Finite Group Databasebeta

← #27307218

Subgroups — #27307218

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×#13133201C211yesmaximal, characteristic
2C2×#16810502C211yesmaximal, characteristic
3C2×#16810500C211yesmaximal, characteristic
4C2×#16810484C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic53C211yesmaximal, characteristic, complemented
6C22×#13133124C211yesmaximal, characteristic, complemented
7#20272984C212yesmaximal, complemented
8#20272957C212yesmaximal, complemented
9#20272951C212yesmaximal, complemented
10#20272944C212yesmaximal, complemented
11C2×C53×#385C211yesmaximal, characteristic, complemented
12C23×C22⋊D53C2211yescharacteristic
13C24×Dic53C2211yescharacteristic
14C24×Dic53C2211yescharacteristic
15C2×#13133201—24no—
16C2×#13133201—24no—
17C2×#13133201C418yescomplemented
18C22×C4⋊Dic53C2212yes—
19C22×C22⋊Dic53C2211yescharacteristic
20C22×#11719921C2211yescharacteristic
21C22×#11719921C2212yes—
22C22×#11719921C2212yes—
23C22×#11719921C2211yescharacteristic
24C22×C4×Dic53C2212yes—
25#16810502—24no—
26#16810500—24no—
27#16810484—24no—
28C22⋊C4×Dic53—24no—
29C2×#13133124—24no—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C2×#13133124C2212yes—
37C2×#13133124C2211yescharacteristic
38C24×C4×C53C2211yescharacteristic
39C22×C4⋊C4×C53C2212yes—
40C22×C22⋊C4×C53C2211yescharacteristic
41C22×C22⋊C4×C53C2211yescharacteristic
42C53×#385—24no—
43C2×#95×C53C2212yes—
44C24×D53C2311yescharacteristic
45C22×C22⋊D53—22no—
46C22×C22⋊D53—22no—
47C22×C22⋊D53—22no—
48C22×C22⋊D53—22no—
49C22×C22⋊D53—22no—
50C22×C22⋊D53—22no—
51C22×C22⋊D53C2×C414yes—
52C23×Dic53—22no—
53C23×Dic53—22no—
54C23×Dic53—22no—
55C23×Dic53—22no—
56C23×Dic53—22no—
57C23×Dic53—22no—
58C23×Dic53—22no—
59C23×Dic53—22no—
60C23×Dic53—24no—
61C23×Dic53—42no—
62C23×Dic53C2×C414yes—
63C23×Dic53D414yes—
64C23×Dic53C2312yes—
65C23×Dic53C2311yescharacteristic
66C23×Dic53C2312yes—
67C23×Dic53C2311yescharacteristic
68C23×Dic53C2311yescharacteristic
69#13133201—232no—
70C2×C4⋊Dic53—24no—
71C2×C4⋊Dic53—24no—
72C2×C4⋊Dic53C2×C418yescomplemented
73C2×C22⋊Dic53—22no—
74C2×C22⋊Dic53—22no—
75C2×C22⋊Dic53D414yes—
76C2×#11719921—24no—
77C2×#11719921—24no—
78C2×#11719921—24no—
79C2×#11719921—22no—
80C2×#11719921—22no—
81C2×#11719921—24no—
82C2×#11719921—24no—
83C2×#11719921—42no—
84C2×#11719921—42no—
85C2×#11719921C2×C418yescomplemented
86C2×C4×Dic53—24no—
87C2×C4×Dic53—24no—
88C2×C4×Dic53—42no—
89#13133124—24no—
90#13133124—22no—
91#13133124—22no—
92#13133124—24no—
93#13133124—24no—
94#13133124—24no—
95#13133124—24no—
96#13133124—24no—
97C25×C53C2311yescharacteristic
98C23×C4×C53—22no—
99C23×C4×C53—24no—
100C23×C4×C53—22no—
101C23×C4×C53—22no—
102C23×C4×C53—42no—
103C23×C4×C53C2311yescharacteristic
104C23×C4×C53C2311yescharacteristic
105C23×C4×C53C2312yes—
106C23×C4×C53C2312yes—
107C2×C4⋊C4×C53—24no—
108C2×C4⋊C4×C53—24no—
109C2×C4⋊C4×C53—42no—
110C2×C22⋊C4×C53—22no—
111C2×C22⋊C4×C53—22no—
112C2×C22⋊C4×C53—22no—
113C2×C22⋊C4×C53C2×C414yes—
114C2×C22⋊C4×C53D414yes—
115C2×C22⋊C4×C53D414yes—
116#95×C53—24no—
117C24×C53—22no—
118C24×C53—22no—
119C24×C53—22no—
120C24×C53—22no—
121C24×C53C22×C412yes—
122C24×C53C2×D412yes—
123C24×C53C2×D412yes—
124C24×C53C2×D412yes—
125C24×C53C2×D412yes—
126C24×C53#4112yes—
127C24×C53#4112yes—
128C24×C53C2411yescharacteristic
129C23×D53—21no—
130C23×D53—21no—
131C23×D53—21no—
132C23×D53—21no—
133C23×D53—22no—
134C23×D53—22no—
135C23×D53—21no—
136C23×D53—21no—
137C23×D53—22no—
138C23×D53—22no—
139C23×D53C22×C412yes—
140C22×C4×C53—22no—
141C22×C4×C53—22no—
142C22×C4×C53—22no—
143C22×C4×C53—22no—
144C22×C4×C53—28no—
145C22×C4×C53—22no—
146C22×C4×C53—22no—
147C22×C4×C53—22no—
148C22×C4×C53—22no—
149C22×C4×C53—22no—
150C22×C4×C53—22no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53—21no—
155C22×C4×C53—21no—
156C22×C4×C53—21no—
157C22×C4×C53—22no—
158C22×C4×C53—22no—
159C22×C4×C53—22no—
160C22×C4×C53—22no—
161C22×C4×C53—48no—
162C22×C4×C53—48no—
163C22×C4×C53—44no—
164C22×C4×C53—44no—
165C22×C4×C53C22×C414yes—
166C22×C4×C53C2×D414yes—
167C22×C4×C53C2×D414yes—
168C22×C4×C53#4114yes—
169C2×C22⋊D53—28no—
170C2×C22⋊D53—28no—
171C2×C22⋊D53—28no—
172C2×C22⋊D53—44no—
173C2×C22⋊D53—44no—
174C2×C22⋊D53—44no—
175C2×C22⋊D53—44no—
176C22×Dic53—21no—
177C22×Dic53—21no—
178C22×Dic53—22no—
179C22×Dic53—28no—
180C22×Dic53—28no—
181C22×Dic53—28no—
182C22×Dic53—28no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—21no—
186C22×Dic53—21no—
187C22×Dic53—21no—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—21no—
192C22×Dic53—21no—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53—22no—
196C22×Dic53—22no—
197C22×Dic53—22no—
198C22×Dic53—21no—
199C22×Dic53—22no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—22no—
203C22×Dic53—22no—
204C22×Dic53—22no—
205C22×Dic53—28no—
206C22×Dic53—44no—
207C22×Dic53—48no—
208C22×Dic53—48no—
209C22×Dic53—44no—
210C22×Dic53—44no—
211C22×Dic53—44no—
212C22×Dic53—44no—
213C22×Dic53C22×C414yes—
214C22×Dic53C22×C412yes—
215C22×Dic53C2×D414yes—
216C22×Dic53C2×D412yes—
217C22×Dic53C2×D412yes—
218C22×Dic53#4114yes—
219C4⋊C4×C53—48no—
220C22⋊C4×C53—44no—
221C22⋊C4×C53C22⋊C4116yescomplemented
222C22⋊Dic53—28no—
223#11719921—216no—
224#11719921—48no—
225#11719921—44no—
226#11719921—44no—
227C4⋊Dic53—216no—
228C4×Dic53—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×C53C2×C22⋊C414yes—
246C23×C53C4×D414yes—
247C23×C53C4×D414yes—
248C23×C53#12114yes—
249C23×C53#12114yes—
250C23×C53#12414yes—
251C23×C53#12714yes—
252C23×C53C23×C411yescharacteristic
253C23×C53C22×D411yescharacteristic
254C23×C53C22×D411yescharacteristic
255C23×C53C22×D411yescharacteristic
256C23×C53C22×D411yescharacteristic
257C23×C53C2×#4112yes—
258C23×C53C2×#4112yes—
259C23×C53C2×#4111yescharacteristic
260C23×C53C2×#4111yescharacteristic
261C23×C53H(5,𝔽2)12yes—
262C23×C532−1+412yes—
263C22×D53—22no—
264C22×D53—22no—
265C22×D53—22no—
266C22×D53—24no—
267C22×D53—24no—
268C22×D53—41no—
269C22×D53—41no—
270C22×D53—41no—
271C22×D53—41no—
272C22×D53—41no—
273C22×D53—42no—
274C22×D53—41no—
275C22×D53—41no—
276C22×D53—41no—
277C22×D53—42no—
278C22×D53—42no—
279C22×D53—42no—
280C22×D53—42no—
281C22×D53—42no—
282C22×D53—42no—
283C22×D53—42no—
284C22×D53—42no—
285C22×D53—42no—
286C2×C4×C53—24no—
287C2×C4×C53—24no—
288C2×C4×C53—24no—
289C2×C4×C53—24no—
290C2×C4×C53—24no—
291C2×C4×C53—24no—
292C2×C4×C53—24no—
293C2×C4×C53—24no—
294C2×C4×C53—24no—
295C2×C4×C53—416no—
296C2×C4×C53—42no—
297C2×C4×C53—42no—
298C2×C4×C53—42no—
299C2×C4×C53—42no—
300C2×C4×C53—41no—
301C2×C4×C53—41no—
302C2×C4×C53—41no—
303C2×C4×C53—41no—
304C2×C4×C53—41no—
305C2×C4×C53—41no—
306C2×C4×C53—42no—
307C2×C4×C53—42no—
308C2×C4×C53—42no—
309C2×C4×C53—42no—
310C2×C4×C53C2×C22⋊C418yes—
311C22⋊D53—416no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—24no—
315C2×Dic53—24no—
316C2×Dic53—24no—
317C2×Dic53—22no—
318C2×Dic53—24no—
319C2×Dic53—24no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—24no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—24no—
327C2×Dic53—24no—
328C2×Dic53—416no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53—41no—
332C2×Dic53—41no—
333C2×Dic53—42no—
334C2×Dic53—41no—
335C2×Dic53—42no—
336C2×Dic53—42no—
337C2×Dic53—41no—
338C2×Dic53—42no—
339C2×Dic53—42no—
340C2×Dic53—42no—
341C2×Dic53—42no—
342C2×Dic53—42no—
343C2×Dic53—416no—
344C2×Dic53#12314yescomplemented
345#13996—531nomaximal, 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#39018yes—
357C22×C53C22×C22⋊C411yescharacteristic
358C22×C53C2×C4×D411yescharacteristic
359C22×C53C2×C4×D411yescharacteristic
360C22×C53C4×#4112yes—
361C22×C53#52012yes—
362C22×C53C2×#12111yescharacteristic
363C22×C53C2×#12111yescharacteristic
364C22×C53C2×#12311yescharacteristic
365C22×C53#52511yescharacteristic
366C22×C53C2×#12411yescharacteristic
367C22×C53#52912yes—
368C22×C53C2×#12711yescharacteristic
369C22×C53#53411yescharacteristic
370C22×C53#53611yescharacteristic
371C22×C53#53912yes—
372C22×C53#54612yes—
373C22×C53#54612yes—
374C22×C53#54612yes—
375C22×C53#54712yes—
376C22×C53#54712yes—
377C22×C53#54712yes—
378C22×C53#55112yes—
379C22×C53#55212yes—
380C2×D53—42no—
381C2×D53—44no—
382C2×D53—44no—
383C2×D53—42no—
384C2×D53—42no—
385C2×D53—81no—
386C2×D53—81no—
387C2×D53—82no—
388C2×D53—82no—
389C2×D53—81no—
390C2×D53—81no—
391C4×C53—28no—
392C4×C53—44no—
393C4×C53—81no—
394C4×C53—81no—
395Dic53—24no—
396Dic53—42no—
397Dic53—44no—
398Dic53—44no—
399Dic53—42no—
400C22×#123—531no—
401C2×#386—531no—
402C2×#386—531no—
403C2×#385D5311yescharacteristic, complemented
404C2×#381—531no—
405C2×C4×C22⋊C4—531no—
406C22×#95—531no—
407#1445—532no—
408#1439—532no—
409#1437—532no—
410C4⋊#95—532no—
411C2×C53—28no—
412C2×C53C2×#39011yescharacteristic
413C2×C53C4×#12311yescharacteristic
414C2×C53#232211yescharacteristic
415C2×C53#233912yes—
416C2×C53#235912yes—
417C2×C53#241211yescharacteristic
418C2×C53#241311yescharacteristic
419C2×C53#242512yes—
420C2×C53#248812yes—
421C2×C53#250111yescharacteristic
422C2×C53#253911yescharacteristic
423D53—82no—
424C23×D4—531no—
425C24×C4—531no—
426C24×C4—531no—
427C24×C4C2×D5311yescharacteristic
428C2×#123—538no—
429C2×#123—1064no—
430C2×#123—1064no—
431C22×C4⋊C4—532no—
432C22×C4⋊C4C2×D5312yes—
433C22×C22⋊C4—531no—
434C22×C22⋊C4—532no—
435C22×C22⋊C4—531no—
436C22×C22⋊C4—532no—
437C22×C22⋊C4—531no—
438C22×C22⋊C4C2×D5311yescharacteristic
439C22×C22⋊C4C2×D5311yescharacteristic
440C22×C42—532no—
441#386—1064no—
442#386—1064no—
443#385—24no—
444#381—1064no—
445C4×C22⋊C4—1064no—
446C2×#95—531no—
447C2×#95—532no—
448C2×#95—532no—
449C2×#95—532no—
450C2×#95—532no—
451C2×#95—532no—
452C2×#95—532no—
453C2×#95—531no—
454C2×#95—1064no—
455C2×#95C2×D5312yes—
456C53#1399611yescharacteristic, complemented, Sylow
457C25—531no—
458C25C22×D5311yescharacteristic
459C22×D4—534no—
460C22×D4—1062no—
461C22×D4—1062no—
462C22×D4—1062no—
463C22×D4—1062no—
464C22×D4—1062no—
465C22×D4—1062no—
466C23×C4—22no—
467C23×C4—24no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—42no—
471C23×C4—531no—
472C23×C4—534no—
473C23×C4—532no—
474C23×C4—532no—
475C23×C4—531no—
476C23×C4—531no—
477C23×C4—534no—
478C23×C4—1064no—
479C23×C4—1062no—
480C23×C4—1062no—
481C23×C4—1062no—
482C23×C4—1062no—
483C23×C4—1062no—
484C23×C4—1062no—
485C23×C4—1062no—
486C23×C4—1062no—
487C23×C4—2122no—
488C23×C4C22×D5311yescharacteristic
489C23×C4C22×D5311yescharacteristic
490C23×C4C22×D5312yes—
491C23×C4C22×D5312yes—
492#123—10632no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—42no—
496C2×C4⋊C4—538no—
497C2×C4⋊C4—1064no—
498C2×C4⋊C4—1064no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—534no—
503C2×C22⋊C4—538no—
504C2×C22⋊C4—1062no—
505C2×C22⋊C4—1062no—
506C2×C22⋊C4—1064no—
507C2×C22⋊C4—1064no—
508C2×C22⋊C4—1064no—
509C2×C22⋊C4—1064no—
510C2×C22⋊C4—1062no—
511C2×C22⋊C4—1062no—
512C2×C22⋊C4—1064no—
513C2×C22⋊C4—2122no—
514C2×C22⋊C4—2122no—
515C2×C22⋊C4C4×D5314yes—
516C2×C22⋊C4D21214yes—
517C2×C22⋊C4C22⋊D5314yes—
518C2×C42—1064no—
519C2×C42—1064no—
520C2×C42—2122no—
521#95—24no—
522#95—1064no—
523#95—1064no—
524#95—1064no—
525#95—1064no—
526#95—1064no—
527#95—1062no—
528#95—1062no—
529#95—1064no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—532no—
535C24—1061no—
536C24—1061no—
537C24—1061no—
538C24—1061no—
539C24—1062no—
540C24—1062no—
541C24—1061no—
542C24—1061no—
543C24—1062no—
544C24—1062no—
545C24C2×C4×D5312yes—
546C24C2×D21212yes—
547C24D4×D5312yes—
548C24D4×D5312yes—
549C24#1171994912yes—
550C24#1171994912yes—
551C24C2×C22⋊D5312yes—
552C24C23×D5311yescharacteristic
553C2×D4—1068no—
554C2×D4—1068no—
555C2×D4—1068no—
556C2×D4—2124no—
557C2×D4—2124no—
558C2×D4—2124no—
559C2×D4—2124no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—28no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—532no—
586C22×C4—534no—
587C22×C4—534no—
588C22×C4—532no—
589C22×C4—534no—
590C22×C4—532no—
591C22×C4—1068no—
592C22×C4—1061no—
593C22×C4—1061no—
594C22×C4—1062no—
595C22×C4—1068no—
596C22×C4—1068no—
597C22×C4—1068no—
598C22×C4—1068no—
599C22×C4—1062no—
600C22×C4—1062no—
601C22×C4—1061no—
602C22×C4—1061no—
603C22×C4—1062no—
604C22×C4—1061no—
605C22×C4—1061no—
606C22×C4—1062no—
607C22×C4—1062no—
608C22×C4—1061no—
609C22×C4—1062no—
610C22×C4—1062no—
611C22×C4—1062no—
612C22×C4—1062no—
613C22×C4—1062no—
614C22×C4—1062no—
615C22×C4—1061no—
616C22×C4—1061no—
617C22×C4—1061no—
618C22×C4—1062no—
619C22×C4—1062no—
620C22×C4—1062no—
621C22×C4—2124no—
622C22×C4—2128no—
623C22×C4—2128no—
624C22×C4—2124no—
625C22×C4—2124no—
626C22×C4—2124no—
627C22×C4—2124no—
628C22×C4C2×C4×D5314yes—
629C22×C4C2×D21214yes—
630C22×C4#1171994714yes—
631C22×C4C2×C22⋊D5314yes—
632C4⋊C4—48no—
633C4⋊C4—10616no—
634C22⋊C4—44no—
635C22⋊C4—1068no—
636C22⋊C4—10616no—
637C22⋊C4—2128no—
638C22⋊C4—2124no—
639C22⋊C4—2124no—
640C22⋊C4#11719921116yescomplemented
641C42—2128no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—22no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—1062no—
659C23—1062no—
660C23—1062no—
661C23—1064no—
662C23—1064no—
663C23—2122no—
664C23—2122no—
665C23—2122no—
666C23—2122no—
667C23—2122no—
668C23—2122no—
669C23—2122no—
670C23—2121no—
671C23—2121no—
672C23—2121no—
673C23—2121no—
674C23—2121no—
675C23—2122no—
676C23—2121no—
677C23—2121no—
678C23—2121no—
679C23—2122no—
680C23—2122no—
681C23C2×#1171992114yes—
682C23#1313317914yes—
683C23#1313317914yes—
684C23#1313319214yes—
685C23#1313319214yes—
686C23#1313320614yes—
687C23#1313321314yes—
688C23C22×C4×D5311yescharacteristic
689C23C2×D4×D5311yescharacteristic
690C23C2×D4×D5311yescharacteristic
691C23C22×C22⋊D5311yescharacteristic
692C23C22×D21211yescharacteristic
693C23#41×D5312yes—
694C23C2×#1171994712yes—
695C23C2×#1171994911yescharacteristic
696C23C2×#1171994911yescharacteristic
697C23#1313326212yes—
698C23#1313326412yes—
699D4—21216no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—416no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—534no—
725C2×C4—1064no—
726C2×C4—1064no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1064no—
730C2×C4—1064no—
731C2×C4—1062no—
732C2×C4—1064no—
733C2×C4—1064no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—1064no—
737C2×C4—1062no—
738C2×C4—1062no—
739C2×C4—1062no—
740C2×C4—1064no—
741C2×C4—21216no—
742C2×C4—2122no—
743C2×C4—2122no—
744C2×C4—2122no—
745C2×C4—21216no—
746C2×C4—2122no—
747C2×C4—2122no—
748C2×C4—2122no—
749C2×C4—2121no—
750C2×C4—2121no—
751C2×C4—2122no—
752C2×C4—2121no—
753C2×C4—2122no—
754C2×C4—2122no—
755C2×C4—2121no—
756C2×C4—2122no—
757C2×C4C2×#1171992118yes—
758C22—28no—
759C22—28no—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—28no—
766C22—24no—
767C22—28no—
768C22—4242no—
769C22—4241no—
770C22—4241no—
771C22—4241no—
772C22—4241no—
773C22—4242no—
774C22—2124no—
775C22—2122no—
776C22—2122no—
777C22—2124no—
778C22—2122no—
779C22#1681052418yes—
780C22C22×#1171992111yescharacteristic
781C22C2×#1313317911yescharacteristic
782C22C2×#1313317911yescharacteristic
783C22C4×#1171994712yes—
784C22#1681110212yes—
785C22C2×#1313319211yescharacteristic
786C22C2×#1313319211yescharacteristic
787C22#123×D5311yescharacteristic
788C22#1681112911yescharacteristic
789C22C2×#1313320611yescharacteristic
790C22#1681115912yes—
791C22C2×#1313321311yescharacteristic
792C22#1681118311yescharacteristic
793C22#1681119511yescharacteristic
794C22#1681122212yes—
795C22#1681126012yes—
796C22#1681126712yes—
797C22#1681126812yes—
798C22#1681127112yes—
799C22#1681127212yes—
800C22#1681127712yes—
801C22#1681130012yes—
802C22#1681131512yes—
803C4—28no—
804C4—44no—
805C4—81no—
806C4—81no—
807C4—1064no—
808C4—2122no—
809C4—2124no—
810C4—2122no—
811C4—2124no—
812C2—28no—
813C2—4242no—
814C2C2×#1681052411yescharacteristic
815C2#2027723411yescharacteristic
816C2#2027738311yescharacteristic
817C2#2027754012yes—
818C2#2027770512yes—
819C2#2027810911yescharacteristic
820C2#2027812011yescharacteristic
821C2#2027826412yes—
822C2#2027904712yes—
823C2#2027918411yescharacteristic
824C2#2027964311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#385C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC2×#385D53
hypocenterC53#13996
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C2×#16810484C2semidirect
5. C2×C22⋊C4×Dic53C2semidirect
6. C22×#13133124C2semidirect
7. #20272984C2semidirect
8. #20272957C2semidirect
9. #20272951C2semidirect
10. #20272944C2semidirect
11. C2×C53×#385C2semidirect
17. C2×#13133201C4semidirect
72. C2×C4⋊Dic53C2×C4semidirect
85. C2×#11719921C2×C4semidirect
221. C22⋊C4×C53C22⋊C4semidirect
344. C2×Dic53#123semidirect
403. C2×#385D53semidirect
456. C53#13996semidirect
640. C22⋊C4#11719921semidirect

Maximal subgroups

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

subgroupindex
C22×#131332012
C2×#168105022
C2×#168105002
C2×#168104842
C2×C22⋊C4×Dic532
C22×#131331242
#202729842
#202729572
#202729512
#202729442
C2×C53×#3852
#1399653