Finite Group Databasebeta

← C53×#13996 #27221508

Subgroups — C53×#13996 #27221508

Order 13568.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C53C211yesmaximal, characteristic
2C2×C53×#386C211yesmaximal, characteristic
3C2×C53×#386C211yesmaximal, characteristic
4C2×C53×#385C211yesmaximal, characteristic, complemented
5C2×C53×#381C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C53C211yesmaximal, characteristic, complemented
7C22×#95×C53C211yesmaximal, characteristic, complemented
8C53×#1445C212yesmaximal, complemented
9C53×#1439C212yesmaximal, complemented
10C53×#1437C212yesmaximal, complemented
11C53×C4⋊#95C212yesmaximal, complemented
12C23×D4×C53C2211yescharacteristic
13C24×C4×C53C2211yescharacteristic
14C24×C4×C53C2211yescharacteristic
15C24×C4×C53C2211yescharacteristic
16C2×#123×C53—24no—
17C2×#123×C53—24no—
18C2×#123×C53C418yescomplemented
19C22×C4⋊C4×C53C2212yes—
20C22×C4⋊C4×C53C2212yes—
21C22×C22⋊C4×C53C2211yescharacteristic
22C22×C22⋊C4×C53C2211yescharacteristic
23C22×C22⋊C4×C53C2212yes—
24C22×C22⋊C4×C53C2212yes—
25C22×C22⋊C4×C53C2211yescharacteristic
26C22×C22⋊C4×C53C2211yescharacteristic
27C22×C22⋊C4×C53C2211yescharacteristic
28C22×C42×C53C2212yes—
29C53×#386—24no—
30C53×#386—24no—
31C53×#385—24no—
32C53×#381—24no—
33C4×C22⋊C4×C53—24no—
34C2×#95×C53—24no—
35C2×#95×C53C2211yescharacteristic
36C2×#95×C53C2212yes—
37C2×#95×C53C2212yes—
38C2×#95×C53C2212yes—
39C2×#95×C53C2212yes—
40C2×#95×C53C2212yes—
41C2×#95×C53C2212yes—
42C2×#95×C53C2212yes—
43C2×#95×C53C2211yescharacteristic
44C25×C53C2311yescharacteristic
45C25×C53C2311yescharacteristic
46C22×D4×C53—22no—
47C22×D4×C53—22no—
48C22×D4×C53—22no—
49C22×D4×C53—22no—
50C22×D4×C53—22no—
51C22×D4×C53—22no—
52C22×D4×C53C2×C414yes—
53C23×C4×C53—22no—
54C23×C4×C53—22no—
55C23×C4×C53—22no—
56C23×C4×C53—22no—
57C23×C4×C53—22no—
58C23×C4×C53—22no—
59C23×C4×C53—22no—
60C23×C4×C53—22no—
61C23×C4×C53—22no—
62C23×C4×C53—24no—
63C23×C4×C53—24no—
64C23×C4×C53—22no—
65C23×C4×C53—22no—
66C23×C4×C53—42no—
67C23×C4×C53—42no—
68C23×C4×C53C2×C414yes—
69C23×C4×C53D414yes—
70C23×C4×C53C2311yescharacteristic
71C23×C4×C53C2311yescharacteristic
72C23×C4×C53C2312yes—
73C23×C4×C53C2311yescharacteristic
74C23×C4×C53C2312yes—
75C23×C4×C53C2311yescharacteristic
76C23×C4×C53C2312yes—
77C23×C4×C53C2312yes—
78C23×C4×C53C2311yescharacteristic
79#123×C53—232no—
80C2×C4⋊C4×C53—24no—
81C2×C4⋊C4×C53—24no—
82C2×C4⋊C4×C53—24no—
83C2×C4⋊C4×C53—24no—
84C2×C4⋊C4×C53—42no—
85C2×C4⋊C4×C53C2×C418yescomplemented
86C2×C22⋊C4×C53—22no—
87C2×C22⋊C4×C53—22no—
88C2×C22⋊C4×C53—22no—
89C2×C22⋊C4×C53—22no—
90C2×C22⋊C4×C53—22no—
91C2×C22⋊C4×C53—24no—
92C2×C22⋊C4×C53—24no—
93C2×C22⋊C4×C53—24no—
94C2×C22⋊C4×C53—22no—
95C2×C22⋊C4×C53—22no—
96C2×C22⋊C4×C53—24no—
97C2×C22⋊C4×C53—24no—
98C2×C22⋊C4×C53—42no—
99C2×C22⋊C4×C53—42no—
100C2×C22⋊C4×C53C2×C414yes—
101C2×C22⋊C4×C53C2×C418yescomplemented
102C2×C22⋊C4×C53D414yes—
103C2×C22⋊C4×C53D414yes—
104C2×C22⋊C4×C53D414yes—
105C2×C42×C53—24no—
106C2×C42×C53—24no—
107C2×C42×C53—42no—
108#95×C53—24no—
109#95×C53—24no—
110#95×C53—24no—
111#95×C53—24no—
112#95×C53—24no—
113#95×C53—24no—
114#95×C53—24no—
115#95×C53—22no—
116#95×C53—22no—
117C24×C53—22no—
118C24×C53—22no—
119C24×C53—22no—
120C24×C53—22no—
121C24×C53—21no—
122C24×C53—21no—
123C24×C53—21no—
124C24×C53—21no—
125C24×C53—22no—
126C24×C53—22no—
127C24×C53—21no—
128C24×C53—21no—
129C24×C53—22no—
130C24×C53—22no—
131C24×C53C22×C412yes—
132C24×C53C22×C412yes—
133C24×C53C2×D412yes—
134C24×C53C2×D412yes—
135C24×C53C2×D412yes—
136C24×C53C2×D412yes—
137C24×C53#4112yes—
138C24×C53#4112yes—
139C24×C53C2411yescharacteristic
140C2×D4×C53—28no—
141C2×D4×C53—28no—
142C2×D4×C53—28no—
143C2×D4×C53—44no—
144C2×D4×C53—44no—
145C2×D4×C53—44no—
146C2×D4×C53—44no—
147C22×C4×C53—21no—
148C22×C4×C53—22no—
149C22×C4×C53—22no—
150C22×C4×C53—21no—
151C22×C4×C53—22no—
152C22×C4×C53—22no—
153C22×C4×C53—22no—
154C22×C4×C53—28no—
155C22×C4×C53—28no—
156C22×C4×C53—28no—
157C22×C4×C53—28no—
158C22×C4×C53—28no—
159C22×C4×C53—22no—
160C22×C4×C53—22no—
161C22×C4×C53—21no—
162C22×C4×C53—22no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—22no—
166C22×C4×C53—22no—
167C22×C4×C53—22no—
168C22×C4×C53—22no—
169C22×C4×C53—22no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—22no—
173C22×C4×C53—22no—
174C22×C4×C53—22no—
175C22×C4×C53—22no—
176C22×C4×C53—22no—
177C22×C4×C53—21no—
178C22×C4×C53—22no—
179C22×C4×C53—22no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—22no—
183C22×C4×C53—22no—
184C22×C4×C53—22no—
185C22×C4×C53—22no—
186C22×C4×C53—22no—
187C22×C4×C53—28no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—22no—
195C22×C4×C53—22no—
196C22×C4×C53—22no—
197C22×C4×C53—22no—
198C22×C4×C53—44no—
199C22×C4×C53—48no—
200C22×C4×C53—48no—
201C22×C4×C53—48no—
202C22×C4×C53—48no—
203C22×C4×C53—44no—
204C22×C4×C53—44no—
205C22×C4×C53—44no—
206C22×C4×C53—44no—
207C22×C4×C53—44no—
208C22×C4×C53—44no—
209C22×C4×C53C22×C414yes—
210C22×C4×C53C22×C412yes—
211C22×C4×C53C22×C414yes—
212C22×C4×C53C2×D414yes—
213C22×C4×C53C2×D412yes—
214C22×C4×C53C2×D414yes—
215C22×C4×C53C2×D414yes—
216C22×C4×C53C2×D412yes—
217C22×C4×C53#4114yes—
218C22×C4×C53#4114yes—
219C4⋊C4×C53—216no—
220C4⋊C4×C53—48no—
221C22⋊C4×C53—28no—
222C22⋊C4×C53—216no—
223C22⋊C4×C53—48no—
224C22⋊C4×C53—44no—
225C22⋊C4×C53—44no—
226C22⋊C4×C53—44no—
227C22⋊C4×C53C22⋊C4116yescomplemented
228C42×C53—48no—
229C23×C53—24no—
230C23×C53—24no—
231C23×C53—22no—
232C23×C53—22no—
233C23×C53—24no—
234C23×C53—22no—
235C23×C53—22no—
236C23×C53—24no—
237C23×C53—24no—
238C23×C53—24no—
239C23×C53—24no—
240C23×C53—24no—
241C23×C53—24no—
242C23×C53—24no—
243C23×C53—24no—
244C23×C53—24no—
245C23×C53—22no—
246C23×C53—22no—
247C23×C53—22no—
248C23×C53—24no—
249C23×C53—24no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53—42no—
256C23×C53—41no—
257C23×C53—41no—
258C23×C53—41no—
259C23×C53—42no—
260C23×C53—42no—
261C23×C53—42no—
262C23×C53—42no—
263C23×C53—42no—
264C23×C53—42no—
265C23×C53—42no—
266C23×C53—42no—
267C23×C53—42no—
268C23×C53C2×C22⋊C414yes—
269C23×C53C4×D414yes—
270C23×C53C4×D414yes—
271C23×C53#12114yes—
272C23×C53#12114yes—
273C23×C53#12414yes—
274C23×C53#12714yes—
275C23×C53C23×C411yescharacteristic
276C23×C53C22×D411yescharacteristic
277C23×C53C22×D411yescharacteristic
278C23×C53C22×D411yescharacteristic
279C23×C53C22×D411yescharacteristic
280C23×C53C2×#4111yescharacteristic
281C23×C53C2×#4111yescharacteristic
282C23×C53C2×#4112yes—
283C23×C53C2×#4112yes—
284C23×C53H(5,𝔽2)12yes—
285C23×C532−1+412yes—
286D4×C53—416no—
287C2×C4×C53—24no—
288C2×C4×C53—24no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—24no—
292C2×C4×C53—24no—
293C2×C4×C53—24no—
294C2×C4×C53—24no—
295C2×C4×C53—24no—
296C2×C4×C53—24no—
297C2×C4×C53—24no—
298C2×C4×C53—22no—
299C2×C4×C53—24no—
300C2×C4×C53—24no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—24no—
305C2×C4×C53—22no—
306C2×C4×C53—24no—
307C2×C4×C53—22no—
308C2×C4×C53—24no—
309C2×C4×C53—24no—
310C2×C4×C53—24no—
311C2×C4×C53—24no—
312C2×C4×C53—416no—
313C2×C4×C53—416no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53—41no—
317C2×C4×C53—41no—
318C2×C4×C53—42no—
319C2×C4×C53—41no—
320C2×C4×C53—42no—
321C2×C4×C53—42no—
322C2×C4×C53—42no—
323C2×C4×C53—41no—
324C2×C4×C53—42no—
325C2×C4×C53—42no—
326C2×C4×C53—42no—
327C2×C4×C53—42no—
328C2×C4×C53—42no—
329C2×C4×C53—42no—
330C2×C4×C53—42no—
331C2×C4×C53—42no—
332C2×C4×C53—416no—
333C2×C4×C53—41no—
334C2×C4×C53—41no—
335C2×C4×C53—41no—
336C2×C4×C53—41no—
337C2×C4×C53—41no—
338C2×C4×C53—41no—
339C2×C4×C53—42no—
340C2×C4×C53—42no—
341C2×C4×C53—42no—
342C2×C4×C53—42no—
343C2×C4×C53C2×C22⋊C418yes—
344C2×C4×C53#12314yescomplemented
345#13996C5311yesmaximal, characteristic, direct product factor, Sylow
346C22×C53—24no—
347C22×C53—28no—
348C22×C53—28no—
349C22×C53—24no—
350C22×C53—24no—
351C22×C53—28no—
352C22×C53—28no—
353C22×C53—24no—
354C22×C53—24no—
355C22×C53—24no—
356C22×C53—42no—
357C22×C53—44no—
358C22×C53—44no—
359C22×C53—42no—
360C22×C53—42no—
361C22×C53—81no—
362C22×C53—81no—
363C22×C53—82no—
364C22×C53—82no—
365C22×C53—81no—
366C22×C53—81no—
367C22×C53#39018yes—
368C22×C53C22×C22⋊C411yescharacteristic
369C22×C53C2×C4×D411yescharacteristic
370C22×C53C2×C4×D411yescharacteristic
371C22×C53C4×#4112yes—
372C22×C53#52012yes—
373C22×C53C2×#12111yescharacteristic
374C22×C53C2×#12111yescharacteristic
375C22×C53C2×#12311yescharacteristic
376C22×C53#52511yescharacteristic
377C22×C53C2×#12411yescharacteristic
378C22×C53#52912yes—
379C22×C53C2×#12711yescharacteristic
380C22×C53#53411yescharacteristic
381C22×C53#53611yescharacteristic
382C22×C53#53912yes—
383C22×C53#54612yes—
384C22×C53#54612yes—
385C22×C53#54612yes—
386C22×C53#54712yes—
387C22×C53#54712yes—
388C22×C53#54712yes—
389C22×C53#55112yes—
390C22×C53#55212yes—
391C4×C53—28no—
392C4×C53—24no—
393C4×C53—42no—
394C4×C53—44no—
395C4×C53—44no—
396C4×C53—44no—
397C4×C53—42no—
398C4×C53—81no—
399C4×C53—81no—
400C22×#123C2×C5311yescharacteristic
401C2×#386C2×C5311yescharacteristic
402C2×#386C2×C5311yescharacteristic
403C2×#385C2×C5311yescharacteristic, complemented
404C2×#381C2×C5311yescharacteristic, complemented
405C2×C4×C22⋊C4C2×C5311yescharacteristic, complemented
406C22×#95C2×C5311yescharacteristic, complemented
407#1445C2×C5312yescomplemented
408#1439C2×C5312yescomplemented
409#1437C2×C5312yescomplemented
410C4⋊#95C2×C5312yescomplemented
411C2×C53—28no—
412C2×C53—82no—
413C2×C53C2×#39011yescharacteristic
414C2×C53C4×#12311yescharacteristic
415C2×C53#232211yescharacteristic
416C2×C53#233912yes—
417C2×C53#235912yes—
418C2×C53#241211yescharacteristic
419C2×C53#241311yescharacteristic
420C2×C53#242512yes—
421C2×C53#248812yes—
422C2×C53#250111yescharacteristic
423C2×C53#253911yescharacteristic
424C23×D4C22×C5311yescharacteristic
425C24×C4C22×C5311yescharacteristic
426C24×C4C22×C5311yescharacteristic
427C24×C4C22×C5311yescharacteristic
428C2×#123—24no—
429C2×#123—24no—
430C2×#123C4×C5318yescomplemented
431C22×C4⋊C4C22×C5312yes—
432C22×C4⋊C4C22×C5312yes—
433C22×C22⋊C4C22×C5311yescharacteristic
434C22×C22⋊C4C22×C5311yescharacteristic
435C22×C22⋊C4C22×C5312yes—
436C22×C22⋊C4C22×C5312yes—
437C22×C22⋊C4C22×C5311yescharacteristic
438C22×C22⋊C4C22×C5311yescharacteristic
439C22×C22⋊C4C22×C5311yescharacteristic
440C22×C42C22×C5312yes—
441#386—24no—
442#386—24no—
443#385—24no—
444#381—24no—
445C4×C22⋊C4—24no—
446C2×#95—24no—
447C2×#95C22×C5311yescharacteristic
448C2×#95C22×C5312yes—
449C2×#95C22×C5312yes—
450C2×#95C22×C5312yes—
451C2×#95C22×C5312yes—
452C2×#95C22×C5312yes—
453C2×#95C22×C5312yes—
454C2×#95C22×C5312yes—
455C2×#95C22×C5311yescharacteristic
456C53#1399611yescharacteristic, direct product factor, Sylow
457C25C23×C5311yescharacteristic
458C25C23×C5311yescharacteristic
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4C2×C4×C5314yes—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—24no—
476C23×C4—24no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—42no—
480C23×C4—42no—
481C23×C4C2×C4×C5314yes—
482C23×C4D4×C5314yes—
483C23×C4C23×C5311yescharacteristic
484C23×C4C23×C5311yescharacteristic
485C23×C4C23×C5312yes—
486C23×C4C23×C5311yescharacteristic
487C23×C4C23×C5312yes—
488C23×C4C23×C5311yescharacteristic
489C23×C4C23×C5312yes—
490C23×C4C23×C5312yes—
491C23×C4C23×C5311yescharacteristic
492#123—232no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—42no—
498C2×C4⋊C4C2×C4×C5318yescomplemented
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4C2×C4×C5314yes—
514C2×C22⋊C4C2×C4×C5318yescomplemented
515C2×C22⋊C4D4×C5314yes—
516C2×C22⋊C4D4×C5314yes—
517C2×C22⋊C4D4×C5314yes—
518C2×C42—24no—
519C2×C42—24no—
520C2×C42—42no—
521#95—24no—
522#95—24no—
523#95—24no—
524#95—24no—
525#95—24no—
526#95—24no—
527#95—24no—
528#95—22no—
529#95—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—21no—
541C24—21no—
542C24—22no—
543C24—22no—
544C24C22×C4×C5312yes—
545C24C22×C4×C5312yes—
546C24C2×D4×C5312yes—
547C24C2×D4×C5312yes—
548C24C2×D4×C5312yes—
549C24C2×D4×C5312yes—
550C24#41×C5312yes—
551C24#41×C5312yes—
552C24C24×C5311yescharacteristic
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—28no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—44no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
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—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—28no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—44no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4C22×C4×C5314yes—
623C22×C4C22×C4×C5312yes—
624C22×C4C22×C4×C5314yes—
625C22×C4C2×D4×C5314yes—
626C22×C4C2×D4×C5312yes—
627C22×C4C2×D4×C5314yes—
628C22×C4C2×D4×C5314yes—
629C22×C4C2×D4×C5312yes—
630C22×C4#41×C5314yes—
631C22×C4#41×C5314yes—
632C4⋊C4—216no—
633C4⋊C4—48no—
634C22⋊C4—28no—
635C22⋊C4—216no—
636C22⋊C4—48no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4C22⋊C4×C53116yescomplemented
641C42—48no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—42no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23C2×C22⋊C4×C5314yes—
682C23C4×D4×C5314yes—
683C23C4×D4×C5314yes—
684C23#121×C5314yes—
685C23#121×C5314yes—
686C23#124×C5314yes—
687C23#127×C5314yes—
688C23C23×C4×C5311yescharacteristic
689C23C22×D4×C5311yescharacteristic
690C23C22×D4×C5311yescharacteristic
691C23C22×D4×C5311yescharacteristic
692C23C22×D4×C5311yescharacteristic
693C23C2×#41×C5311yescharacteristic
694C23C2×#41×C5311yescharacteristic
695C23C2×#41×C5312yes—
696C23C2×#41×C5312yes—
697C23H(5,𝔽2)×C5312yes—
698C232−1+4×C5312yes—
699D4—416no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—416no—
726C2×C4—416no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—416no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4C2×C22⋊C4×C5318yes—
757C2×C4#123×C5314yescomplemented
758C22—28no—
759C22—28no—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—24no—
764C22—28no—
765C22—28no—
766C22—24no—
767C22—24no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—44no—
772C22—44no—
773C22—82no—
774C22—82no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22C53×#39018yes—
780C22C22×C22⋊C4×C5311yescharacteristic
781C22C2×C4×D4×C5311yescharacteristic
782C22C2×C4×D4×C5311yescharacteristic
783C22C4×#41×C5312yes—
784C22C53×#52012yes—
785C22C2×#121×C5311yescharacteristic
786C22C2×#121×C5311yescharacteristic
787C22C2×#123×C5311yescharacteristic
788C22C53×#52511yescharacteristic
789C22C2×#124×C5311yescharacteristic
790C22C53×#52912yes—
791C22C2×#127×C5311yescharacteristic
792C22C53×#53411yescharacteristic
793C22C53×#53611yescharacteristic
794C22C53×#53912yes—
795C22C53×#54612yes—
796C22C53×#54612yes—
797C22C53×#54612yes—
798C22C53×#54712yes—
799C22C53×#54712yes—
800C22C53×#54712yes—
801C22C53×#55112yes—
802C22C53×#55212yes—
803C4—28no—
804C4—24no—
805C4—44no—
806C4—44no—
807C4—44no—
808C4—42no—
809C4—42no—
810C4—81no—
811C4—81no—
812C2—28no—
813C2—82no—
814C2C2×C53×#39011yescharacteristic
815C2C4×#123×C5311yescharacteristic
816C2C53×#232211yescharacteristic
817C2C53×#233912yes—
818C2C53×#235912yes—
819C2C53×#241211yescharacteristic
820C2C53×#241311yescharacteristic
821C2C53×#242512yes—
822C2C53×#248812yes—
823C2C53×#250111yescharacteristic
824C2C53×#253911yescharacteristic
subgroupG/H
center, socleC24×C53C24
commutatorC23C23×C4×C53
Frattini, cosocleC24C24×C53
prime radicalC23×D4×C53C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C53 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C53×#385C2semidirect
5. C2×C53×#381C2semidirect
6. C2×C4×C22⋊C4×C53C2semidirect
7. C22×#95×C53C2semidirect
8. C53×#1445C2semidirect
9. C53×#1439C2semidirect
10. C53×#1437C2semidirect
11. C53×C4⋊#95C2semidirect
18. C2×#123×C53C4semidirect
85. C2×C4⋊C4×C53C2×C4semidirect
101. C2×C22⋊C4×C53C2×C4semidirect
227. C22⋊C4×C53C22⋊C4semidirect
344. C2×C4×C53#123semidirect
345. #13996C53direct (N × H)
403. C2×#385C2×C53semidirect
404. C2×#381C2×C53semidirect
405. C2×C4×C22⋊C4C2×C53semidirect
406. C22×#95C2×C53semidirect
407. #1445C2×C53semidirect
408. #1439C2×C53semidirect
409. #1437C2×C53semidirect
410. C4⋊#95C2×C53semidirect
430. C2×#123C4×C53semidirect
456. C53#13996direct (N × H)
498. C2×C4⋊C4C2×C4×C53semidirect
514. C2×C22⋊C4C2×C4×C53semidirect
640. C22⋊C4C22⋊C4×C53semidirect
757. C2×C4#123×C53semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C532
C2×C53×#3862
C2×C53×#3852
C2×C53×#3812
C2×C4×C22⋊C4×C532
C22×#95×C532
C53×#14452
C53×#14392
C53×#14372
C53×C4⋊#952
#1399653