Finite Group Databasebeta

← C53×#15430 #27222942

Subgroups — C53×#15430 #27222942

Order 13568.

2010 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C53C211yesmaximal, characteristic
2C2×C53×#399C211yesmaximal, characteristic
3C2×C53×#398C211yesmaximal, characteristic, complemented
4C2×C53×#395C212yesmaximal, complemented
5C2×C53×#385C212yesmaximal
6C2×C53×#384C211yesmaximal, characteristic, complemented
7C53×#1445C211yesmaximal, characteristic, complemented
8C53×#1444C212yesmaximal, complemented
9C53×#1439C212yesmaximal
10C53×#1437C211yesmaximal, characteristic
11C53×#1436C211yesmaximal, characteristic, complemented
12C23×Q8×C53C2211yescharacteristic
13C24×C4×C53C2211yescharacteristic
14C2×C22⋊Q8×C53—24no—
15C2×C22⋊Q8×C53—24no—
16C2×C22⋊Q8×C53—24no—
17C22×C4⋊C4×C53C2211yescharacteristic
18C22×C4⋊C4×C53C2211yescharacteristic
19C22×C4⋊C4×C53C2212yes—
20C22×C4⋊C4×C53C2212yes—
21C22×C4⋊C4×C53C2212yes—
22C22×C4⋊C4×C53C2212yes—
23C22×C4⋊C4×C53C2211yescharacteristic
24C22×C4⋊C4×C53C2211yescharacteristic
25C22×C22⋊C4×C53C2211yescharacteristic
26C22×C22⋊C4×C53C2212yes—
27C22×C22⋊C4×C53C2211yescharacteristic
28C22×C22⋊C4×C53C2212yes—
29C22×C42×C53C2211yescharacteristic
30C53×#399—24no—
31C53×#398—24no—
32C53×#395—28no—
33C53×#385—28no—
34C53×#384—24no—
35C2×#95×C53C2212yes—
36C2×#95×C53C2211yescharacteristic
37C2×#95×C53C2212yes—
38C2×#95×C53C2211yescharacteristic
39C2×#95×C53C2212yes—
40C2×#95×C53C2212yes—
41C2×#95×C53C2212yes—
42C2×#95×C53C2212yes—
43C25×C53C2311yescharacteristic
44C22×Q8×C53—22no—
45C22×Q8×C53—22no—
46C22×Q8×C53—22no—
47C22×Q8×C53—24no—
48C22×Q8×C53—42no—
49C23×C4×C53—22no—
50C23×C4×C53—22no—
51C23×C4×C53—22no—
52C23×C4×C53—24no—
53C23×C4×C53—42no—
54C23×C4×C53C2312yes—
55C23×C4×C53C2311yescharacteristic
56C23×C4×C53C2311yescharacteristic
57C23×C4×C53C2311yescharacteristic
58C23×C4×C53C2312yes—
59C23×C4×C53C2311yescharacteristic
60C23×C4×C53C2312yes—
61C23×C4×C53C2311yescharacteristic
62C23×C4×C53C2311yescharacteristic
63C23×C4×C53C2312yes—
64C22⋊Q8×C53—232no—
65C2×C4⋊C4×C53—22no—
66C2×C4⋊C4×C53—22no—
67C2×C4⋊C4×C53—22no—
68C2×C4⋊C4×C53—22no—
69C2×C4⋊C4×C53—22no—
70C2×C4⋊C4×C53—22no—
71C2×C4⋊C4×C53—22no—
72C2×C4⋊C4×C53—24no—
73C2×C4⋊C4×C53—24no—
74C2×C4⋊C4×C53—22no—
75C2×C4⋊C4×C53—24no—
76C2×C4⋊C4×C53—24no—
77C2×C4⋊C4×C53—24no—
78C2×C4⋊C4×C53—24no—
79C2×C4⋊C4×C53—24no—
80C2×C4⋊C4×C53—24no—
81C2×C4⋊C4×C53—22no—
82C2×C4⋊C4×C53—24no—
83C2×C4⋊C4×C53—22no—
84C2×C4⋊C4×C53—42no—
85C2×C4⋊C4×C53—42no—
86C2×C4⋊C4×C53—42no—
87C2×C4⋊C4×C53D414yes—
88C2×C4⋊C4×C53D414yes—
89C2×C22⋊C4×C53—22no—
90C2×C22⋊C4×C53—24no—
91C2×C22⋊C4×C53—22no—
92C2×C22⋊C4×C53—22no—
93C2×C22⋊C4×C53—22no—
94C2×C22⋊C4×C53—22no—
95C2×C22⋊C4×C53—24no—
96C2×C22⋊C4×C53—24no—
97C2×C22⋊C4×C53—24no—
98C2×C22⋊C4×C53—42no—
99C2×C22⋊C4×C53D414yes—
100C2×C22⋊C4×C53Q818yescomplemented
101C2×C42×C53—22no—
102C2×C42×C53—24no—
103#95×C53—24no—
104#95×C53—24no—
105#95×C53—24no—
106#95×C53—22no—
107#95×C53—24no—
108#95×C53—22no—
109#95×C53—24no—
110#95×C53D418yes—
111C24×C53—21no—
112C24×C53—21no—
113C24×C53—22no—
114C24×C53—22no—
115C24×C53—22no—
116C24×C53—22no—
117C24×C53—22no—
118C24×C53C2×D412yes—
119C24×C53C2×Q814yes—
120C24×C53C2411yescharacteristic
121C2×Q8×C53—28no—
122C2×Q8×C53—48no—
123C2×Q8×C53—48no—
124C2×Q8×C53—44no—
125C2×Q8×C53—44no—
126C22×C4×C53—22no—
127C22×C4×C53—21no—
128C22×C4×C53—21no—
129C22×C4×C53—22no—
130C22×C4×C53—22no—
131C22×C4×C53—22no—
132C22×C4×C53—22no—
133C22×C4×C53—22no—
134C22×C4×C53—22no—
135C22×C4×C53—28no—
136C22×C4×C53—22no—
137C22×C4×C53—22no—
138C22×C4×C53—22no—
139C22×C4×C53—22no—
140C22×C4×C53—22no—
141C22×C4×C53—22no—
142C22×C4×C53—22no—
143C22×C4×C53—21no—
144C22×C4×C53—21no—
145C22×C4×C53—21no—
146C22×C4×C53—21no—
147C22×C4×C53—21no—
148C22×C4×C53—21no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53—22no—
152C22×C4×C53—22no—
153C22×C4×C53—22no—
154C22×C4×C53—22no—
155C22×C4×C53—22no—
156C22×C4×C53—22no—
157C22×C4×C53—22no—
158C22×C4×C53—22no—
159C22×C4×C53—22no—
160C22×C4×C53—22no—
161C22×C4×C53—22no—
162C22×C4×C53—22no—
163C22×C4×C53—22no—
164C22×C4×C53—22no—
165C22×C4×C53—22no—
166C22×C4×C53—22no—
167C22×C4×C53—22no—
168C22×C4×C53—22no—
169C22×C4×C53—22no—
170C22×C4×C53—22no—
171C22×C4×C53—48no—
172C22×C4×C53—48no—
173C22×C4×C53—44no—
174C22×C4×C53—44no—
175C22×C4×C53C2×D414yes—
176C22×C4×C53C2×D412yes—
177C22×C4×C53C2×D412yes—
178C22×C4×C53C2×D412yes—
179C22×C4×C53C2×D412yes—
180C22×C4×C53C2×D412yes—
181C22×C4×C53C2×D412yes—
182C22×C4×C53C2×D412yes—
183C22×C4×C53C2×D414yes—
184C22×C4×C53C2×D414yes—
185C22×C4×C53C2×D412yes—
186C22×C4×C53C2×Q814yes—
187C22×C4×C53C2×Q814yes—
188C22×C4×C53#4114yes—
189C4⋊C4×C53—28no—
190C4⋊C4×C53—28no—
191C4⋊C4×C53—28no—
192C4⋊C4×C53—48no—
193C4⋊C4×C53—48no—
194C4⋊C4×C53—48no—
195C4⋊C4×C53—44no—
196C4⋊C4×C53—48no—
197C22⋊C4×C53—28no—
198C22⋊C4×C53—28no—
199C22⋊C4×C53—216no—
200C22⋊C4×C53—48no—
201C42×C53—28no—
202C23×C53—22no—
203C23×C53—24no—
204C23×C53—22no—
205C23×C53—24no—
206C23×C53—24no—
207C23×C53—24no—
208C23×C53—24no—
209C23×C53—24no—
210C23×C53—24no—
211C23×C53—24no—
212C23×C53—41no—
213C23×C53—41no—
214C23×C53—41no—
215C23×C53—41no—
216C23×C53—42no—
217C23×C53—42no—
218C23×C53—42no—
219C23×C53—42no—
220C23×C53—42no—
221C23×C53—42no—
222C23×C53C4⋊Q814yes—
223C23×C53C22×D411yescharacteristic
224C23×C53C22×D411yescharacteristic
225C23×C53C22×D411yescharacteristic
226C23×C53C22×D412yes—
227C23×C53C22×Q812yes—
228C23×C53C2×#4112yes—
229C23×C53H(5,𝔽2)12yes—
230C23×C532−1+412yes—
231C23×C532−1+412yes—
232Q8×C53—416no—
233C2×C4×C53—22no—
234C2×C4×C53—22no—
235C2×C4×C53—24no—
236C2×C4×C53—22no—
237C2×C4×C53—22no—
238C2×C4×C53—24no—
239C2×C4×C53—24no—
240C2×C4×C53—24no—
241C2×C4×C53—24no—
242C2×C4×C53—24no—
243C2×C4×C53—24no—
244C2×C4×C53—24no—
245C2×C4×C53—24no—
246C2×C4×C53—24no—
247C2×C4×C53—22no—
248C2×C4×C53—22no—
249C2×C4×C53—22no—
250C2×C4×C53—22no—
251C2×C4×C53—24no—
252C2×C4×C53—24no—
253C2×C4×C53—24no—
254C2×C4×C53—24no—
255C2×C4×C53—24no—
256C2×C4×C53—24no—
257C2×C4×C53—24no—
258C2×C4×C53—24no—
259C2×C4×C53—24no—
260C2×C4×C53—24no—
261C2×C4×C53—416no—
262C2×C4×C53—41no—
263C2×C4×C53—41no—
264C2×C4×C53—41no—
265C2×C4×C53—41no—
266C2×C4×C53—42no—
267C2×C4×C53—41no—
268C2×C4×C53—41no—
269C2×C4×C53—41no—
270C2×C4×C53—41no—
271C2×C4×C53—42no—
272C2×C4×C53—42no—
273C2×C4×C53—42no—
274C2×C4×C53—42no—
275C2×C4×C53—42no—
276C2×C4×C53—42no—
277C2×C4×C53—42no—
278C2×C4×C53—42no—
279C2×C4×C53—42no—
280C2×C4×C53—42no—
281C2×C4×C53—42no—
282C2×C4×C53—42no—
283C2×C4×C53—42no—
284C2×C4×C53—42no—
285C2×C4×C53—42no—
286C2×C4×C53—42no—
287C2×C4×C53—42no—
288C2×C4×C53—42no—
289C2×C4×C53#12014yes—
290C2×C4×C53C22⋊Q818yescomplemented
291C2×C4×C53#12714yes—
292#15430C5311yesmaximal, characteristic, direct product factor, Sylow
293C22×C53—24no—
294C22×C53—28no—
295C22×C53—42no—
296C22×C53—44no—
297C22×C53—44no—
298C22×C53—42no—
299C22×C53—44no—
300C22×C53—44no—
301C22×C53—44no—
302C22×C53C2×#12011yescharacteristic
303C22×C53C2×C22⋊Q812yes—
304C22×C53#52511yescharacteristic
305C22×C53C2×#12711yescharacteristic
306C22×C53C2×C4⋊Q811yescharacteristic
307C22×C53#53511yescharacteristic
308C22×C53#53611yescharacteristic
309C22×C53#53612yes—
310C22×C53#53611yescharacteristic
311C22×C53#53912yes—
312C22×C53#54412yes—
313C22×C53D4212yes—
314C22×C53D4212yes—
315C22×C53#54712yes—
316C22×C53#54712yes—
317C22×C53#54712yes—
318C22×C53D4×Q812yes—
319C22×C53D4×Q812yes—
320C22×C53D4×Q812yes—
321C22×C53#55412yes—
322C22×C53#56312yes—
323C4×C53—24no—
324C4×C53—24no—
325C4×C53—28no—
326C4×C53—42no—
327C4×C53—44no—
328C4×C53—42no—
329C4×C53—42no—
330C4×C53—42no—
331C4×C53—44no—
332C4×C53—82no—
333C22×C22⋊Q8C2×C5311yescharacteristic
334C2×#399C2×C5311yescharacteristic
335C2×#398C2×C5311yescharacteristic, complemented
336C2×#395C2×C5312yescomplemented
337C2×#385C2×C5312yes—
338C2×#384C2×C5311yescharacteristic, complemented
339#1445C2×C5311yescharacteristic, complemented
340#1444C2×C5312yescomplemented
341#1439C2×C5312yes—
342#1437C2×C5311yescharacteristic
343#1436C2×C5311yescharacteristic, complemented
344C2×C53—44no—
345C2×C53#240611yescharacteristic
346C2×C53#243311yescharacteristic
347C2×C53#243411yescharacteristic
348C2×C53#244012yes—
349C2×C53#244912yes—
350C2×C53#254212yes—
351C2×C53#267712yes—
352C2×C53#268012yes—
353C2×C53#272012yes—
354C23×Q8C22×C5311yescharacteristic
355C24×C4C22×C5311yescharacteristic
356C2×C22⋊Q8—24no—
357C2×C22⋊Q8—24no—
358C2×C22⋊Q8—24no—
359C22×C4⋊C4C22×C5312yes—
360C22×C4⋊C4C22×C5311yescharacteristic
361C22×C4⋊C4C22×C5311yescharacteristic
362C22×C4⋊C4C22×C5312yes—
363C22×C4⋊C4C22×C5312yes—
364C22×C4⋊C4C22×C5312yes—
365C22×C4⋊C4C22×C5311yescharacteristic
366C22×C4⋊C4C22×C5311yescharacteristic
367C22×C22⋊C4C22×C5311yescharacteristic
368C22×C22⋊C4C22×C5312yes—
369C22×C22⋊C4C22×C5311yescharacteristic
370C22×C22⋊C4C22×C5312yes—
371C22×C42C22×C5311yescharacteristic
372#399—24no—
373#398—24no—
374#395—28no—
375#385—28no—
376#384—24no—
377C2×#95C22×C5312yes—
378C2×#95C22×C5312yes—
379C2×#95C22×C5311yescharacteristic
380C2×#95C22×C5312yes—
381C2×#95C22×C5311yescharacteristic
382C2×#95C22×C5312yes—
383C2×#95C22×C5312yes—
384C2×#95C22×C5312yes—
385C53#1543011yescharacteristic, direct product factor, Sylow
386C25C23×C5311yescharacteristic
387C22×Q8—22no—
388C22×Q8—22no—
389C22×Q8—22no—
390C22×Q8—24no—
391C22×Q8—42no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—24no—
396C23×C4—42no—
397C23×C4C23×C5312yes—
398C23×C4C23×C5311yescharacteristic
399C23×C4C23×C5311yescharacteristic
400C23×C4C23×C5311yescharacteristic
401C23×C4C23×C5312yes—
402C23×C4C23×C5311yescharacteristic
403C23×C4C23×C5312yes—
404C23×C4C23×C5311yescharacteristic
405C23×C4C23×C5311yescharacteristic
406C23×C4C23×C5312yes—
407C22⋊Q8—232no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4D4×C5314yes—
431C2×C4⋊C4D4×C5314yes—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—42no—
442C2×C22⋊C4D4×C5314yes—
443C2×C22⋊C4Q8×C5318yescomplemented
444C2×C42—22no—
445C2×C42—24no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—22no—
450#95—24no—
451#95—22no—
452#95—24no—
453#95D4×C5318yes—
454C24—21no—
455C24—21no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24C2×D4×C5312yes—
462C24C2×Q8×C5314yes—
463C24C24×C5311yescharacteristic
464C2×Q8—28no—
465C2×Q8—48no—
466C2×Q8—48no—
467C2×Q8—44no—
468C2×Q8—44no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—28no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—48no—
515C22×C4—48no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4C2×D4×C5314yes—
519C22×C4C2×D4×C5312yes—
520C22×C4C2×D4×C5312yes—
521C22×C4C2×D4×C5312yes—
522C22×C4C2×D4×C5312yes—
523C22×C4C2×D4×C5312yes—
524C22×C4C2×D4×C5312yes—
525C22×C4C2×D4×C5312yes—
526C22×C4C2×D4×C5314yes—
527C22×C4C2×D4×C5314yes—
528C22×C4C2×D4×C5312yes—
529C22×C4C2×Q8×C5314yes—
530C22×C4C2×Q8×C5314yes—
531C22×C4#41×C5314yes—
532C4⋊C4—28no—
533C4⋊C4—28no—
534C4⋊C4—28no—
535C4⋊C4—48no—
536C4⋊C4—48no—
537C4⋊C4—48no—
538C4⋊C4—44no—
539C4⋊C4—48no—
540C22⋊C4—28no—
541C22⋊C4—28no—
542C22⋊C4—216no—
543C22⋊C4—48no—
544C42—28no—
545C23—22no—
546C23—24no—
547C23—22no—
548C23—24no—
549C23—24no—
550C23—24no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—42no—
559C23—41no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23C4⋊Q8×C5314yes—
566C23C22×D4×C5311yescharacteristic
567C23C22×D4×C5311yescharacteristic
568C23C22×D4×C5311yescharacteristic
569C23C22×D4×C5312yes—
570C23C22×Q8×C5312yes—
571C23C2×#41×C5312yes—
572C23H(5,𝔽2)×C5312yes—
573C232−1+4×C5312yes—
574C232−1+4×C5312yes—
575Q8—416no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—416no—
605C2×C4—41no—
606C2×C4—42no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4#120×C5314yes—
633C2×C4C22⋊Q8×C5318yescomplemented
634C2×C4#127×C5314yes—
635C22—24no—
636C22—28no—
637C22—44no—
638C22—42no—
639C22—44no—
640C22—44no—
641C22—44no—
642C22—42no—
643C22—44no—
644C22C2×#120×C5311yescharacteristic
645C22C2×C22⋊Q8×C5312yes—
646C22C53×#52511yescharacteristic
647C22C2×#127×C5311yescharacteristic
648C22C2×C4⋊Q8×C5311yescharacteristic
649C22C53×#53511yescharacteristic
650C22C53×#53611yescharacteristic
651C22C53×#53612yes—
652C22C53×#53611yescharacteristic
653C22C53×#53912yes—
654C22C53×#54412yes—
655C22D42×C5312yes—
656C22D42×C5312yes—
657C22C53×#54712yes—
658C22C53×#54712yes—
659C22C53×#54712yes—
660C22D4×Q8×C5312yes—
661C22D4×Q8×C5312yes—
662C22D4×Q8×C5312yes—
663C22C53×#55412yes—
664C22C53×#56312yes—
665C4—24no—
666C4—28no—
667C4—24no—
668C4—44no—
669C4—42no—
670C4—42no—
671C4—42no—
672C4—44no—
673C4—42no—
674C4—82no—
675C2—44no—
676C2C53×#240611yescharacteristic
677C2C53×#243311yescharacteristic
678C2C53×#243411yescharacteristic
679C2C53×#244012yes—
680C2C53×#244912yes—
681C2C53×#254212yes—
682C2C53×#267712yes—
683C2C53×#268012yes—
684C2C53×#272012yes—
subgroupG/H
center, socleC24×C53C24
commutator, Frattini, cosocleC24C24×C53
prime radicalC25×C53C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C53 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C53×#398C2semidirect
4. C2×C53×#395C2semidirect
6. C2×C53×#384C2semidirect
7. C53×#1445C2semidirect
8. C53×#1444C2semidirect
11. C53×#1436C2semidirect
100. C2×C22⋊C4×C53Q8semidirect
290. C2×C4×C53C22⋊Q8semidirect
292. #15430C53direct (N × H)
335. C2×#398C2×C53semidirect
336. C2×#395C2×C53semidirect
338. C2×#384C2×C53semidirect
339. #1445C2×C53semidirect
340. #1444C2×C53semidirect
343. #1436C2×C53semidirect
385. C53#15430direct (N × H)
443. C2×C22⋊C4Q8×C53semidirect
633. C2×C4C22⋊Q8×C53semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C532
C2×C53×#3992
C2×C53×#3982
C2×C53×#3952
C2×C53×#3852
C2×C53×#3842
C53×#14452
C53×#14442
C53×#14392
C53×#14372
C53×#14362
#1543053