,𝔽4)—21no—
388#560C22×C5312yescomplemented
389#559C22×C5312yescomplemented
390#556—21no—
391#555—21no—
392#551—21no—
393#548—21no—
394#546—21no—
395#542—22no—
396#542—21no—
397#538—22no—
398#536—21no—
399#536C22×C5311yescharacteristic
400#535C22×C5311yescharacteristic
401#525—21no—
402#525—21no—
403#525C22×C5311yescharacteristic
404#458—21no—
405#458—22no—
406#458C22×C5312yescomplemented
407#458C22×C5314yescomplemented
408B(4,𝔽2)—21no—
409B(4,𝔽2)C22×C5312yescomplemented
410#454—22no—
411#453C22×C5314yes—
412#421—21no—
413#413C22×C5311yescharacteristic
414#410—21no—
415#410—21no—
416#410C22×C5311yescharacteristic
417#410C22×C5311yescharacteristic
418#353C22×C5314yescomplemented
419#352C22×C5312yescomplemented
420#352C22×C5314yescomplemented
421AΣL(1,𝔽16)C22×C5312yescomplemented
422C53#3355611yescharacteristic, direct product factor, Sylow
4232−1+4—21no—
4242−1+4—41no—
425H(5,𝔽2)—21no—
426H(5,𝔽2)—21no—
427H(5,𝔽2)—41no—
428H(5,𝔽2)C23×C5312yes—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—42no—
434C2×#41C23×C5311yescharacteristic
435C22×Q8D4×C5311yescharacteristic, complemented
436C22×D4D4×C5311yescharacteristic, complemented
437C23×C4D4×C5311yescharacteristic
438AGL(1,ℤ/8)—24no—
439AGL(1,ℤ/8)—42no—
440C2×SD16—41no—
441C2×D8—41no—
442C2×M16—21no—
443C4⋊Q8—21no—
444C4⋊Q8—21no—
445C4⋊Q8—41no—
446#127C23×C5312yes—
447#126—22no—
448#126—22no—
449#126—22no—
450#124—22no—
451#124—21no—
452#124—22no—
453#124—22no—
454#124—21no—
455#124—22no—
456#124—22no—
457#124—41no—
458#124D4×C5312yescomplemented
459#123—22no—
460#123—22no—
461#123—22no—
462#123—22no—
463#123—24no—
464#123D4×C5311yescharacteristic
465#123D4×C5312yescomplemented
466#123C23×C5311yescharacteristic
467#123C23×C5312yes—
468C22⋊Q8—21no—
469C22⋊Q8—22no—
470C22⋊Q8—22no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—42no—
475C22⋊Q8—41no—
476#121—21no—
477#121—21no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—22no—
482#121—22no—
483#121—41no—
484#120—22no—
485#120—22no—
486#120—21no—
487#120—21no—
488#120—22no—
489#120D4×C5311yescharacteristic
490#120C23×C5311yescharacteristic
491C4×Q8—21no—
492C4×Q8—22no—
493C4×D4—22no—
494C4×D4—21no—
495C4×D4—22no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—22no—
499C4×D4—42no—
500#117—21no—
501#117—22no—
502#117—21no—
503#117—21no—
504#117D4×C5311yescharacteristic
505#117D4×C5311yescharacteristic, complemented
506#117D4×C5311yescharacteristic, complemented
507C2×C22⋊C4—22no—
508#104—24no—
509#101—21no—
510#100C23×C5312yes—
511#99—21no—
512#99—21no—
513#99—22no—
514#99—22no—
515#99—24no—
516#99C23×C5312yes—
517#99C23×C5312yes—
518C24—21no—
519C24C2×D4×C5311yescharacteristic
520#41—22no—
521#41—22no—
522#41—41no—
523#41—41no—
524#41—42no—
525#41—41no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—42no—
531#41—42no—
532#41—42no—
533#41—41no—
534#41—41no—
535#41—41no—
536#41—81no—
537#41—81no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—22no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—42no—
547C2×Q8C2×D4×C5311yescharacteristic
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—41no—
566C2×D4—42no—
567C2×D4C2×D4×C5311yescharacteristic
568C2×D4C2×D4×C5311yescharacteristic
569C2×D4C2×D4×C5312yes—
570C2×D4C24×C5311yescharacteristic
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4C2×D4×C5311yescharacteristic
581C22×C4C2×D4×C5311yescharacteristic
582C22×C4C2×D4×C5311yescharacteristic
583C22×C4C2×D4×C5311yescharacteristic
584C22×C4C2×D4×C5312yes—
585SD16—44no—
586D8—44no—
587M16—22no—
588M16—41no—
589C2×C8—41no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4—42no—
603C4⋊C4—44no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—21no—
611C22⋊C4—22no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—44no—
624C22⋊C4C2×D4×C5311yescharacteristic
625C22⋊C4C2×D4×C5311yescharacteristic
626C22⋊C4C2×D4×C5312yes—
627C42—22no—
628C42—22no—
629C42—21no—
630C42—21no—
631C42—41no—
632C42—41no—
633C42C2×D4×C5312yes—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—81no—
641C23—81no—
642C23—82no—
643C23#120×C5311yescharacteristic
644C23C22×D4×C5311yescharacteristic
645C23C22×D4×C5311yescharacteristic
646Q8—22no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653Q8—81no—
654Q8—82no—
655D4—22no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—42no—
660D4—41no—
661D4—41no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—81no—
670D4—82no—
671D4—82no—
672D4—82no—
673D4—81no—
674D4—82no—
675D4—84no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—81no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4#120×C5311yescharacteristic
705C2×C4#120×C5311yescharacteristic
706C2×C4#120×C5311yescharacteristic
707C2×C4C22×D4×C5311yescharacteristic
708C8—42no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—42no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—41no—
722C22—42no—
723C22—82no—
724C22—82no—
725C22—81no—
726C22—161no—
727C22—162no—
728C22C2×#120×C5311yescharacteristic
729C4—21no—
730C4—21no—
731C4—21no—
732C4—41no—
733C4—42no—
734C4—42no—
735C4—41no—
736C4—42no—
737C4—41no—
738C4—42no—
739C4—82no—
740C4—82no—
741C4C53×B(4,𝔽2)11yescharacteristic
742C4C53×B(4,𝔽2)11yescharacteristic
743C2—21no—
744C2—41no—
745C2—41no—
746C2—41no—
747C2—81no—
748C2—82no—
749C2—82no—
750C2C2×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×#3028C2semidirect
3. C53×#3025C2semidirect
4. C53×#3021C2semidirect
5. C53×#2200C2semidirect
6. C53×#2198C2semidirect
7. C53×#2128C2semidirect
8. C53×#2123C2semidirect
9. C53×#2120C2semidirect
13. C53×#560C22semidirect
14. C53×#559C22semidirect
31. C53×#458C22semidirect
32. C53×#458C22semidirect
34. C53×B(4,𝔽2)C22semidirect
43. C53×#353C22semidirect
44. C53×#352C22semidirect
45. C53×#352C22semidirect
46. C53×AΣL(1,𝔽16)C22semidirect
59. C22×Q8×C53D4semidirect
60. C22×D4×C53D4semidirect
82. #124×C53D4semidirect
89. #123×C53D4semidirect
129. #117×C53D4semidirect
130. #117×C53D4semidirect
333. #33556C53direct (N × H)
368. #3540C2×C53semidirect
369. #3028C2×C53semidirect
370. #3025C2×C53semidirect
371. #3021C2×C53semidirect
372. #2200C2×C53semidirect
373. #2198C2×C53semidirect
374. #2128C2×C53semidirect
375. #2123C2×C53semidirect
376. #2120C2×C53semidirect
388. #560C22×C53semidirect
389. #559C22×C53semidirect
406. #458C22×C53semidirect
407. #458C22×C53semidirect
409. B(4,𝔽2)C22×C53semidirect
418. #353C22×C53semidirect
419. #352C22×C53semidirect
420. #352C22×C53semidirect
421. AΣL(1,𝔽16)C22×C53semidirect
422. C53#33556direct (N × H)
435. C22×Q8D4×C53semidirect
436. C22×D4D4×C53semidirect
458. #124D4×C53semidirect
465. #123D4×C53semidirect
505. #117D4×C53semidirect
506. #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×#30282
C53×#30252
C53×#30212
C53×#22002
C53×#21982
C53×#21282
C53×#21232
C53×#21202
#3355653