Finite Group Databasebeta

← #27307178

Subgroups — #27307178

Order 13568.

1746 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810519C211yesmaximal, characteristic, complemented
2C2×#16810483C211yesmaximal, characteristic
3C2×C4⋊C4×Dic53C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic53C211yesmaximal, characteristic
5#20272975C212yesmaximal, complemented
6#20272958C212yesmaximal
7#20272952C212yesmaximal
8#20272950C212yesmaximal, complemented
9#20272944C211yesmaximal, characteristic, complemented
10#20272944C211yesmaximal, characteristic, complemented
11C2×C53×#380C211yesmaximal, characteristic
12C22×C4⋊Dic53C2211yescharacteristic
13C22×C4⋊Dic53C2211yescharacteristic
14C22×#11719919C2212yes—
15C22×C22⋊Dic53C2211yescharacteristic
16C22×C22⋊Dic53C2211yescharacteristic
17C22×C22⋊Dic53C2212yes—
18C22×C4×Dic53C2211yescharacteristic
19C22×C4×Dic53C2211yescharacteristic
20C22×C4×Dic53C2212yes—
21#16810519—24no—
22#16810483C418yescomplemented
23C4⋊C4×Dic53—24no—
24C4×C22⋊Dic53—24no—
25C2×#13133124C2212yes—
26C2×#13133124C2211yescharacteristic
27C2×#13133124C2211yescharacteristic
28C2×#13133124C2212yes—
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C24×C4×C53C2211yescharacteristic
35C22×C4⋊C4×C53C2211yescharacteristic
36C22×C4⋊C4×C53C2211yescharacteristic
37C22×C22⋊C4×C53C2212yes—
38C53×#380—24no—
39C2×#95×C53C2212yes—
40C23×Dic53C2312yes—
41C23×Dic53C2312yes—
42C23×Dic53C2311yescharacteristic
43C23×Dic53C2311yescharacteristic
44C23×Dic53C2311yescharacteristic
45C23×Dic53C2311yescharacteristic
46C2×C4⋊Dic53—22no—
47C2×C4⋊Dic53—22no—
48C2×C4⋊Dic53—22no—
49C2×C4⋊Dic53—22no—
50C2×C4⋊Dic53C2×C414yes—
51C2×C4⋊Dic53C2×C414yes—
52C2×#11719919—24no—
53C2×#11719919—24no—
54C2×#11719919—42no—
55C2×C22⋊Dic53—22no—
56C2×C22⋊Dic53—22no—
57C2×C22⋊Dic53—22no—
58C2×C22⋊Dic53—22no—
59C2×C22⋊Dic53—22no—
60C2×C22⋊Dic53—42no—
61C2×C22⋊Dic53—42no—
62C2×C22⋊Dic53C2×C418yes—
63C2×C22⋊Dic53Q814yes—
64C2×C4×Dic53—22no—
65C2×C4×Dic53—22no—
66C2×C4×Dic53—22no—
67C2×C4×Dic53—22no—
68C2×C4×Dic53—22no—
69C2×C4×Dic53—24no—
70C2×C4×Dic53—42no—
71C2×C4×Dic53—42no—
72C2×C4×Dic53D414yes—
73#13133124—24no—
74#13133124—22no—
75#13133124—22no—
76#13133124—24no—
77#13133124—24no—
78#13133124—42no—
79#13133124—42no—
80#13133124—42no—
81#13133124C2×C418yes—
82C25×C53C2311yescharacteristic
83C23×C4×C53—22no—
84C23×C4×C53—22no—
85C23×C4×C53—22no—
86C23×C4×C53—22no—
87C23×C4×C53—22no—
88C23×C4×C53—22no—
89C23×C4×C53C2×C414yes—
90C23×C4×C53C2312yes—
91C23×C4×C53C2311yescharacteristic
92C23×C4×C53C2312yes—
93C23×C4×C53C2311yescharacteristic
94C2×C4⋊C4×C53—22no—
95C2×C4⋊C4×C53—22no—
96C2×C4⋊C4×C53—22no—
97C2×C4⋊C4×C53—22no—
98C2×C4⋊C4×C53—22no—
99C2×C4⋊C4×C53D414yes—
100C2×C22⋊C4×C53—24no—
101C2×C22⋊C4×C53—24no—
102C2×C22⋊C4×C53—42no—
103#95×C53—24no—
104C24×C53—21no—
105C24×C53—21no—
106C24×C53—21no—
107C24×C53—21no—
108C24×C53—21no—
109C24×C53—21no—
110C24×C53—21no—
111C24×C53—21no—
112C24×C53—21no—
113C24×C53—21no—
114C24×C53—21no—
115C24×C53—21no—
116C24×C53C22×C412yes—
117C24×C53C2×Q812yes—
118C24×C53#4112yes—
119C24×C53C2411yescharacteristic
120C22×C4×C53—21no—
121C22×C4×C53—22no—
122C22×C4×C53—21no—
123C22×C4×C53—22no—
124C22×C4×C53—22no—
125C22×C4×C53—21no—
126C22×C4×C53—21no—
127C22×C4×C53—21no—
128C22×C4×C53—21no—
129C22×C4×C53—22no—
130C22×C4×C53—22no—
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—22no—
138C22×C4×C53—22no—
139C22×C4×C53—22no—
140C22×C4×C53—22no—
141C22×C4×C53—22no—
142C22×C4×C53—44no—
143C22×C4×C53—44no—
144C22×C4×C53—44no—
145C22×C4×C53—44no—
146C22×C4×C53C22×C412yes—
147C22×C4×C53C22×C412yes—
148C22×C4×C53C2×D414yes—
149C22×C4×C53C2×D412yes—
150C22×C4×C53C2×D412yes—
151C22×C4×C53#4112yes—
152C22×C4×C53#4112yes—
153C22×C4×C53#4112yes—
154C22×C4×C53#4112yes—
155C22×Dic53—21no—
156C22×Dic53—21no—
157C22×Dic53—21no—
158C22×Dic53—21no—
159C22×Dic53—21no—
160C22×Dic53—21no—
161C22×Dic53—21no—
162C22×Dic53—22no—
163C22×Dic53—22no—
164C22×Dic53—21no—
165C22×Dic53—22no—
166C22×Dic53—21no—
167C22×Dic53—21no—
168C22×Dic53—21no—
169C22×Dic53—21no—
170C22×Dic53—21no—
171C22×Dic53—21no—
172C22×Dic53—21no—
173C22×Dic53—21no—
174C22×Dic53—22no—
175C22×Dic53—22no—
176C22×Dic53—22no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—21no—
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—21no—
186C22×Dic53—22no—
187C22×Dic53—21no—
188C22×Dic53—21no—
189C22×Dic53C22×C414yes—
190C22×Dic53C22×C414yes—
191C22×Dic53C2×D412yes—
192C22×Dic53C2×D412yes—
193C22×Dic53C2×Q812yes—
194C22×Dic53C2×Q812yes—
195C22×Dic53#4112yes—
196C22×Dic53#4112yes—
197C4⋊C4×C53—28no—
198C4⋊C4×C53—44no—
199C22⋊C4×C53—48no—
200C22⋊Dic53—28no—
201C22⋊Dic53—28no—
202C22⋊Dic53—48no—
203C4⋊Dic53—28no—
204C4⋊Dic53—28no—
205#11719919—48no—
206C4×Dic53—28no—
207C4×Dic53—48no—
208C4×Dic53—44no—
209C23×C53—22no—
210C23×C53—22no—
211C23×C53—22no—
212C23×C53—22no—
213C23×C53—22no—
214C23×C53—22no—
215C23×C53—22no—
216C23×C53—22no—
217C23×C53—22no—
218C23×C53—22no—
219C23×C53—22no—
220C23×C53—22no—
221C23×C53—22no—
222C23×C53—22no—
223C23×C53—22no—
224C23×C53—22no—
225C23×C53—22no—
226C23×C53—22no—
227C23×C53—41no—
228C23×C53—41no—
229C23×C53—41no—
230C23×C53—41no—
231C23×C53—41no—
232C23×C53—41no—
233C23×C53—41no—
234C23×C53—41no—
235C23×C53—41no—
236C23×C53—41no—
237C23×C53—41no—
238C23×C53—41no—
239C23×C53—41no—
240C23×C53—41no—
241C23×C53—41no—
242C23×C53—41no—
243C23×C53C4×Q814yes—
244C23×C53C23×C411yescharacteristic
245C23×C53C22×D411yescharacteristic
246C23×C53C22×D411yescharacteristic
247C23×C53C22×Q811yescharacteristic
248C23×C53C2×#4111yescharacteristic
249C23×C53C2×#4111yescharacteristic
250C23×C53C2×#4111yescharacteristic
251C23×C53C2×#4111yescharacteristic
252C23×C53C2×#4111yescharacteristic
253C23×C53C2×#4111yescharacteristic
254C23×C53C2×#4111yescharacteristic
255C23×C53H(5,𝔽2)11yescharacteristic
256C23×C53H(5,𝔽2)11yescharacteristic
257C23×C53H(5,𝔽2)11yescharacteristic
258C23×C532−1+411yescharacteristic
259C2×C4×C53—22no—
260C2×C4×C53—22no—
261C2×C4×C53—22no—
262C2×C4×C53—24no—
263C2×C4×C53—24no—
264C2×C4×C53—24no—
265C2×C4×C53—41no—
266C2×C4×C53—41no—
267C2×C4×C53—42no—
268C2×C4×C53—41no—
269C2×C4×C53—41no—
270C2×C4×C53—42no—
271C2×C4×C53—42no—
272C2×C4×C53—42no—
273C2×C4×C53—416no—
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#11714yes—
282C2×C4×C53C4×D414yes—
283C2×C4×C53C4×D414yes—
284C2×C4×C53#12114yes—
285C2×C4×C53#12314yes—
286C2×C4×C53#12414yes—
287C2×C4×C53#12614yes—
288C2×Dic53—22no—
289C2×Dic53—22no—
290C2×Dic53—22no—
291C2×Dic53—22no—
292C2×Dic53—22no—
293C2×Dic53—22no—
294C2×Dic53—24no—
295C2×Dic53—24no—
296C2×Dic53—24no—
297C2×Dic53—24no—
298C2×Dic53—24no—
299C2×Dic53—24no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53—41no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53—41no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53—41no—
321C2×Dic53—41no—
322C2×Dic53—42no—
323C2×Dic53—41no—
324C2×Dic53—41no—
325C2×Dic53—42no—
326C2×Dic53—41no—
327C2×Dic53—41no—
328C2×Dic53—41no—
329C2×Dic53C22⋊Q814yes—
330#13993—531nomaximal, Sylow
331C22×C53—24no—
332C22×C53—24no—
333C22×C53—24no—
334C22×C53—42no—
335C22×C53—42no—
336C22×C53—42no—
337C22×C53—42no—
338C22×C53—42no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53—42no—
342C22×C53—42no—
343C22×C53—42no—
344C22×C53—42no—
345C22×C53—42no—
346C22×C53C2×#11711yescharacteristic
347C22×C53C2×C4×D411yescharacteristic
348C22×C53C2×C4×D411yescharacteristic
349C22×C53C2×C4×Q811yescharacteristic
350C22×C53C4×#4111yescharacteristic
351C22×C53#51811yescharacteristic
352C22×C53#52011yescharacteristic
353C22×C53C2×#12111yescharacteristic
354C22×C53C2×C22⋊Q811yescharacteristic
355C22×C53C2×#12311yescharacteristic
356C22×C53#52511yescharacteristic
357C22×C53C2×#12411yescharacteristic
358C22×C53C2×#12611yescharacteristic
359C22×C53#52911yescharacteristic
360C22×C53#53311yescharacteristic
361C22×C53#53511yescharacteristic
362C22×C53#53711yescharacteristic
363C22×C53#54011yescharacteristic
364C22×C53#54211yescharacteristic
365C22×C53#54611yescharacteristic
366C22×C53#54611yescharacteristic
367C22×C53D4×Q811yescharacteristic
368C22×C53#55011yescharacteristic
369C22×C53#55211yescharacteristic
370C22×C53#55311yescharacteristic
371C22×C53#55311yescharacteristic
372C22×C53#55311yescharacteristic
373C22×C53#55311yescharacteristic
374C22×C53#55311yescharacteristic
375C22×C53#55411yescharacteristic
376C22×C53#55411yescharacteristic
377C22×C53#55411yescharacteristic
378C22×C53#55511yescharacteristic
379C22×C53#55611yescharacteristic
380C22×C53#55611yescharacteristic
381C4×C53—44no—
382C4×C53—42no—
383C4×C53—82no—
384C4×C53#38818yes—
385Dic53—24no—
386Dic53—44no—
387Dic53—44no—
388Dic53—42no—
389Dic53—42no—
390Dic53—42no—
391C2×#389—531no—
392C2×#380—531no—
393C2×#380D5311yescharacteristic
394C2×C4×C4⋊C4—531no—
395C2×C4×C22⋊C4—531no—
396#1443—532no—
397#1439—532no—
398#1437—532no—
399#1436—532no—
400C4⋊#95—531no—
401C4⋊#95—531no—
402C2×C53—44no—
403C2×C53C2×#38811yescharacteristic
404C2×C53C4×C22⋊Q811yescharacteristic
405C2×C53#232411yescharacteristic
406C2×C53#234511yescharacteristic
407C2×C53#234711yescharacteristic
408C2×C53#236011yescharacteristic
409C2×C53#236311yescharacteristic
410C2×C53#248511yescharacteristic
411C2×C53#248711yescharacteristic
412C2×C53#249011yescharacteristic
413C2×C53#249211yescharacteristic
414C2×C53#249411yescharacteristic
415C2×C53#249711yescharacteristic
416C2×C53#253511yescharacteristic
417C2×C53#253811yescharacteristic
418C24×C4C2×D5311yescharacteristic
419C22×C4⋊C4—531no—
420C22×C4⋊C4—531no—
421C22×C4⋊C4—532no—
422C22×C4⋊C4C2×D5311yescharacteristic
423C22×C4⋊C4C2×D5311yescharacteristic
424C22×C22⋊C4—531no—
425C22×C22⋊C4—532no—
426C22×C22⋊C4—531no—
427C22×C22⋊C4C2×D5312yes—
428C22×C42—531no—
429C22×C42—531no—
430C22×C42—532no—
431#389—1064no—
432#380—24no—
433#380—538no—
434C4×C4⋊C4—1064no—
435C4×C22⋊C4—1064no—
436C2×#95—532no—
437C2×#95—532no—
438C2×#95—531no—
439C2×#95—532no—
440C2×#95—532no—
441C2×#95—531no—
442C2×#95—532no—
443C2×#95—532no—
444C2×#95—532no—
445C2×#95C2×D5312yes—
446C53#1399311yescharacteristic, complemented, Sylow
447C25C22×D5311yescharacteristic
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—22no—
453C23×C4—22no—
454C23×C4—531no—
455C23×C4—532no—
456C23×C4—531no—
457C23×C4—532no—
458C23×C4—531no—
459C23×C4—531no—
460C23×C4C4×D5314yes—
461C23×C4C22×D5312yes—
462C23×C4C22×D5311yescharacteristic
463C23×C4C22×D5312yes—
464C23×C4C22×D5311yescharacteristic
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—534no—
471C2×C4⋊C4—534no—
472C2×C4⋊C4—1062no—
473C2×C4⋊C4—1062no—
474C2×C4⋊C4—1062no—
475C2×C4⋊C4—1062no—
476C2×C4⋊C4—1064no—
477C2×C4⋊C4—1064no—
478C2×C4⋊C4—2122no—
479C2×C4⋊C4C22⋊D5314yes—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—534no—
484C2×C22⋊C4—538no—
485C2×C22⋊C4—1062no—
486C2×C22⋊C4—1062no—
487C2×C22⋊C4—1062no—
488C2×C22⋊C4—1062no—
489C2×C22⋊C4—1062no—
490C2×C22⋊C4—2122no—
491C2×C22⋊C4—2122no—
492C2×C42—534no—
493C2×C42—1062no—
494C2×C42—1062no—
495C2×C42—1064no—
496C2×C42—1062no—
497C2×C42—1062no—
498C2×C42—1062no—
499C2×C42—2122no—
500C2×C42—2122no—
501#95—24no—
502#95—538no—
503#95—1064no—
504#95—1062no—
505#95—1062no—
506#95—1064no—
507#95—1064no—
508#95—2122no—
509#95—2122no—
510#95—2122no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24C2×C4×D5312yes—
524C24#1171994712yes—
525C24Q8×D5312yes—
526C24C23×D5311yescharacteristic
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—532no—
554C22×C4—532no—
555C22×C4—532no—
556C22×C4—534no—
557C22×C4—534no—
558C22×C4—532no—
559C22×C4—532no—
560C22×C4—532no—
561C22×C4—1061no—
562C22×C4—1061no—
563C22×C4—1061no—
564C22×C4—1061no—
565C22×C4—1061no—
566C22×C4—1061no—
567C22×C4—1062no—
568C22×C4—1061no—
569C22×C4—1062no—
570C22×C4—1061no—
571C22×C4—1062no—
572C22×C4—1061no—
573C22×C4—1061no—
574C22×C4—1062no—
575C22×C4—1061no—
576C22×C4—1061no—
577C22×C4—1061no—
578C22×C4—1061no—
579C22×C4—1061no—
580C22×C4—1062no—
581C22×C4—1061no—
582C22×C4—1062no—
583C22×C4—1061no—
584C22×C4—1062no—
585C22×C4—1061no—
586C22×C4—1061no—
587C22×C4—1062no—
588C22×C4—1062no—
589C22×C4—1062no—
590C22×C4—1062no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—1062no—
594C22×C4—1061no—
595C22×C4C2×C4×D5312yes—
596C22×C4C2×C4×D5312yes—
597C22×C4#1171994512yes—
598C22×C4D4×D5312yes—
599C22×C4#1171994712yes—
600C22×C4#1171994712yes—
601C22×C4#1171994712yes—
602C22×C4C2×C22⋊D5314yes—
603C22×C4C2×C22⋊D5312yes—
604C4⋊C4—28no—
605C4⋊C4—44no—
606C4⋊C4—1068no—
607C4⋊C4—1068no—
608C4⋊C4—2128no—
609C22⋊C4—48no—
610C22⋊C4—1068no—
611C22⋊C4—1068no—
612C22⋊C4—2128no—
613C42—1068no—
614C42—2128no—
615C42—2124no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23#1313318214yes—
651C23C22×C4×D5311yescharacteristic
652C23C2×D4×D5311yescharacteristic
653C23C22×C22⋊D5311yescharacteristic
654C23C2×Q8×D5311yescharacteristic
655C23#41×D5311yescharacteristic
656C23#41×D5311yescharacteristic
657C23C2×#1171994711yescharacteristic
658C23C2×#1171994711yescharacteristic
659C23C2×#1171994711yescharacteristic
660C23C2×#1171994711yescharacteristic
661C23C2×#1171994511yescharacteristic
662C23#1313326211yescharacteristic
663C23#1313326311yescharacteristic
664C23#1313326311yescharacteristic
665C23#1313326511yescharacteristic
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—416no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—534no—
689C2×C4—1062no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—1062no—
694C2×C4—1062no—
695C2×C4—1062no—
696C2×C4—1062no—
697C2×C4—1062no—
698C2×C4—1064no—
699C2×C4—1064no—
700C2×C4—1064no—
701C2×C4—1064no—
702C2×C4—1064no—
703C2×C4—1064no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—1062no—
707C2×C4—1062no—
708C2×C4—1062no—
709C2×C4—1062no—
710C2×C4—2121no—
711C2×C4—2121no—
712C2×C4—2122no—
713C2×C4—2121no—
714C2×C4—2122no—
715C2×C4—2121no—
716C2×C4—2121no—
717C2×C4—2121no—
718C2×C4—2122no—
719C2×C4—2121no—
720C2×C4—2121no—
721C2×C4—2121no—
722C2×C4—2121no—
723C2×C4—2122no—
724C2×C4—2121no—
725C2×C4—2121no—
726C2×C4—2122no—
727C2×C4—2122no—
728C2×C4—2122no—
729C2×C4—2122no—
730C2×C4#1313317314yes—
731C2×C4#1313317714yes—
732C2×C4C4×C22⋊D5314yes—
733C2×C4#1313318914yes—
734C2×C4#1313319914yes—
735C2×C4#1313320414yes—
736C2×C4#1313321014yes—
737C22—24no—
738C22—24no—
739C22—24no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22C2×#1313317311yescharacteristic
753C22C2×#1313317711yescharacteristic
754C22C2×C4×C22⋊D5311yescharacteristic
755C22C2×#1313318211yescharacteristic
756C22#1681109111yescharacteristic
757C22#1681109711yescharacteristic
758C22#1681110411yescharacteristic
759C22C2×#1313318911yescharacteristic
760C22C22⋊Q8×D5311yescharacteristic
761C22C2×#1313319911yescharacteristic
762C22#1681113311yescharacteristic
763C22C2×#1313320411yescharacteristic
764C22C2×#1313321011yescharacteristic
765C22#1681115411yescharacteristic
766C22#1681117511yescharacteristic
767C22#1681118911yescharacteristic
768C22#1681120311yescharacteristic
769C22#1681122611yescharacteristic
770C22#1681124611yescharacteristic
771C22#1681126111yescharacteristic
772C22#1681126711yescharacteristic
773C22Q8×C22⋊D5311yescharacteristic
774C22#1681129211yescharacteristic
775C22#1681130811yescharacteristic
776C22#1681131711yescharacteristic
777C22#1681132011yescharacteristic
778C22#1681132011yescharacteristic
779C22#1681132511yescharacteristic
780C22#1681132511yescharacteristic
781C22#1681132811yescharacteristic
782C22#1681133111yescharacteristic
783C22#1681133111yescharacteristic
784C22#1681133611yescharacteristic
785C22#1681134411yescharacteristic
786C22#1681134411yescharacteristic
787C4—44no—
788C4—42no—
789C4—82no—
790C4—1064no—
791C4—2122no—
792C4—2122no—
793C4—2124no—
794C4—2122no—
795C4—2124no—
796C4#1681051718yes—
797C2—44no—
798C2C2×#1681051711yescharacteristic
799C2#2027724311yescharacteristic
800C2#2027740411yescharacteristic
801C2#2027759411yescharacteristic
802C2#2027761011yescharacteristic
803C2#2027772011yescharacteristic
804C2#2027775311yescharacteristic
805C2#2027900811yescharacteristic
806C2#2027902811yescharacteristic
807C2#2027906911yescharacteristic
808C2#2027909111yescharacteristic
809C2#2027911111yescharacteristic
810C2#2027914411yescharacteristic
811C2#2027961411yescharacteristic
812C2#2027963411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#380C2
socle, cosocleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×#380D53
hypocenterC53#13993
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C2×#16810519C2semidirect
3. C2×C4⋊C4×Dic53C2semidirect
5. #20272975C2semidirect
8. #20272950C2semidirect
9. #20272944C2semidirect
10. #20272944C2semidirect
22. #16810483C4semidirect
446. C53#13993semidirect

Maximal subgroups

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

subgroupindex
C2×#168105192
C2×#168104832
C2×C4⋊C4×Dic532
C2×C4×C22⋊Dic532
#202729752
#202729582
#202729522
#202729502
#202729442
C2×C53×#3802
#1399353