Finite Group Databasebeta

← C53×#18447 #27225959

Subgroups — C53×#18447 #27225959

Order 13568.

982 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3534C211yesmaximal, characteristic
2C53×#3193C211yesmaximal, characteristic, complemented
3C53×#3190C211yesmaximal, characteristic, complemented
4C53×#2814C211yesmaximal, characteristic, complemented
5C53×#1612C211yesmaximal, characteristic, complemented
6C53×#1610C211yesmaximal, characteristic, complemented
7C53×#1609C211yesmaximal, characteristic, complemented
8C53×#1607C211yesmaximal, characteristic, complemented
9C53×#1606C211yesmaximal, characteristic, complemented
10C53×#1604C211yesmaximal, characteristic, complemented
11C53×#1603C211yesmaximal, characteristic, complemented
12C53×#1601C211yesmaximal, characteristic, complemented
13C53×#1519C211yesmaximal, characteristic, complemented
14C53×#1513C211yesmaximal, characteristic, complemented
15C53×#1468C211yesmaximal, characteristic, complemented
16C53×#562—21no—
17C53×#560—21no—
18C53×#553—21no—
19C53×#551—21no—
20C53×#546—21no—
21C53×#546—21no—
22C53×#546—21no—
23D42×C53—21no—
24C53×#540—21no—
25C53×#539—21no—
26C53×#539C2211yescharacteristic
27C53×#538—21no—
28C53×#538C2211yescharacteristic
29C53×#537C2211yescharacteristic
30C53×#534—21no—
31C53×#534C2211yescharacteristic
32C53×#525C2211yescharacteristic
33C2×#123×C53C2211yescharacteristic
34C2×C22⋊Q8×C53C2211yescharacteristic, complemented
35C2×#121×C53C2211yescharacteristic
36C53×#485—21no—
37C53×#484—21no—
38C53×#483C2211yescharacteristic, complemented
39C53×#480C2211yescharacteristic
40C53×#480C2211yescharacteristic, complemented
41C53×#480C2211yescharacteristic, complemented
42C53×#468—21no—
43C53×#468—21no—
44C53×#467—21no—
45C53×#465—21no—
46C53×#452—21no—
47C53×#451C2211yescharacteristic, complemented
48C53×#450—21no—
49C53×#448C2211yescharacteristic
50C53×#448C2211yescharacteristic, complemented
51C53×#448C2211yescharacteristic, complemented
52C53×#407C2211yescharacteristic, complemented
53C2×C22⋊C8×C53C2211yescharacteristic, complemented
54C53×#398—21no—
55C53×#398C2211yescharacteristic, complemented
56C53×#397—21no—
57C53×#397C2211yescharacteristic, complemented
58C53×#396—21no—
59C53×#395C2211yescharacteristic, complemented
60C53×#394—21no—
61C53×#393C2211yescharacteristic, complemented
62C53×#380C2211yescharacteristic, complemented
63C53×#328C2211yescharacteristic, complemented
64C53×#328C2211yescharacteristic, complemented
65C53×#327C2211yescharacteristic
66C53×#327C2211yescharacteristic
67C53×#327C2211yescharacteristic, complemented
68C53×#327C2211yescharacteristic, complemented
69C53×#327C2211yescharacteristic, complemented
70C53×#327C2211yescharacteristic, complemented
71C53×#324C2211yescharacteristic, complemented
72C53×#324C2211yescharacteristic, complemented
73C53×#323C2211yescharacteristic, complemented
74C53×#323C2211yescharacteristic, complemented
75C2×#41×C53—21no—
76C2×#41×C53D411yescharacteristic
77C22×Q8×C53C2311yescharacteristic
78C22×D4×C53—21no—
79C22×D4×C53—21no—
80C22×D4×C53—21no—
81C22×D4×C53D411yescharacteristic
82C22×D4×C53D411yescharacteristic
83C23×C4×C53C2311yescharacteristic
84C2×Q16×C53—21no—
85C2×SD16×C53—21no—
86C2×SD16×C53—21no—
87C2×SD16×C53—21no—
88C2×M16×C53—21no—
89C22×C8×C53—21no—
90#127×C53—21no—
91#126×C53—21no—
92#126×C53—21no—
93#126×C53—21no—
94#126×C53—21no—
95#125×C53—21no—
96#125×C53—21no—
97#124×C53—21no—
98#124×C53—21no—
99#124×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—21no—
111#123×C53—21no—
112#123×C53—21no—
113#123×C53—21no—
114C22⋊Q8×C53—21no—
115C22⋊Q8×C53—21no—
116C22⋊Q8×C53—21no—
117C22⋊Q8×C53—21no—
118C22⋊Q8×C53—21no—
119C22⋊Q8×C53—21no—
120C22⋊Q8×C53—21no—
121C22⋊Q8×C53—21no—
122C22⋊Q8×C53—21no—
123C22⋊Q8×C53D411yescharacteristic
124C22⋊Q8×C53C2311yescharacteristic
125#121×C53—21no—
126#121×C53—21no—
127#121×C53—21no—
128#121×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×C53D411yescharacteristic
141#121×C53D411yescharacteristic
142#121×C53D411yescharacteristic
143#121×C53C2311yescharacteristic
144#121×C53C2311yescharacteristic
145#121×C53C2311yescharacteristic
146#120×C53—21no—
147#120×C53—21no—
148#120×C53—21no—
149#120×C53—21no—
150#120×C53—21no—
151#120×C53—21no—
152#120×C53—21no—
153#120×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—
160C4×D4×C53—21no—
161C4×D4×C53—21no—
162#117×C53—21no—
163#117×C53D411yescharacteristic
164C2×C4⋊C4×C53—21no—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53—21no—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53D411yescharacteristic
169C2×C4⋊C4×C53D411yescharacteristic
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C22⋊C4×C53—21no—
173C2×C22⋊C4×C53—21no—
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176C2×C22⋊C4×C53—21no—
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179C2×C22⋊C4×C53D411yescharacteristic
180C2×C22⋊C4×C53D411yescharacteristic
181C2×C22⋊C4×C53C2311yescharacteristic
182#107×C53—21no—
183#107×C53—21no—
184#107×C53—21no—
185#106×C53—21no—
186#103×C53—21no—
187#103×C53—21no—
188#103×C53—21no—
189#103×C53—21no—
190#103×C53—21no—
191#102×C53—21no—
192#102×C53—21no—
193#102×C53—21no—
194C22⋊C8×C53—21no—
195C22⋊C8×C53—21no—
196C22⋊C8×C53C2311yescharacteristic
197C22⋊C8×C53C2311yescharacteristic
198C22⋊C8×C53C2311yescharacteristic
199C22⋊C8×C53C2311yescharacteristic
200#95×C53—21no—
201#95×C53—21no—
202#95×C53—21no—
203#95×C53—21no—
204#95×C53C2311yescharacteristic
205#95×C53C2311yescharacteristic
206C24×C53—21no—
207C24×C53—21no—
208C24×C53C2×D411yescharacteristic
209C24×C53C2×D411yescharacteristic
210#41×C53—81no—
211#41×C53—81no—
212#41×C53—81no—
213C2×Q8×C53—21no—
214C2×Q8×C53—21no—
215C2×Q8×C53—21no—
216C2×Q8×C53—81no—
217C2×Q8×C53C2×D411yescharacteristic
218C2×D4×C53—21no—
219C2×D4×C53—21no—
220C2×D4×C53—21no—
221C2×D4×C53—21no—
222C2×D4×C53—21no—
223C2×D4×C53—21no—
224C2×D4×C53—21no—
225C2×D4×C53—21no—
226C2×D4×C53—21no—
227C2×D4×C53—21no—
228C2×D4×C53—21no—
229C2×D4×C53—21no—
230C2×D4×C53—21no—
231C2×D4×C53—21no—
232C2×D4×C53—21no—
233C2×D4×C53—21no—
234C2×D4×C53—21no—
235C2×D4×C53—81no—
236C2×D4×C53—81no—
237C2×D4×C53—81no—
238C2×D4×C53—81no—
239C2×D4×C53—81no—
240C2×D4×C53—81no—
241C2×D4×C53—82no—
242C2×D4×C53C2×D411yescharacteristic
243C2×D4×C53C2×D411yescharacteristic
244C2×D4×C53C2×D411yescharacteristic
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—21no—
256C22×C4×C53—81no—
257C22×C4×C53C2×D411yescharacteristic
258C22×C4×C53C2×D411yescharacteristic
259C22×C4×C53C2×D411yescharacteristic
260C22×C4×C53C2×D411yescharacteristic
261C22×C4×C53C2×D411yescharacteristic
262C22×C4×C53C2×D411yescharacteristic
263C22×C4×C53C2×D411yescharacteristic
264C22×C4×C53C2×D411yescharacteristic
265C22×C4×C53C2411yescharacteristic
266Q16×C53—81no—
267SD16×C53—81no—
268SD16×C53—81no—
269SD16×C53—81no—
270M16×C53—81no—
271C2×C8×C53—21no—
272C2×C8×C53—21no—
273C2×C8×C53—21no—
274C2×C8×C53—21no—
275C2×C8×C53—81no—
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—21no—
291C4⋊C4×C53—41no—
292C4⋊C4×C53—41no—
293C4⋊C4×C53—81no—
294C4⋊C4×C53—81no—
295C4⋊C4×C53—81no—
296C4⋊C4×C53C2×D411yescharacteristic
297C4⋊C4×C53C2×D411yescharacteristic
298C4⋊C4×C53C2×D411yescharacteristic
299C4⋊C4×C53C2×D411yescharacteristic
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—21no—
317C22⋊C4×C53—21no—
318C22⋊C4×C53—21no—
319C22⋊C4×C53—21no—
320C22⋊C4×C53—21no—
321C22⋊C4×C53—21no—
322C22⋊C4×C53—21no—
323C22⋊C4×C53—21no—
324C22⋊C4×C53—21no—
325C22⋊C4×C53—41no—
326C22⋊C4×C53—41no—
327C22⋊C4×C53—81no—
328C22⋊C4×C53—81no—
329C22⋊C4×C53—81no—
330C42×C53—21no—
331C42×C53—21no—
332C42×C53—21no—
333C23×C53—21no—
334C23×C53—21no—
335C23×C53—21no—
336C23×C53—21no—
337C23×C53—21no—
338C23×C53—21no—
339C23×C53—21no—
340C23×C53—21no—
341C23×C53—41no—
342C23×C53—41no—
343C23×C53—42no—
344C23×C53—41no—
345C23×C53—41no—
346C23×C53—81no—
347C23×C53—81no—
348C23×C53—81no—
349C23×C53—81no—
350C23×C53—81no—
351C23×C53#12011yescharacteristic
352C23×C53#12011yescharacteristic
353C23×C53C22×D411yescharacteristic
354Q8×C53—41no—
355Q8×C53—41no—
356Q8×C53—41no—
357Q8×C53—41no—
358Q8×C53—41no—
359Q8×C53—81no—
360D4×C53—41no—
361D4×C53—41no—
362D4×C53—41no—
363D4×C53—42no—
364D4×C53—42no—
365D4×C53—41no—
366D4×C53—41no—
367D4×C53—41no—
368D4×C53—41no—
369D4×C53—41no—
370D4×C53—41no—
371D4×C53—81no—
372D4×C53—81no—
373D4×C53—81no—
374D4×C53—81no—
375D4×C53—81no—
376D4×C53—81no—
377D4×C53—81no—
378D4×C53—81no—
379D4×C53—81no—
380D4×C53—81no—
381D4×C53—81no—
382D4×C53—81no—
383C2×C4×C53—21no—
384C2×C4×C53—21no—
385C2×C4×C53—21no—
386C2×C4×C53—21no—
387C2×C4×C53—21no—
388C2×C4×C53—21no—
389C2×C4×C53—21no—
390C2×C4×C53—21no—
391C2×C4×C53—21no—
392C2×C4×C53—21no—
393C2×C4×C53—41no—
394C2×C4×C53—41no—
395C2×C4×C53—41no—
396C2×C4×C53—41no—
397C2×C4×C53—41no—
398C2×C4×C53—41no—
399C2×C4×C53—41no—
400C2×C4×C53—41no—
401C2×C4×C53—41no—
402C2×C4×C53—41no—
403C2×C4×C53—41no—
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—41no—
413C2×C4×C53—81no—
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#12011yescharacteristic
421C2×C4×C53#12011yescharacteristic
422C2×C4×C53C22×D411yescharacteristic
423C2×C4×C53C22×D411yescharacteristic
424C8×C53—41no—
425C8×C53—41no—
426C8×C53—41no—
427C8×C53—41no—
428#18447C5311yesmaximal, characteristic, direct product factor, Sylow
429C22×C53—21no—
430C22×C53—21no—
431C22×C53—21no—
432C22×C53—21no—
433C22×C53—21no—
434C22×C53—21no—
435C22×C53—21no—
436C22×C53—21no—
437C22×C53—41no—
438C22×C53—41no—
439C22×C53—41no—
440C22×C53—41no—
441C22×C53—41no—
442C22×C53—41no—
443C22×C53—41no—
444C22×C53—41no—
445C22×C53—41no—
446C22×C53—41no—
447C22×C53—41no—
448C22×C53—41no—
449C22×C53—81no—
450C22×C53—81no—
451C22×C53—81no—
452C22×C53—81no—
453C22×C53—162no—
454C22×C53—162no—
455C22×C53C2×#12011yescharacteristic
456C22×C53#57611yescharacteristic
457C22×C53#57711yescharacteristic
458C4×C53—21no—
459C4×C53—21no—
460C4×C53—21no—
461C4×C53—21no—
462C4×C53—41no—
463C4×C53—41no—
464C4×C53—41no—
465C4×C53—41no—
466C4×C53—41no—
467C4×C53—41no—
468C4×C53—41no—
469C4×C53—41no—
470C4×C53—81no—
471C4×C53—81no—
472C4×C53—81no—
473C4×C53—81no—
474#3534C2×C5311yescharacteristic
475#3193C2×C5311yescharacteristic, complemented
476#3190C2×C5311yescharacteristic, complemented
477#2814C2×C5311yescharacteristic, complemented
478#1612C2×C5311yescharacteristic, complemented
479#1610C2×C5311yescharacteristic, complemented
480#1609C2×C5311yescharacteristic, complemented
481#1607C2×C5311yescharacteristic, complemented
482#1606C2×C5311yescharacteristic, complemented
483#1604C2×C5311yescharacteristic, complemented
484#1603C2×C5311yescharacteristic, complemented
485#1601C2×C5311yescharacteristic, complemented
486#1519C2×C5311yescharacteristic, complemented
487#1513C2×C5311yescharacteristic, complemented
488#1468C2×C5311yescharacteristic, complemented
489C2×C53—21no—
490C2×C53—21no—
491C2×C53—41no—
492C2×C53—41no—
493C2×C53—81no—
494C2×C53—81no—
495C2×C53—81no—
496C2×C53—81no—
497C2×C53#301211yescharacteristic
498C2×C53#302211yescharacteristic
499C2×C53#302611yescharacteristic
500#562—21no—
501#560—21no—
502#553—21no—
503#551—21no—
504#546—21no—
505#546—21no—
506#546—21no—
507D42—21no—
508#540—21no—
509#539—21no—
510#539C22×C5311yescharacteristic
511#538—21no—
512#538C22×C5311yescharacteristic
513#537C22×C5311yescharacteristic
514#534—21no—
515#534C22×C5311yescharacteristic
516#525C22×C5311yescharacteristic
517C2×#123C22×C5311yescharacteristic
518C2×C22⋊Q8C22×C5311yescharacteristic, complemented
519C2×#121C22×C5311yescharacteristic
520#485—21no—
521#484—21no—
522#483C22×C5311yescharacteristic, complemented
523#480C22×C5311yescharacteristic
524#480C22×C5311yescharacteristic, complemented
525#480C22×C5311yescharacteristic, complemented
526#468—21no—
527#468—21no—
528#467—21no—
529#465—21no—
530#452—21no—
531#451C22×C5311yescharacteristic, complemented
532#450—21no—
533#448C22×C5311yescharacteristic
534#448C22×C5311yescharacteristic, complemented
535#448C22×C5311yescharacteristic, complemented
536#407C22×C5311yescharacteristic, complemented
537C2×C22⋊C8C22×C5311yescharacteristic, complemented
538#398—21no—
539#398C22×C5311yescharacteristic, complemented
540#397—21no—
541#397C22×C5311yescharacteristic, complemented
542#396—21no—
543#395C22×C5311yescharacteristic, complemented
544#394—21no—
545#393C22×C5311yescharacteristic, complemented
546#380C22×C5311yescharacteristic, complemented
547#328C22×C5311yescharacteristic, complemented
548#328C22×C5311yescharacteristic, complemented
549#327C22×C5311yescharacteristic
550#327C22×C5311yescharacteristic
551#327C22×C5311yescharacteristic, complemented
552#327C22×C5311yescharacteristic, complemented
553#327C22×C5311yescharacteristic, complemented
554#327C22×C5311yescharacteristic, complemented
555#324C22×C5311yescharacteristic, complemented
556#324C22×C5311yescharacteristic, complemented
557#323C22×C5311yescharacteristic, complemented
558#323C22×C5311yescharacteristic, complemented
559C53#1844711yescharacteristic, direct product factor, Sylow
560C2×#41—21no—
561C2×#41D4×C5311yescharacteristic
562C22×Q8C23×C5311yescharacteristic
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4D4×C5311yescharacteristic
567C22×D4D4×C5311yescharacteristic
568C23×C4C23×C5311yescharacteristic
569C2×Q16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×M16—21no—
574C22×C8—21no—
575#127—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#125—21no—
581#125—21no—
582#124—21no—
583#124—21no—
584#124—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—21no—
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8D4×C5311yescharacteristic
609C22⋊Q8C23×C5311yescharacteristic
610#121—21no—
611#121—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—21no—
625#121D4×C5311yescharacteristic
626#121D4×C5311yescharacteristic
627#121D4×C5311yescharacteristic
628#121C23×C5311yescharacteristic
629#121C23×C5311yescharacteristic
630#121C23×C5311yescharacteristic
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635#120—21no—
636#120—21no—
637#120—21no—
638#120—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—21no—
647#117—21no—
648#117D4×C5311yescharacteristic
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4D4×C5311yescharacteristic
654C2×C4⋊C4D4×C5311yescharacteristic
655C2×C4⋊C4C23×C5311yescharacteristic
656C2×C4⋊C4C23×C5311yescharacteristic
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4D4×C5311yescharacteristic
665C2×C22⋊C4D4×C5311yescharacteristic
666C2×C22⋊C4C23×C5311yescharacteristic
667#107—21no—
668#107—21no—
669#107—21no—
670#106—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#103—21no—
675#103—21no—
676#102—21no—
677#102—21no—
678#102—21no—
679C22⋊C8—21no—
680C22⋊C8—21no—
681C22⋊C8C23×C5311yescharacteristic
682C22⋊C8C23×C5311yescharacteristic
683C22⋊C8C23×C5311yescharacteristic
684C22⋊C8C23×C5311yescharacteristic
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95C23×C5311yescharacteristic
690#95C23×C5311yescharacteristic
691C24—21no—
692C24—21no—
693C24C2×D4×C5311yescharacteristic
694C24C2×D4×C5311yescharacteristic
695#41—81no—
696#41—81no—
697#41—81no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—81no—
702C2×Q8C2×D4×C5311yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—81no—
726C2×D4—82no—
727C2×D4C2×D4×C5311yescharacteristic
728C2×D4C2×D4×C5311yescharacteristic
729C2×D4C2×D4×C5311yescharacteristic
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—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—81no—
742C22×C4C2×D4×C5311yescharacteristic
743C22×C4C2×D4×C5311yescharacteristic
744C22×C4C2×D4×C5311yescharacteristic
745C22×C4C2×D4×C5311yescharacteristic
746C22×C4C2×D4×C5311yescharacteristic
747C22×C4C2×D4×C5311yescharacteristic
748C22×C4C2×D4×C5311yescharacteristic
749C22×C4C2×D4×C5311yescharacteristic
750C22×C4C24×C5311yescharacteristic
751Q16—81no—
752SD16—81no—
753SD16—81no—
754SD16—81no—
755M16—81no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
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—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—41no—
777C4⋊C4—41no—
778C4⋊C4—81no—
779C4⋊C4—81no—
780C4⋊C4—81no—
781C4⋊C4C2×D4×C5311yescharacteristic
782C4⋊C4C2×D4×C5311yescharacteristic
783C4⋊C4C2×D4×C5311yescharacteristic
784C4⋊C4C2×D4×C5311yescharacteristic
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—21no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—41no—
811C22⋊C4—41no—
812C22⋊C4—81no—
813C22⋊C4—81no—
814C22⋊C4—81no—
815C42—21no—
816C42—21no—
817C42—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23#120×C5311yescharacteristic
837C23#120×C5311yescharacteristic
838C23C22×D4×C5311yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
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—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4#120×C5311yescharacteristic
906C2×C4#120×C5311yescharacteristic
907C2×C4C22×D4×C5311yescharacteristic
908C2×C4C22×D4×C5311yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×#120×C5311yescharacteristic
940C22C53×#57611yescharacteristic
941C22C53×#57711yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—81no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2C53×#301211yescharacteristic
967C2C53×#302211yescharacteristic
968C2C53×#302611yescharacteristic
subgroupG/H
center, socleC22×C53C2×#120
commutator, Frattini, cosocleC22×C4C24×C53
prime radicalC53×#3534C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C53 ◁ C23×C4×C53 ◁ G

Complements

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

NH ≅ G/Ntype
2. C53×#3193C2semidirect
3. C53×#3190C2semidirect
4. C53×#2814C2semidirect
5. C53×#1612C2semidirect
6. C53×#1610C2semidirect
7. C53×#1609C2semidirect
8. C53×#1607C2semidirect
9. C53×#1606C2semidirect
10. C53×#1604C2semidirect
11. C53×#1603C2semidirect
12. C53×#1601C2semidirect
13. C53×#1519C2semidirect
14. C53×#1513C2semidirect
15. C53×#1468C2semidirect
34. C2×C22⋊Q8×C53C22semidirect
38. C53×#483C22semidirect
40. C53×#480C22semidirect
41. C53×#480C22semidirect
47. C53×#451C22semidirect
50. C53×#448C22semidirect
51. C53×#448C22semidirect
52. C53×#407C22semidirect
53. C2×C22⋊C8×C53C22semidirect
55. C53×#398C22semidirect
57. C53×#397C22semidirect
59. C53×#395C22semidirect
61. C53×#393C22semidirect
62. C53×#380C22semidirect
63. C53×#328C22semidirect
64. C53×#328C22semidirect
67. C53×#327C22semidirect
68. C53×#327C22semidirect
69. C53×#327C22semidirect
70. C53×#327C22semidirect
71. C53×#324C22semidirect
72. C53×#324C22semidirect
73. C53×#323C22semidirect
74. C53×#323C22semidirect
428. #18447C53direct (N × H)
475. #3193C2×C53semidirect
476. #3190C2×C53semidirect
477. #2814C2×C53semidirect
478. #1612C2×C53semidirect
479. #1610C2×C53semidirect
480. #1609C2×C53semidirect
481. #1607C2×C53semidirect
482. #1606C2×C53semidirect
483. #1604C2×C53semidirect
484. #1603C2×C53semidirect
485. #1601C2×C53semidirect
486. #1519C2×C53semidirect
487. #1513C2×C53semidirect
488. #1468C2×C53semidirect
518. C2×C22⋊Q8C22×C53semidirect
522. #483C22×C53semidirect
524. #480C22×C53semidirect
525. #480C22×C53semidirect
531. #451C22×C53semidirect
534. #448C22×C53semidirect
535. #448C22×C53semidirect
536. #407C22×C53semidirect
537. C2×C22⋊C8C22×C53semidirect
539. #398C22×C53semidirect
541. #397C22×C53semidirect
543. #395C22×C53semidirect
545. #393C22×C53semidirect
546. #380C22×C53semidirect
547. #328C22×C53semidirect
548. #328C22×C53semidirect
551. #327C22×C53semidirect
552. #327C22×C53semidirect
553. #327C22×C53semidirect
554. #327C22×C53semidirect
555. #324C22×C53semidirect
556. #324C22×C53semidirect
557. #323C22×C53semidirect
558. #323C22×C53semidirect
559. C53#18447direct (N × H)

Maximal subgroups

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

subgroupindex
C53×#35342
C53×#31932
C53×#31902
C53×#28142
C53×#16122
C53×#16102
C53×#16092
C53×#16072
C53×#16062
C53×#16042
C53×#16032
C53×#16012
C53×#15192
C53×#15132
C53×#14682
#1844753