Finite Group Databasebeta

← #27307511

Subgroups — #27307511

Order 13568.

2178 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810502C211yesmaximal, characteristic
2C2×#16810502C211yesmaximal, characteristic
3C2×#16810502C211yesmaximal, characteristic
4C2×C4×C22⋊Dic53C211yesmaximal, characteristic, complemented
5#20272976C212yesmaximal, complemented
6#20272963C212yesmaximal, complemented
7#20272951C212yesmaximal, complemented
8#20272941C212yesmaximal, complemented
9#20272938C211yesmaximal, characteristic, complemented
10#20272938C211yesmaximal, characteristic, complemented
11C22×#95×C53C211yesmaximal, characteristic, complemented
12C23×C22⋊D53C2211yescharacteristic
13C22×C22⋊Dic53C2211yescharacteristic
14C22×C22⋊Dic53C2211yescharacteristic
15C22×C22⋊Dic53C2211yescharacteristic
16C22×#11719921C2211yescharacteristic
17C22×#11719921C2212yes—
18C22×#11719921C2211yescharacteristic
19C22×#11719921C2212yes—
20C22×C4×Dic53C2212yes—
21#16810502—24no—
22#16810502—24no—
23#16810502C418yescomplemented
24C4×C22⋊Dic53—24no—
25C2×#13133124C2212yes—
26C2×#13133124C2211yescharacteristic
27C2×#13133124C2212yes—
28C2×#13133124C2212yes—
29C2×#13133124C2211yescharacteristic
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C24×C4×C53C2211yescharacteristic
35C24×C4×C53C2211yescharacteristic
36C24×C4×C53C2211yescharacteristic
37C2×#95×C53—24no—
38C2×#95×C53C2212yes—
39C2×#95×C53C2212yes—
40C24×D53C2311yescharacteristic
41C22×C22⋊D53—22no—
42C22×C22⋊D53—22no—
43C22×C22⋊D53—22no—
44C22×C22⋊D53—22no—
45C22×C22⋊D53—22no—
46C22×C22⋊D53—22no—
47C22×C22⋊D53C2×C414yes—
48C23×Dic53C2311yescharacteristic
49C23×Dic53C2311yescharacteristic
50C23×Dic53C2312yes—
51C23×Dic53C2311yescharacteristic
52C23×Dic53C2312yes—
53C2×C22⋊Dic53—22no—
54C2×C22⋊Dic53—22no—
55C2×C22⋊Dic53—22no—
56C2×C22⋊Dic53—22no—
57C2×C22⋊Dic53—22no—
58C2×C22⋊Dic53—22no—
59C2×C22⋊Dic53—22no—
60C2×C22⋊Dic53C2×C414yes—
61C2×C22⋊Dic53D414yes—
62C2×#11719921—22no—
63C2×#11719921—22no—
64C2×#11719921—24no—
65C2×#11719921—24no—
66C2×#11719921—24no—
67C2×#11719921—42no—
68C2×#11719921—42no—
69C2×#11719921—42no—
70C2×#11719921—42no—
71C2×#11719921C2×C418yescomplemented
72C2×C4×Dic53—24no—
73C2×C4×Dic53—24no—
74C2×C4×Dic53—42no—
75#13133124—22no—
76#13133124—22no—
77#13133124—24no—
78#13133124—24no—
79#13133124—24no—
80#13133124—42no—
81#13133124—42no—
82#13133124—42no—
83#13133124C2×C418yescomplemented
84C25×C53C2311yescharacteristic
85C23×C4×C53—22no—
86C23×C4×C53—22no—
87C23×C4×C53—22no—
88C23×C4×C53—22no—
89C23×C4×C53—22no—
90C23×C4×C53—24no—
91C23×C4×C53—24no—
92C23×C4×C53—22no—
93C23×C4×C53—22no—
94C23×C4×C53—42no—
95C23×C4×C53—42no—
96C23×C4×C53—42no—
97C23×C4×C53—42no—
98C23×C4×C53C2×C414yes—
99C23×C4×C53D414yes—
100C23×C4×C53C2312yes—
101C23×C4×C53C2311yescharacteristic
102C23×C4×C53C2312yes—
103C23×C4×C53C2311yescharacteristic
104#95×C53—24no—
105#95×C53—24no—
106C24×C53—22no—
107C24×C53—22no—
108C24×C53—22no—
109C24×C53—22no—
110C24×C53C22×C412yes—
111C24×C53C2×D412yes—
112C24×C53C2×D412yes—
113C24×C53#4112yes—
114C24×C53#4112yes—
115C24×C53#4112yes—
116C24×C53#4112yes—
117C24×C53C2411yescharacteristic
118C23×D53—21no—
119C23×D53—21no—
120C23×D53—22no—
121C23×D53—22no—
122C23×D53—21no—
123C23×D53—21no—
124C23×D53—21no—
125C23×D53—21no—
126C23×D53—22no—
127C23×D53—22no—
128C23×D53C22×C412yes—
129C22×C4×C53—21no—
130C22×C4×C53—21no—
131C22×C4×C53—22no—
132C22×C4×C53—28no—
133C22×C4×C53—28no—
134C22×C4×C53—28no—
135C22×C4×C53—22no—
136C22×C4×C53—22no—
137C22×C4×C53—21no—
138C22×C4×C53—22no—
139C22×C4×C53—22no—
140C22×C4×C53—21no—
141C22×C4×C53—22no—
142C22×C4×C53—22no—
143C22×C4×C53—22no—
144C22×C4×C53—22no—
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—28no—
152C22×C4×C53—48no—
153C22×C4×C53—44no—
154C22×C4×C53—48no—
155C22×C4×C53—48no—
156C22×C4×C53—48no—
157C22×C4×C53—48no—
158C22×C4×C53—44no—
159C22×C4×C53—44no—
160C22×C4×C53—44no—
161C22×C4×C53—48no—
162C22×C4×C53—44no—
163C22×C4×C53C22×C414yes—
164C22×C4×C53C2×D412yes—
165C22×C4×C53C2×D412yes—
166C22×C4×C53#4114yes—
167C22×C4×C53#4114yes—
168C2×C22⋊D53—28no—
169C2×C22⋊D53—28no—
170C2×C22⋊D53—28no—
171C2×C22⋊D53—44no—
172C2×C22⋊D53—44no—
173C2×C22⋊D53—44no—
174C2×C22⋊D53—44no—
175C22×Dic53—21no—
176C22×Dic53—21no—
177C22×Dic53—22no—
178C22×Dic53—22no—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—21no—
186C22×Dic53—21no—
187C22×Dic53—21no—
188C22×Dic53—21no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—21no—
194C22×Dic53—21no—
195C22×Dic53—22no—
196C22×Dic53—22no—
197C22×Dic53—21no—
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—22no—
202C22×Dic53—22no—
203C22×Dic53C22×C412yes—
204C22×Dic53C22×C414yes—
205C22×Dic53C2×D414yes—
206C22⋊Dic53—28no—
207C22⋊Dic53—28no—
208C22⋊Dic53—44no—
209#11719921—48no—
210#11719921—48no—
211#11719921—44no—
212#11719921—44no—
213C4×Dic53—48no—
214C23×C53—24no—
215C23×C53—24no—
216C23×C53—22no—
217C23×C53—22no—
218C23×C53—24no—
219C23×C53—22no—
220C23×C53—22no—
221C23×C53—24no—
222C23×C53—24no—
223C23×C53—24no—
224C23×C53—24no—
225C23×C53—24no—
226C23×C53—24no—
227C23×C53—24no—
228C23×C53—24no—
229C23×C53—24no—
230C23×C53#11714yes—
231C23×C53C4×D414yes—
232C23×C53C4×D414yes—
233C23×C53#12114yes—
234C23×C53#12314yes—
235C23×C53#12414yes—
236C23×C53#12614yes—
237C23×C53C23×C411yescharacteristic
238C23×C53C22×D411yescharacteristic
239C23×C53C22×D411yescharacteristic
240C23×C53C2×#4111yescharacteristic
241C23×C53C2×#4111yescharacteristic
242C23×C53C2×#4112yes—
243C23×C53C2×#4112yes—
244C23×C53C2×#4111yescharacteristic
245C23×C53C2×#4111yescharacteristic
246C23×C53H(5,𝔽2)12yes—
247C23×C53H(5,𝔽2)12yes—
248C22×D53—22no—
249C22×D53—22no—
250C22×D53—22no—
251C22×D53—24no—
252C22×D53—24no—
253C22×D53—41no—
254C22×D53—41no—
255C22×D53—41no—
256C22×D53—41no—
257C22×D53—41no—
258C22×D53—41no—
259C22×D53—42no—
260C22×D53—41no—
261C22×D53—41no—
262C22×D53—42no—
263C22×D53—42no—
264C22×D53—42no—
265C22×D53—42no—
266C22×D53—42no—
267C22×D53—42no—
268C22×D53—42no—
269C22×D53—42no—
270C22×D53—42no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—24no—
274C2×C4×C53—24no—
275C2×C4×C53—24no—
276C2×C4×C53—24no—
277C2×C4×C53—24no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—24no—
281C2×C4×C53—22no—
282C2×C4×C53—24no—
283C2×C4×C53—24no—
284C2×C4×C53—416no—
285C2×C4×C53—416no—
286C2×C4×C53—416no—
287C2×C4×C53—42no—
288C2×C4×C53—42no—
289C2×C4×C53—42no—
290C2×C4×C53—42no—
291C2×C4×C53—42no—
292C2×C4×C53—42no—
293C2×C4×C53—42no—
294C2×C4×C53—42no—
295C2×C4×C53—42no—
296C2×C4×C53—42no—
297C2×C4×C53#12314yes—
298C22⋊D53—416no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—24no—
303C2×Dic53—24no—
304C2×Dic53—24no—
305C2×Dic53—24no—
306C2×Dic53—24no—
307C2×Dic53—24no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53—42no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53—41no—
321C2×Dic53—41no—
322C2×Dic53—41no—
323C2×Dic53—41no—
324C2×Dic53—41no—
325C2×Dic53—41no—
326C2×Dic53—42no—
327C2×Dic53—42no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330#14020—531nomaximal, Sylow
331C22×C53—24no—
332C22×C53—24no—
333C22×C53—28no—
334C22×C53—28no—
335C22×C53—24no—
336C22×C53—24no—
337C22×C53—28no—
338C22×C53—24no—
339C22×C53—28no—
340C22×C53—24no—
341C22×C53#38818yes—
342C22×C53C2×#11711yescharacteristic
343C22×C53C2×C4×D411yescharacteristic
344C22×C53C2×C4×D411yescharacteristic
345C22×C53C4×#4112yes—
346C22×C53#51812yes—
347C22×C53C2×#12111yescharacteristic
348C22×C53C2×#12311yescharacteristic
349C22×C53C2×#12311yescharacteristic
350C22×C53#52511yescharacteristic
351C22×C53C2×#12411yescharacteristic
352C22×C53C2×#12611yescharacteristic
353C22×C53#52912yes—
354C22×C53#53411yescharacteristic
355C22×C53#53511yescharacteristic
356C22×C53#53812yes—
357C22×C53#54612yes—
358C22×C53#54612yes—
359C22×C53#55112yes—
360C22×C53#55112yes—
361C22×C53#55312yes—
362C22×C53#55312yes—
363C22×C53#55312yes—
364C22×C53#55312yes—
365C2×D53—42no—
366C2×D53—44no—
367C2×D53—44no—
368C2×D53—42no—
369C2×D53—42no—
370C2×D53—81no—
371C2×D53—81no—
372C2×D53—81no—
373C2×D53—82no—
374C2×D53—81no—
375C2×D53—82no—
376C4×C53—24no—
377C4×C53—44no—
378C4×C53—44no—
379C4×C53—42no—
380Dic53—44no—
381Dic53—44no—
382Dic53—42no—
383Dic53—81no—
384Dic53—81no—
385C2×#386—531no—
386C2×#386—531no—
387C2×#386—531no—
388C2×C4×C22⋊C4—531no—
389C22×#95D5311yescharacteristic, complemented
390#1443—532no—
391#1440—532no—
392#1437—532no—
393#1434—532no—
394C22⋊#95—531no—
395C22⋊#95—531no—
396C2×C53—28no—
397C2×C53C2×#38811yescharacteristic
398C2×C53C4×#12311yescharacteristic
399C2×C53#232111yescharacteristic
400C2×C53#235312yes—
401C2×C53#236412yes—
402C2×C53#241111yescharacteristic
403C2×C53#241211yescharacteristic
404C2×C53#244412yes—
405C2×C53#250411yescharacteristic
406C2×C53#251012yes—
407C2×C53#259111yescharacteristic
408D53—82no—
409C23×D4—531no—
410C24×C4C2×D5311yescharacteristic
411C24×C4C2×D5311yescharacteristic
412C24×C4C2×D5311yescharacteristic
413C22×C22⋊C4—531no—
414C22×C22⋊C4—531no—
415C22×C22⋊C4—532no—
416C22×C22⋊C4—531no—
417C22×C22⋊C4—531no—
418C22×C22⋊C4—532no—
419C22×C22⋊C4—531no—
420C22×C42—532no—
421#386—538no—
422#386—1064no—
423#386—1064no—
424C4×C22⋊C4—1064no—
425C2×#95—24no—
426C2×#95—532no—
427C2×#95—532no—
428C2×#95—531no—
429C2×#95—532no—
430C2×#95—532no—
431C2×#95—531no—
432C2×#95—532no—
433C2×#95—532no—
434C2×#95—532no—
435C2×#95C2×D5312yes—
436C2×#95C2×D5312yes—
437C53#1402011yescharacteristic, complemented, Sylow
438C25—531no—
439C25C22×D5311yescharacteristic
440C22×D4—534no—
441C22×D4—1062no—
442C22×D4—1062no—
443C22×D4—1062no—
444C22×D4—1062no—
445C22×D4—1062no—
446C22×D4—1062no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—24no—
453C23×C4—24no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—42no—
457C23×C4—42no—
458C23×C4—42no—
459C23×C4—42no—
460C23×C4—532no—
461C23×C4—532no—
462C23×C4—531no—
463C23×C4—531no—
464C23×C4—531no—
465C23×C4C4×D5314yes—
466C23×C4C22⋊D5314yes—
467C23×C4C22×D5312yes—
468C23×C4C22×D5312yes—
469C23×C4C22×D5311yescharacteristic
470C23×C4C22×D5311yescharacteristic
471C2×C22⋊C4—534no—
472C2×C22⋊C4—534no—
473C2×C22⋊C4—538no—
474C2×C22⋊C4—1062no—
475C2×C22⋊C4—1062no—
476C2×C22⋊C4—1062no—
477C2×C22⋊C4—1062no—
478C2×C22⋊C4—1064no—
479C2×C22⋊C4—1062no—
480C2×C22⋊C4—1062no—
481C2×C22⋊C4—1062no—
482C2×C22⋊C4—1064no—
483C2×C22⋊C4—1064no—
484C2×C22⋊C4—1062no—
485C2×C22⋊C4—1062no—
486C2×C22⋊C4—2122no—
487C2×C22⋊C4—2122no—
488C2×C22⋊C4—2122no—
489C2×C22⋊C4—2122no—
490C2×C42—1064no—
491C2×C42—1064no—
492C2×C42—2122no—
493#95—24no—
494#95—24no—
495#95—538no—
496#95—1064no—
497#95—1064no—
498#95—1064no—
499#95—1062no—
500#95—1062no—
501#95—2122no—
502#95—2122no—
503#95—2122no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—532no—
509C24—1061no—
510C24—1061no—
511C24—1061no—
512C24—1062no—
513C24—1062no—
514C24—1061no—
515C24—1061no—
516C24—1061no—
517C24—1062no—
518C24—1062no—
519C24C2×C4×D5312yes—
520C24#1171994512yes—
521C24D4×D5312yes—
522C24#1171994712yes—
523C24#1171994912yes—
524C24#1171994912yes—
525C24C2×C22⋊D5312yes—
526C24C23×D5311yescharacteristic
527C2×D4—1068no—
528C2×D4—1068no—
529C2×D4—1068no—
530C2×D4—2124no—
531C2×D4—2124no—
532C2×D4—2124no—
533C2×D4—2124no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—28no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—28no—
557C22×C4—48no—
558C22×C4—44no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—48no—
567C22×C4—44no—
568C22×C4—532no—
569C22×C4—534no—
570C22×C4—534no—
571C22×C4—1061no—
572C22×C4—1062no—
573C22×C4—1061no—
574C22×C4—1061no—
575C22×C4—1062no—
576C22×C4—1062no—
577C22×C4—1062no—
578C22×C4—1062no—
579C22×C4—1062no—
580C22×C4—1061no—
581C22×C4—1062no—
582C22×C4—1062no—
583C22×C4—1061no—
584C22×C4—1061no—
585C22×C4—1062no—
586C22×C4—1062no—
587C22×C4—1062no—
588C22×C4—1062no—
589C22×C4—1061no—
590C22×C4—1061no—
591C22×C4—1062no—
592C22×C4—1062no—
593C22×C4—1061no—
594C22×C4—1061no—
595C22×C4—1061no—
596C22×C4—1061no—
597C22×C4—1062no—
598C22×C4—1062no—
599C22×C4C2×C4×D5314yes—
600C22×C4#1171994514yes—
601C22×C4#1171994514yes—
602C22×C4C2×C22⋊D5312yes—
603C22×C4C2×C22⋊D5312yes—
604C22⋊C4—1068no—
605C22⋊C4—1068no—
606C22⋊C4—2128no—
607C22⋊C4—2128no—
608C22⋊C4—2124no—
609C22⋊C4—2124no—
610C22⋊C4—2124no—
611C42—2128no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—22no—
621C23—22no—
622C23—24no—
623C23—22no—
624C23—22no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—1062no—
629C23—1062no—
630C23—1062no—
631C23—1064no—
632C23—1064no—
633C23—2122no—
634C23—2122no—
635C23—2122no—
636C23—2122no—
637C23—2122no—
638C23—2122no—
639C23—2121no—
640C23—2121no—
641C23—2121no—
642C23—2121no—
643C23—2121no—
644C23—2121no—
645C23—2122no—
646C23—2121no—
647C23—2121no—
648C23—2122no—
649C23—2122no—
650C23—2122no—
651C23#1313317514yes—
652C23C4×C22⋊D5314yes—
653C23#1313317914yes—
654C23#1313318914yes—
655C23#1313320214yes—
656C23#1313320614yes—
657C23#1313321214yes—
658C23C22×C4×D5311yescharacteristic
659C23C2×D4×D5311yescharacteristic
660C23C22×C22⋊D5311yescharacteristic
661C23C2×#1171994711yescharacteristic
662C23C2×#1171994512yes—
663C23C2×#1171994512yes—
664C23C2×#1171994511yescharacteristic
665C23C2×#1171994911yescharacteristic
666C23C2×#1171994911yescharacteristic
667C23#1313326212yes—
668C23#1313326212yes—
669D4—21216no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—416no—
684C2×C4—416no—
685C2×C4—416no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—1062no—
697C2×C4—1062no—
698C2×C4—1064no—
699C2×C4—1062no—
700C2×C4—1064no—
701C2×C4—1064no—
702C2×C4—1064no—
703C2×C4—1064no—
704C2×C4—1064no—
705C2×C4—2122no—
706C2×C4—2122no—
707C2×C4—2122no—
708C2×C4—2122no—
709C2×C4—2121no—
710C2×C4—2121no—
711C2×C4—2121no—
712C2×C4—2121no—
713C2×C4—2121no—
714C2×C4—2121no—
715C2×C4—2122no—
716C2×C4—2122no—
717C2×C4—2122no—
718C2×C4—2122no—
719C2×C4—2121no—
720C2×C4—2121no—
721C2×C4—2121no—
722C2×C4—2121no—
723C2×C4—2122no—
724C2×C4—2122no—
725C2×C4—2122no—
726C2×C4—2122no—
727C2×C4#1313320014yes—
728C22—28no—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—24no—
733C22—28no—
734C22—24no—
735C22—28no—
736C22—28no—
737C22—24no—
738C22—4241no—
739C22—4241no—
740C22—4241no—
741C22—4241no—
742C22—4242no—
743C22—4242no—
744C22—2124no—
745C22—2122no—
746C22—2124no—
747C22—2122no—
748C22—2122no—
749C22#1681051318yes—
750C22C2×#1313317511yescharacteristic
751C22C2×C4×C22⋊D5311yescharacteristic
752C22C2×#1313317911yescharacteristic
753C22C4×#1171994512yes—
754C22#1681109612yes—
755C22C2×#1313318911yescharacteristic
756C22C2×#1313320011yescharacteristic
757C22C2×#1313320211yescharacteristic
758C22#1681113411yescharacteristic
759C22C2×#1313320611yescharacteristic
760C22C2×#1313321211yescharacteristic
761C22#1681115712yes—
762C22#1681118211yescharacteristic
763C22#1681119011yescharacteristic
764C22#1681121112yes—
765C22#1681126312yes—
766C22#1681126312yes—
767C22#1681129912yes—
768C22#1681129912yes—
769C22#1681132112yes—
770C22#1681132112yes—
771C22#1681132112yes—
772C22#1681132112yes—
773C4—24no—
774C4—44no—
775C4—42no—
776C4—44no—
777C4—4241no—
778C4—4241no—
779C4—2124no—
780C4—2122no—
781C4—2124no—
782C2—28no—
783C2—4242no—
784C2C2×#1681051311yescharacteristic
785C2C4×#1313320011yescharacteristic
786C2#2027737311yescharacteristic
787C2#2027765112yes—
788C2#2027776212yes—
789C2#2027810011yescharacteristic
790C2#2027811111yescharacteristic
791C2#2027846512yes—
792C2#2027920311yescharacteristic
793C2#2027927512yes—
794C2#2028019511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC22×#95×C53C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC22×#95D53
hypocenterC53#14020
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
4. C2×C4×C22⋊Dic53C2semidirect
5. #20272976C2semidirect
6. #20272963C2semidirect
7. #20272951C2semidirect
8. #20272941C2semidirect
9. #20272938C2semidirect
10. #20272938C2semidirect
11. C22×#95×C53C2semidirect
23. #16810502C4semidirect
71. C2×#11719921C2×C4semidirect
83. #13133124C2×C4semidirect
389. C22×#95D53semidirect
437. C53#14020semidirect

Maximal subgroups

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

subgroupindex
C2×#168105022
C2×C4×C22⋊Dic532
#202729762
#202729632
#202729512
#202729412
#202729382
C22×#95×C532
#1402053