Finite Group Databasebeta

← C53×#33552 #27241064

Subgroups — C53×#33552 #27241064

Order 13568.

1156 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3533C211yesmaximal, characteristic, complemented
2C53×#3026C211yesmaximal, characteristic, complemented
3C2×C53×#458C211yesmaximal, characteristic, complemented
4C53×#3019C211yesmaximal, characteristic, complemented
5C53×#2201C212yesmaximal, complemented
6C53×#2200C212yesmaximal, complemented
7C53×#2198C212yesmaximal, complemented
8C53×#2197C212yesmaximal, complemented
9C53×#2127C211yesmaximal, characteristic, complemented
10C53×#2121C211yesmaximal, characteristic, complemented
11C2×C53×#352C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C53C2211yescharacteristic
13C53×#575—21no—
14C53×#563C2211yescharacteristic, complemented
15C53×#562—21no—
16C53×#560C2211yescharacteristic, complemented
17C53×#559C2211yescharacteristic, complemented
18C53×#553—21no—
19C53×#552—21no—
20C53×#551—21no—
21C53×#551C2211yescharacteristic, complemented
22C53×#547—21no—
23C53×#546—21no—
24C53×#542—21no—
25C53×#540—21no—
26C53×#539—21no—
27C53×#538—21no—
28C53×#538—21no—
29C53×#535C2211yescharacteristic
30C53×#534—21no—
31C53×#534C2211yescharacteristic
32C53×#525—21no—
33C2×#123×C53—21no—
34C2×#123×C53C2211yescharacteristic
35C53×#458—21no—
36C53×#458—21no—
37C53×#458—21no—
38C53×#458C2212yes—
39C53×#458C2212yes—
40C53×#458C2212yes—
41C53×B(4,𝔽2)—21no—
42C53×B(4,𝔽2)C2212yes—
43C53×#455—21no—
44C53×#455C2212yes—
45C53×#453—21no—
46C53×#453C2212yes—
47C53×#421—21no—
48C2×#100×C53C2211yescharacteristic
49C2×#99×C53—21no—
50C2×#99×C53—21no—
51C2×#99×C53C2211yescharacteristic
52C2×#99×C53C2211yescharacteristic
53C53×#354C2212yescomplemented
54C53×#353C2212yescomplemented
55C53×#352C2212yescomplemented
56C53×#352C2212yescomplemented
57C53×#352C2212yescomplemented
58C53×AΣL(1,𝔽16)C2212yescomplemented
59H(5,𝔽2)×C53—21no—
60H(5,𝔽2)×C53—21no—
61H(5,𝔽2)×C53—21no—
62H(5,𝔽2)×C53—42no—
63H(5,𝔽2)×C53C2312yes—
64C2×#41×C53—21no—
65C2×#41×C53—21no—
66C2×#41×C53—41no—
67C2×#41×C53D411yescharacteristic, complemented
68C22×D4×C53—21no—
69C22×D4×C53—21no—
70C22×D4×C53—41no—
71C22×D4×C53D411yescharacteristic
72C22×D4×C53C2311yescharacteristic
73C23×C4×C53D411yescharacteristic, complemented
74#137×C53—22no—
75#137×C53—41no—
76AGL(1,ℤ/8)×C53—22no—
77AGL(1,ℤ/8)×C53—41no—
78#135×C53—42no—
79C2×M16×C53—21no—
80C4⋊Q8×C53—21no—
81#127×C53D411yescharacteristic, complemented
82#127×C53C2311yescharacteristic
83#126×C53—21no—
84#126×C53—21no—
85#126×C53—21no—
86#126×C53—21no—
87#126×C53—21no—
88#126×C53—21no—
89#125×C53—21no—
90#125×C53—21no—
91#125×C53—21no—
92#124×C53—21no—
93#124×C53—21no—
94#124×C53—21no—
95#124×C53—21no—
96#124×C53D411yescharacteristic, complemented
97#124×C53C2311yescharacteristic
98#123×C53—21no—
99#123×C53—21no—
100#123×C53—21no—
101#123×C53—21no—
102#123×C53—21no—
103#123×C53—21no—
104#123×C53—21no—
105#123×C53—21no—
106#123×C53—21no—
107#123×C53—21no—
108#123×C53—21no—
109#123×C53—21no—
110#123×C53—22no—
111#123×C53—22no—
112#123×C53—22no—
113#123×C53—41no—
114#123×C53—42no—
115#123×C53D411yescharacteristic
116#123×C53D411yescharacteristic, complemented
117#123×C53D411yescharacteristic, complemented
118#123×C53C2311yescharacteristic
119#123×C53C2311yescharacteristic
120#123×C53C2311yescharacteristic
121C22⋊Q8×C53—21no—
122C22⋊Q8×C53—21no—
123C22⋊Q8×C53—21no—
124C22⋊Q8×C53—21no—
125C22⋊Q8×C53—21no—
126C22⋊Q8×C53—21no—
127C22⋊Q8×C53—21no—
128C22⋊Q8×C53—21no—
129#121×C53—21no—
130#121×C53—21no—
131#121×C53—21no—
132#121×C53—21no—
133#121×C53—21no—
134#121×C53—21no—
135#121×C53—21no—
136#121×C53—21no—
137#121×C53—21no—
138#121×C53—21no—
139#121×C53—21no—
140#121×C53—21no—
141#121×C53—42no—
142#120×C53—21no—
143#120×C53—21no—
144#120×C53—21no—
145#120×C53—21no—
146#120×C53—22no—
147#120×C53—41no—
148#120×C53D411yescharacteristic
149#120×C53C2311yescharacteristic
150C4×Q8×C53—21no—
151C4×D4×C53—21no—
152C4×D4×C53—21no—
153C4×D4×C53—21no—
154C4×D4×C53—21no—
155C4×D4×C53—21no—
156C4×D4×C53—21no—
157C4×D4×C53—21no—
158C4×D4×C53—21no—
159C4×D4×C53—21no—
160#117×C53—21no—
161#117×C53—21no—
162#117×C53—21no—
163#117×C53D411yescharacteristic, complemented
164C2×C4⋊C4×C53—21no—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53—41no—
167C2×C22⋊C4×C53—21no—
168C2×C22⋊C4×C53—21no—
169C2×C22⋊C4×C53—21no—
170C2×C22⋊C4×C53—21no—
171C2×C22⋊C4×C53—41no—
172C2×C22⋊C4×C53D411yescharacteristic
173C2×C22⋊C4×C53D411yescharacteristic, complemented
174#104×C53—22no—
175#104×C53—22no—
176#100×C53—21no—
177#100×C53C2312yes—
178#99×C53—22no—
179#99×C53—22no—
180#99×C53—22no—
181#99×C53—22no—
182#99×C53—21no—
183#99×C53—21no—
184#99×C53C2312yes—
185#99×C53C2312yes—
186C24×C53—21no—
187C24×C53—21no—
188C24×C53C2×D411yescharacteristic
189C24×C53C2×D411yescharacteristic
190C24×C53C2×D411yescharacteristic
191#41×C53—22no—
192#41×C53—22no—
193#41×C53—42no—
194#41×C53—41no—
195#41×C53—42no—
196#41×C53—42no—
197#41×C53—41no—
198#41×C53—41no—
199#41×C53—42no—
200#41×C53—41no—
201#41×C53—81no—
202#41×C53—81no—
203C2×Q8×C53—21no—
204C2×Q8×C53—21no—
205C2×Q8×C53—21no—
206C2×Q8×C53C2×D411yescharacteristic
207C2×D4×C53—21no—
208C2×D4×C53—22no—
209C2×D4×C53—22no—
210C2×D4×C53—21no—
211C2×D4×C53—21no—
212C2×D4×C53—22no—
213C2×D4×C53—22no—
214C2×D4×C53—21no—
215C2×D4×C53—21no—
216C2×D4×C53—21no—
217C2×D4×C53—21no—
218C2×D4×C53—21no—
219C2×D4×C53—21no—
220C2×D4×C53—21no—
221C2×D4×C53—21no—
222C2×D4×C53—21no—
223C2×D4×C53—41no—
224C2×D4×C53—41no—
225C2×D4×C53—42no—
226C2×D4×C53—42no—
227C2×D4×C53—41no—
228C2×D4×C53—41no—
229C2×D4×C53—41no—
230C2×D4×C53—41no—
231C2×D4×C53—42no—
232C2×D4×C53—42no—
233C2×D4×C53—41no—
234C2×D4×C53—41no—
235C2×D4×C53—41no—
236C2×D4×C53—41no—
237C2×D4×C53—41no—
238C2×D4×C53—42no—
239C2×D4×C53C2×D411yescharacteristic
240C2×D4×C53C2×D411yescharacteristic
241C2×D4×C53C2×D411yescharacteristic
242C2×D4×C53C2×D411yescharacteristic
243C2×D4×C53C2411yescharacteristic
244C22×C4×C53—21no—
245C22×C4×C53—21no—
246C22×C4×C53—21no—
247C22×C4×C53—21no—
248C22×C4×C53—21no—
249C22×C4×C53—21no—
250C22×C4×C53—21no—
251C22×C4×C53—21no—
252C22×C4×C53—21no—
253C22×C4×C53—21no—
254C22×C4×C53—21no—
255C22×C4×C53—41no—
256C22×C4×C53—41no—
257C22×C4×C53—41no—
258C22×C4×C53—41no—
259C22×C4×C53—41no—
260C22×C4×C53C2×D411yescharacteristic
261C22×C4×C53C2×D411yescharacteristic
262C22×C4×C53C2×D411yescharacteristic
263C22×C4×C53C2×D411yescharacteristic
264Q16×C53—42no—
265SD16×C53—42no—
266SD16×C53—42no—
267D8×C53—42no—
268M16×C53—22no—
269M16×C53—41no—
270C2×C8×C53—41no—
271C4⋊C4×C53—21no—
272C4⋊C4×C53—21no—
273C4⋊C4×C53—21no—
274C4⋊C4×C53—21no—
275C4⋊C4×C53—21no—
276C4⋊C4×C53—21no—
277C4⋊C4×C53—21no—
278C4⋊C4×C53—21no—
279C4⋊C4×C53—21no—
280C4⋊C4×C53—21no—
281C4⋊C4×C53—21no—
282C4⋊C4×C53—21no—
283C4⋊C4×C53—21no—
284C4⋊C4×C53—21no—
285C4⋊C4×C53—21no—
286C4⋊C4×C53—21no—
287C4⋊C4×C53—21no—
288C4⋊C4×C53—21no—
289C4⋊C4×C53—21no—
290C4⋊C4×C53—42no—
291C4⋊C4×C53—42no—
292C4⋊C4×C53—42no—
293C22⋊C4×C53—21no—
294C22⋊C4×C53—21no—
295C22⋊C4×C53—21no—
296C22⋊C4×C53—21no—
297C22⋊C4×C53—21no—
298C22⋊C4×C53—21no—
299C22⋊C4×C53—21no—
300C22⋊C4×C53—21no—
301C22⋊C4×C53—21no—
302C22⋊C4×C53—21no—
303C22⋊C4×C53—21no—
304C22⋊C4×C53—21no—
305C22⋊C4×C53—21no—
306C22⋊C4×C53—21no—
307C22⋊C4×C53—21no—
308C22⋊C4×C53—21no—
309C22⋊C4×C53—21no—
310C22⋊C4×C53—21no—
311C22⋊C4×C53—21no—
312C22⋊C4×C53—21no—
313C22⋊C4×C53—21no—
314C22⋊C4×C53—21no—
315C22⋊C4×C53—21no—
316C22⋊C4×C53—22no—
317C22⋊C4×C53—22no—
318C22⋊C4×C53—42no—
319C22⋊C4×C53—41no—
320C22⋊C4×C53—41no—
321C22⋊C4×C53—42no—
322C22⋊C4×C53—42no—
323C22⋊C4×C53—42no—
324C22⋊C4×C53C2×D411yescharacteristic
325C22⋊C4×C53C2×D411yescharacteristic
326C22⋊C4×C53C2×D411yescharacteristic
327C22⋊C4×C53C2×D411yescharacteristic
328C42×C53—21no—
329C42×C53—21no—
330C42×C53—21no—
331C42×C53—21no—
332C42×C53C2×D411yescharacteristic
333C42×C53C2×D411yescharacteristic
334C23×C53—21no—
335C23×C53—21no—
336C23×C53—21no—
337C23×C53—21no—
338C23×C53—22no—
339C23×C53—22no—
340C23×C53—21no—
341C23×C53—21no—
342C23×C53—41no—
343C23×C53—41no—
344C23×C53—41no—
345C23×C53—41no—
346C23×C53—81no—
347C23×C53—81no—
348C23×C53—81no—
349C23×C53—82no—
350C23×C53—161no—
351C23×C53#12011yescharacteristic
352C23×C53#12011yescharacteristic
353C23×C53#12011yescharacteristic
354C23×C53C22×D411yescharacteristic
355C23×C53C22×D411yescharacteristic
356Q8×C53—22no—
357Q8×C53—41no—
358Q8×C53—41no—
359Q8×C53—81no—
360Q8×C53—81no—
361D4×C53—22no—
362D4×C53—41no—
363D4×C53—41no—
364D4×C53—41no—
365D4×C53—41no—
366D4×C53—41no—
367D4×C53—41no—
368D4×C53—42no—
369D4×C53—42no—
370D4×C53—42no—
371D4×C53—42no—
372D4×C53—42no—
373D4×C53—42no—
374D4×C53—41no—
375D4×C53—41no—
376D4×C53—41no—
377D4×C53—41no—
378D4×C53—81no—
379D4×C53—81no—
380D4×C53—81no—
381D4×C53—81no—
382D4×C53—81no—
383D4×C53—81no—
384D4×C53—81no—
385D4×C53—81no—
386D4×C53—81no—
387D4×C53—162no—
388C2×C4×C53—21no—
389C2×C4×C53—21no—
390C2×C4×C53—22no—
391C2×C4×C53—22no—
392C2×C4×C53—21no—
393C2×C4×C53—21no—
394C2×C4×C53—21no—
395C2×C4×C53—21no—
396C2×C4×C53—21no—
397C2×C4×C53—21no—
398C2×C4×C53—21no—
399C2×C4×C53—21no—
400C2×C4×C53—21no—
401C2×C4×C53—21no—
402C2×C4×C53—42no—
403C2×C4×C53—42no—
404C2×C4×C53—41no—
405C2×C4×C53—41no—
406C2×C4×C53—41no—
407C2×C4×C53—41no—
408C2×C4×C53—41no—
409C2×C4×C53—41no—
410C2×C4×C53—41no—
411C2×C4×C53—41no—
412C2×C4×C53—42no—
413C2×C4×C53—42no—
414C2×C4×C53—81no—
415C2×C4×C53—81no—
416C2×C4×C53—81no—
417C2×C4×C53—81no—
418C2×C4×C53—81no—
419C2×C4×C53—81no—
420C2×C4×C53—81no—
421C2×C4×C53—81no—
422C2×C4×C53—82no—
423C2×C4×C53—161no—
424C2×C4×C53#12011yescharacteristic
425C2×C4×C53C22×D411yescharacteristic
426C8×C53—42no—
427#33552C5311yesmaximal, characteristic, direct product factor, Sylow
428C22×C53—21no—
429C22×C53—21no—
430C22×C53—21no—
431C22×C53—21no—
432C22×C53—41no—
433C22×C53—41no—
434C22×C53—41no—
435C22×C53—41no—
436C22×C53—41no—
437C22×C53—42no—
438C22×C53—41no—
439C22×C53—41no—
440C22×C53—41no—
441C22×C53—41no—
442C22×C53—42no—
443C22×C53—41no—
444C22×C53—41no—
445C22×C53—81no—
446C22×C53—81no—
447C22×C53—81no—
448C22×C53—82no—
449C22×C53—82no—
450C22×C53—82no—
451C22×C53—82no—
452C22×C53—161no—
453C22×C53—161no—
454C22×C53B(4,𝔽2)11yescharacteristic
455C22×C53B(4,𝔽2)11yescharacteristic
456C22×C53C2×#12011yescharacteristic
457C4×C53—21no—
458C4×C53—21no—
459C4×C53—41no—
460C4×C53—41no—
461C4×C53—41no—
462C4×C53—41no—
463C4×C53—41no—
464C4×C53—41no—
465C4×C53—42no—
466C4×C53—41no—
467C4×C53—41no—
468C4×C53—41no—
469C4×C53—41no—
470C4×C53—82no—
471C4×C53—82no—
472#3533C2×C5311yescharacteristic, complemented
473#3026C2×C5311yescharacteristic, complemented
474C2×#458C2×C5311yescharacteristic, complemented
475#3019C2×C5311yescharacteristic, complemented
476#2201C2×C5312yescomplemented
477#2200C2×C5312yescomplemented
478#2198C2×C5312yescomplemented
479#2197C2×C5312yescomplemented
480#2127C2×C5311yescharacteristic, complemented
481#2121C2×C5311yescharacteristic, complemented
482C2×#352C2×C5311yescharacteristic, complemented
483C2×C53—21no—
484C2×C53—21no—
485C2×C53—21no—
486C2×C53—41no—
487C2×C53—41no—
488C2×C53—41no—
489C2×C53—41no—
490C2×C53—81no—
491C2×C53—81no—
492C2×C53—82no—
493C2×C53C2×B(4,𝔽2)11yescharacteristic
494C2×H(5,𝔽2)C22×C5311yescharacteristic
495#575—21no—
496#563C22×C5311yescharacteristic, complemented
497#562—21no—
498#560C22×C5311yescharacteristic, complemented
499#559C22×C5311yescharacteristic, complemented
500#553—21no—
501#552—21no—
502#551—21no—
503#551C22×C5311yescharacteristic, complemented
504#547—21no—
505#546—21no—
506#542—21no—
507#540—21no—
508#539—21no—
509#538—21no—
510#538—21no—
511#535C22×C5311yescharacteristic
512#534—21no—
513#534C22×C5311yescharacteristic
514#525—21no—
515C2×#123—21no—
516C2×#123C22×C5311yescharacteristic
517#458—21no—
518#458—21no—
519#458—21no—
520#458C22×C5312yes—
521#458C22×C5312yes—
522#458C22×C5312yes—
523B(4,𝔽2)—21no—
524B(4,𝔽2)C22×C5312yes—
525#455—21no—
526#455C22×C5312yes—
527#453—21no—
528#453C22×C5312yes—
529#421—21no—
530C2×#100C22×C5311yescharacteristic
531C2×#99—21no—
532C2×#99—21no—
533C2×#99C22×C5311yescharacteristic
534C2×#99C22×C5311yescharacteristic
535#354C22×C5312yescomplemented
536#353C22×C5312yescomplemented
537#352C22×C5312yescomplemented
538#352C22×C5312yescomplemented
539#352C22×C5312yescomplemented
540AΣL(1,𝔽16)C22×C5312yescomplemented
541C53#3355211yescharacteristic, direct product factor, Sylow
542H(5,𝔽2)—21no—
543H(5,𝔽2)—21no—
544H(5,𝔽2)—21no—
545H(5,𝔽2)—42no—
546H(5,𝔽2)C23×C5312yes—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—41no—
550C2×#41D4×C5311yescharacteristic, complemented
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—41no—
554C22×D4D4×C5311yescharacteristic
555C22×D4C23×C5311yescharacteristic
556C23×C4D4×C5311yescharacteristic, complemented
557#137—22no—
558#137—41no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—41no—
561#135—42no—
562C2×M16—21no—
563C4⋊Q8—21no—
564#127D4×C5311yescharacteristic, complemented
565#127C23×C5311yescharacteristic
566#126—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#125—21no—
573#125—21no—
574#125—21no—
575#124—21no—
576#124—21no—
577#124—21no—
578#124—21no—
579#124D4×C5311yescharacteristic, complemented
580#124C23×C5311yescharacteristic
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—22no—
594#123—22no—
595#123—22no—
596#123—41no—
597#123—42no—
598#123D4×C5311yescharacteristic
599#123D4×C5311yescharacteristic, complemented
600#123D4×C5311yescharacteristic, complemented
601#123C23×C5311yescharacteristic
602#123C23×C5311yescharacteristic
603#123C23×C5311yescharacteristic
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—42no—
625#120—21no—
626#120—21no—
627#120—21no—
628#120—21no—
629#120—22no—
630#120—41no—
631#120D4×C5311yescharacteristic
632#120C23×C5311yescharacteristic
633C4×Q8—21no—
634C4×D4—21no—
635C4×D4—21no—
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643#117—21no—
644#117—21no—
645#117—21no—
646#117D4×C5311yescharacteristic, complemented
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—41no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4D4×C5311yescharacteristic
656C2×C22⋊C4D4×C5311yescharacteristic, complemented
657#104—22no—
658#104—22no—
659#100—21no—
660#100C23×C5312yes—
661#99—21no—
662#99—21no—
663#99—22no—
664#99—22no—
665#99—22no—
666#99—22no—
667#99C23×C5312yes—
668#99C23×C5312yes—
669C24—21no—
670C24—21no—
671C24C2×D4×C5311yescharacteristic
672C24C2×D4×C5311yescharacteristic
673C24C2×D4×C5311yescharacteristic
674#41—22no—
675#41—22no—
676#41—42no—
677#41—41no—
678#41—42no—
679#41—42no—
680#41—41no—
681#41—41no—
682#41—42no—
683#41—41no—
684#41—81no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8C2×D4×C5311yescharacteristic
690C2×D4—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—41no—
713C2×D4—41no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—41no—
717C2×D4—41no—
718C2×D4—41no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—42no—
722C2×D4C2×D4×C5311yescharacteristic
723C2×D4C2×D4×C5311yescharacteristic
724C2×D4C2×D4×C5311yescharacteristic
725C2×D4C2×D4×C5311yescharacteristic
726C2×D4C24×C5311yescharacteristic
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4C2×D4×C5311yescharacteristic
744C22×C4C2×D4×C5311yescharacteristic
745C22×C4C2×D4×C5311yescharacteristic
746C22×C4C2×D4×C5311yescharacteristic
747Q16—42no—
748SD16—42no—
749SD16—42no—
750D8—42no—
751M16—22no—
752M16—41no—
753C2×C8—41no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—42no—
774C4⋊C4—42no—
775C4⋊C4—42no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—22no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—42no—
805C22⋊C4—42no—
806C22⋊C4—42no—
807C22⋊C4C2×D4×C5311yescharacteristic
808C22⋊C4C2×D4×C5311yescharacteristic
809C22⋊C4C2×D4×C5311yescharacteristic
810C22⋊C4C2×D4×C5311yescharacteristic
811C42—21no—
812C42—21no—
813C42—21no—
814C42—21no—
815C42C2×D4×C5311yescharacteristic
816C42C2×D4×C5311yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—22no—
822C23—22no—
823C23—21no—
824C23—21no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—81no—
830C23—81no—
831C23—81no—
832C23—82no—
833C23—161no—
834C23#120×C5311yescharacteristic
835C23#120×C5311yescharacteristic
836C23#120×C5311yescharacteristic
837C23C22×D4×C5311yescharacteristic
838C23C22×D4×C5311yescharacteristic
839Q8—22no—
840Q8—41no—
841Q8—41no—
842Q8—81no—
843Q8—81no—
844D4—22no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—42no—
852D4—42no—
853D4—42no—
854D4—42no—
855D4—42no—
856D4—42no—
857D4—41no—
858D4—41no—
859D4—41no—
860D4—41no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868D4—81no—
869D4—81no—
870D4—162no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—82no—
906C2×C4—161no—
907C2×C4#120×C5311yescharacteristic
908C2×C4C22×D4×C5311yescharacteristic
909C8—42no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—41no—
926C22—41no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—161no—
935C22—161no—
936C22C53×B(4,𝔽2)11yescharacteristic
937C22C53×B(4,𝔽2)11yescharacteristic
938C22C2×#120×C5311yescharacteristic
939C4—21no—
940C4—21no—
941C4—41no—
942C4—41no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—42no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—82no—
953C4—82no—
954C2—21no—
955C2—21no—
956C2—21no—
957C2—41no—
958C2—41no—
959C2—41no—
960C2—41no—
961C2—81no—
962C2—81no—
963C2—82no—
964C2C2×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 ◁ C23×C53 ◁ C22×D4×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C53×#3533C2semidirect
2. C53×#3026C2semidirect
3. C2×C53×#458C2semidirect
4. C53×#3019C2semidirect
5. C53×#2201C2semidirect
6. C53×#2200C2semidirect
7. C53×#2198C2semidirect
8. C53×#2197C2semidirect
9. C53×#2127C2semidirect
10. C53×#2121C2semidirect
11. C2×C53×#352C2semidirect
14. C53×#563C22semidirect
16. C53×#560C22semidirect
17. C53×#559C22semidirect
21. C53×#551C22semidirect
53. C53×#354C22semidirect
54. C53×#353C22semidirect
55. C53×#352C22semidirect
56. C53×#352C22semidirect
57. C53×#352C22semidirect
58. C53×AΣL(1,𝔽16)C22semidirect
67. C2×#41×C53D4semidirect
73. C23×C4×C53D4semidirect
81. #127×C53D4semidirect
96. #124×C53D4semidirect
116. #123×C53D4semidirect
117. #123×C53D4semidirect
163. #117×C53D4semidirect
173. C2×C22⋊C4×C53D4semidirect
427. #33552C53direct (N × H)
472. #3533C2×C53semidirect
473. #3026C2×C53semidirect
474. C2×#458C2×C53semidirect
475. #3019C2×C53semidirect
476. #2201C2×C53semidirect
477. #2200C2×C53semidirect
478. #2198C2×C53semidirect
479. #2197C2×C53semidirect
480. #2127C2×C53semidirect
481. #2121C2×C53semidirect
482. C2×#352C2×C53semidirect
496. #563C22×C53semidirect
498. #560C22×C53semidirect
499. #559C22×C53semidirect
503. #551C22×C53semidirect
535. #354C22×C53semidirect
536. #353C22×C53semidirect
537. #352C22×C53semidirect
538. #352C22×C53semidirect
539. #352C22×C53semidirect
540. AΣL(1,𝔽16)C22×C53semidirect
541. C53#33552direct (N × H)
550. C2×#41D4×C53semidirect
556. C23×C4D4×C53semidirect
564. #127D4×C53semidirect
579. #124D4×C53semidirect
599. #123D4×C53semidirect
600. #123D4×C53semidirect
646. #117D4×C53semidirect
656. C2×C22⋊C4D4×C53semidirect

Maximal subgroups

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

subgroupindex
C53×#35332
C53×#30262
C2×C53×#4582
C53×#30192
C53×#22012
C53×#22002
C53×#21982
C53×#21972
C53×#21272
C53×#21212
C2×C53×#3522
#3355253