Finite Group Databasebeta

← C2×#20282936 #27590331

Subgroups — C2×#20282936 #27590331

Order 13568.

2110 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20282936C2116yesmaximal, direct product factor
2C2×#16810560C211yesmaximal, characteristic, complemented
3C2×#16810558C211yesmaximal, characteristic, complemented
4C2×#16810557C211yesmaximal, characteristic, complemented
5C2×#16810557C211yesmaximal, characteristic, complemented
6C2×#16810552C211yesmaximal, characteristic, complemented
7C2×#16810552C211yesmaximal, characteristic, complemented
8C2×#16810545C211yesmaximal, characteristic, complemented
9C2×#16810545C211yesmaximal, characteristic, complemented
10C2×#16810541C211yesmaximal, characteristic
11C2×#16810541C211yesmaximal, characteristic
12C2×#16810541C211yesmaximal, characteristic
13C2×#16810520C211yesmaximal, characteristic, complemented
14C2×#16810515C211yesmaximal, characteristic, complemented
15C2×#16810513C211yesmaximal, characteristic, complemented
16C2×C53×#400C211yesmaximal, characteristic, complemented
17C23×D212C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20C22×C4⋊Dic53C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×#11719919C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×#11719919C2211yescharacteristic
27C22×#11719921C2211yescharacteristic
28C22×#11719921C2211yescharacteristic
29C22×#11719921C2211yescharacteristic
30C22×#11719921C2211yescharacteristic
31C22×#11719921C2211yescharacteristic
32C22×#11719921C2211yescharacteristic
33C22×#11719921C2211yescharacteristic
34C22×#11719921C2211yescharacteristic
35C22×#11719921C2211yescharacteristic
36C22×#11719921C2211yescharacteristic
37C22×#11719921C2211yescharacteristic
38C22×#11719921C2211yescharacteristic
39C22×C4×Dic53C2211yescharacteristic
40#16810560C2218yescomplemented
41#16810558C2218yescomplemented
42#16810557C2218yescomplemented
43#16810557C2218yescomplemented
44#16810552C2218yescomplemented
45#16810552C2218yescomplemented
46#16810545C2218yescomplemented
47#16810545C2218yescomplemented
48#16810541C2218yes—
49#16810541C2218yes—
50#16810541C2218yes—
51#16810520C2218yescomplemented
52#16810515C2218yescomplemented
53#16810513C2218yescomplemented
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C22×C4⋊C4×C53C2211yescharacteristic
60C22×C4⋊C4×C53C2211yescharacteristic
61C53×#400C2218yescomplemented
62C2×#95×C53C2211yescharacteristic
63C2×#95×C53C2211yescharacteristic
64C2×#95×C53C2211yescharacteristic
65C2×#95×C53C2211yescharacteristic
66C2×#95×C53C2211yescharacteristic
67C24×D53C2311yescharacteristic
68C24×D53C2311yescharacteristic
69C22×D212—42no—
70C22×D212—42no—
71C22×D212—42no—
72C22×D212C2314yes—
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C2×C4⋊Dic53—42no—
80C2×C4⋊Dic53—42no—
81C2×C4⋊Dic53—42no—
82C2×C4⋊Dic53C2314yes—
83C2×C4⋊Dic53C2314yes—
84C2×C4⋊Dic53C2314yes—
85C2×#11719919—24no—
86C2×#11719919—42no—
87C2×#11719919—42no—
88C2×#11719919—42no—
89C2×#11719919—42no—
90C2×#11719919—42no—
91C2×#11719919C2314yes—
92C2×#11719919C2314yes—
93C2×#11719919C2314yes—
94C2×#11719919C2314yes—
95C2×#11719919C2314yes—
96C2×#11719919C2314yes—
97C2×#11719921—24no—
98C2×#11719921—24no—
99C2×#11719921—42no—
100C2×#11719921—42no—
101C2×#11719921—42no—
102C2×#11719921—42no—
103C2×#11719921—42no—
104C2×#11719921—42no—
105C2×#11719921—42no—
106C2×#11719921—42no—
107C2×#11719921—42no—
108C2×#11719921—42no—
109C2×#11719921C2314yes—
110C2×#11719921C2314yes—
111C2×#11719921C2314yes—
112C2×#11719921C2314yes—
113C2×#11719921C2314yes—
114C2×#11719921C2314yes—
115C2×#11719921C2314yes—
116C2×#11719921C2314yes—
117C2×#11719921C2314yes—
118C2×#11719921C2314yes—
119C2×#11719921C2314yes—
120C2×#11719921C2314yes—
121C2×C4×Dic53—42no—
122C2×C4×Dic53C2314yes—
123#13133124C2314yes—
124#13133124C2314yes—
125#13133124C2314yes—
126#13133124C2314yes—
127#13133124C2314yes—
128C23×C4×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130C23×C4×C53C2311yescharacteristic
131C23×C4×C53C2311yescharacteristic
132C23×C4×C53C2311yescharacteristic
133C23×C4×C53C2311yescharacteristic
134C23×C4×C53C2311yescharacteristic
135C2×C4⋊C4×C53—42no—
136C2×C4⋊C4×C53—42no—
137C2×C4⋊C4×C53C2314yes—
138C2×C4⋊C4×C53C2314yes—
139#95×C53C2314yes—
140#95×C53C2314yes—
141#95×C53C2314yes—
142#95×C53C2314yes—
143#95×C53C2314yes—
144C24×C53C2411yescharacteristic
145C23×D53—22no—
146C23×D53—22no—
147C23×D53—22no—
148C23×D53—22no—
149C23×D53—22no—
150C23×D53—22no—
151C23×D53—22no—
152C23×D53—22no—
153C23×D53—22no—
154C23×D53—22no—
155C23×D53—22no—
156C23×D53—22no—
157C23×D53—22no—
158C23×D53—22no—
159C23×D53C2412yes—
160C23×D53C2412yes—
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—22no—
172C22×C4×C53—22no—
173C22×C4×C53—22no—
174C22×C4×C53—22no—
175C22×C4×C53—22no—
176C22×C4×C53—22no—
177C22×C4×C53—22no—
178C22×C4×C53—22no—
179C22×C4×C53—22no—
180C22×C4×C53—22no—
181C22×C4×C53—22no—
182C22×C4×C53C2412yes—
183C22×C4×C53C2412yes—
184C22×C4×C53C2412yes—
185C22×C4×C53C2412yes—
186C22×C4×C53C2412yes—
187C22×C4×C53C2412yes—
188C22×C4×C53C2412yes—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53—22no—
196C22×Dic53—22no—
197C22×Dic53—22no—
198C22×Dic53—22no—
199C22×Dic53—22no—
200C22×Dic53—22no—
201C22×Dic53—22no—
202C22×Dic53—22no—
203C22×Dic53—22no—
204C22×Dic53—22no—
205C22×Dic53—22no—
206C22×Dic53#4114yes—
207C22×Dic53C2412yes—
208C22×Dic53C2412yes—
209C22×Dic53C2412yes—
210C22×Dic53C2412yes—
211C22×Dic53C2412yes—
212C22×Dic53C2412yes—
213C2×D212—44no—
214C2×D212—44no—
215C2×D212—44no—
216C2×D212—416no—
217C4⋊C4×C53—44no—
218C4⋊C4×C53—44no—
219#11719921—28no—
220#11719921—28no—
221#11719921—44no—
222#11719921—44no—
223#11719921—44no—
224#11719921—44no—
225#11719921—44no—
226#11719921—44no—
227#11719921—44no—
228#11719921—44no—
229#11719921—44no—
230#11719921—44no—
231C4⋊Dic53—44no—
232C4⋊Dic53—44no—
233C4⋊Dic53—44no—
234#11719919—28no—
235#11719919—44no—
236#11719919—44no—
237#11719919—44no—
238#11719919—44no—
239#11719919—44no—
240C4×Dic53—44no—
241C23×C53C2×#4112yes—
242C23×C53H(5,𝔽2)12yes—
243C23×C53H(5,𝔽2)12yes—
244C23×C53H(5,𝔽2)12yes—
245C23×C53H(5,𝔽2)12yes—
246C23×C532−1+412yes—
247C23×C532−1+412yes—
248C23×C53C2511yescharacteristic
249C22×D53—22no—
250C22×D53—22no—
251C22×D53—22no—
252C22×D53—22no—
253C22×D53—22no—
254C22×D53—22no—
255C22×D53—22no—
256C22×D53—22no—
257C22×D53—22no—
258C22×D53—22no—
259C22×D53—22no—
260C22×D53—22no—
261C22×D53—22no—
262C22×D53—22no—
263C22×D53—44no—
264C22×D53—44no—
265C22×D53—44no—
266C22×D53—44no—
267C22×D53—44no—
268C22×D53—44no—
269C22×D53—44no—
270C22×D53—44no—
271C22×D53—44no—
272C22×D53—44no—
273C22×D53—44no—
274C22×D53—44no—
275C22×D53—44no—
276C22×D53—44no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—44no—
299C2×C4×C53—44no—
300C2×C4×C53—44no—
301C2×C4×C53—44no—
302C2×C4×C53—44no—
303C2×C4×C53—44no—
304C2×C4×C53—44no—
305C2×Dic53—28no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—44no—
324C2×Dic53—44no—
325C2×Dic53—44no—
326C2×Dic53—44no—
327C2×Dic53—44no—
328C2×Dic53C2×#4114yes—
329D212—416no—
330C2×#2837—531nomaximal, Sylow
331C22×C53#53914yes—
332C22×C53#54014yes—
333C22×C53#54214yes—
334C22×C53#56014yes—
335C22×C53#56214yes—
336C22×C53#56214yes—
337C22×C53#56314yes—
338C22×C53C22×#4111yescharacteristic
339C22×C53C2×H(5,𝔽2)11yescharacteristic
340C22×C53C2×H(5,𝔽2)11yescharacteristic
341C22×C53C2×H(5,𝔽2)11yescharacteristic
342C22×C53C2×H(5,𝔽2)11yescharacteristic
343C22×C53C2×2−1+411yescharacteristic
344C22×C53C2×2−1+411yescharacteristic
345C2×D53—42no—
346C2×D53—42no—
347C2×D53—42no—
348C2×D53—42no—
349C2×D53—42no—
350C2×D53—42no—
351C2×D53—42no—
352C2×D53—42no—
353C2×D53—42no—
354C2×D53—42no—
355C2×D53—42no—
356C2×D53—42no—
357C2×D53—42no—
358C2×D53—42no—
359C2×D53—88no—
360C2×D53—88no—
361C4×C53—42no—
362C4×C53—42no—
363C4×C53—42no—
364C4×C53—42no—
365C4×C53—42no—
366C4×C53—42no—
367C4×C53—42no—
368Dic53—24no—
369Dic53—42no—
370Dic53—42no—
371Dic53—42no—
372Dic53—42no—
373Dic53—42no—
374#2837—5316no—
375C2×#400D5311yescharacteristic, complemented
376C2×#399—531no—
377C2×#399—531no—
378C2×#398—531no—
379C2×#398—531no—
380C2×#397—531no—
381C2×#397—531no—
382C2×#396—531no—
383C2×#396—531no—
384C2×#394—531no—
385C2×#394—531no—
386C2×#394—531no—
387C2×#389—531no—
388C2×#388—531no—
389C2×#388—531no—
390C2×C53#283718yescomplemented
391C2×C53C2×#53911yescharacteristic
392C2×C53C2×#54011yescharacteristic
393C2×C53C2×#54211yescharacteristic
394C2×C53C2×#56011yescharacteristic
395C2×C53C2×#56211yescharacteristic
396C2×C53C2×#56211yescharacteristic
397C2×C53C2×#56311yescharacteristic
398D53—82no—
399D53—82no—
400C23×D4—531no—
401C22×C4⋊C4—531no—
402C22×C4⋊C4—531no—
403C22×C4⋊C4—531no—
404C22×C4⋊C4—531no—
405C22×C4⋊C4—531no—
406C22×C4⋊C4—531no—
407C22×C4⋊C4—531no—
408C22×C4⋊C4—531no—
409C22×C4⋊C4—531no—
410C22×C4⋊C4C2×D5311yescharacteristic
411C22×C4⋊C4C2×D5311yescharacteristic
412C22×C22⋊C4—531no—
413C22×C22⋊C4—531no—
414C22×C22⋊C4—531no—
415C22×C22⋊C4—531no—
416C22×C22⋊C4—531no—
417C22×C22⋊C4—531no—
418C22×C22⋊C4—531no—
419C22×C22⋊C4—531no—
420C22×C22⋊C4—531no—
421C22×C22⋊C4—531no—
422C22×C22⋊C4—531no—
423C22×C22⋊C4—531no—
424C22×C42—531no—
425#400C2×D5318yescomplemented
426#399—538no—
427#399—538no—
428#398—538no—
429#398—538no—
430#397—538no—
431#397—538no—
432#396—538no—
433#396—538no—
434#394—538no—
435#394—538no—
436#394—538no—
437#389—538no—
438#388—538no—
439#388—538no—
440C2×#95—531no—
441C2×#95—531no—
442C2×#95—531no—
443C2×#95—531no—
444C2×#95—531no—
445C2×#95C2×D5311yescharacteristic
446C2×#95C2×D5311yescharacteristic
447C2×#95C2×D5311yescharacteristic
448C2×#95C2×D5311yescharacteristic
449C2×#95C2×D5311yescharacteristic
450C53C2×#283711yescharacteristic, complemented, Sylow
451C25—531no—
452C25—531no—
453C22×D4—534no—
454C22×D4—2122no—
455C22×D4—2122no—
456C22×D4—2122no—
457C23×C4—531no—
458C23×C4—531no—
459C23×C4—531no—
460C23×C4—531no—
461C23×C4—531no—
462C23×C4—531no—
463C23×C4C22×D5311yescharacteristic
464C23×C4C22×D5311yescharacteristic
465C23×C4C22×D5311yescharacteristic
466C23×C4C22×D5311yescharacteristic
467C23×C4C22×D5311yescharacteristic
468C23×C4C22×D5311yescharacteristic
469C23×C4C22×D5311yescharacteristic
470C2×C4⋊C4—42no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—534no—
473C2×C4⋊C4—534no—
474C2×C4⋊C4—534no—
475C2×C4⋊C4—534no—
476C2×C4⋊C4—534no—
477C2×C4⋊C4—534no—
478C2×C4⋊C4—534no—
479C2×C4⋊C4—534no—
480C2×C4⋊C4—534no—
481C2×C4⋊C4—1064no—
482C2×C4⋊C4—2122no—
483C2×C4⋊C4—2122no—
484C2×C4⋊C4—2122no—
485C2×C4⋊C4—2122no—
486C2×C4⋊C4—2122no—
487C2×C4⋊C4—2122no—
488C2×C4⋊C4—2122no—
489C2×C4⋊C4—2122no—
490C2×C4⋊C4C22×D5314yes—
491C2×C4⋊C4C22×D5314yes—
492C2×C22⋊C4—534no—
493C2×C22⋊C4—534no—
494C2×C22⋊C4—534no—
495C2×C22⋊C4—534no—
496C2×C22⋊C4—534no—
497C2×C22⋊C4—534no—
498C2×C22⋊C4—534no—
499C2×C22⋊C4—534no—
500C2×C22⋊C4—534no—
501C2×C22⋊C4—534no—
502C2×C22⋊C4—534no—
503C2×C22⋊C4—534no—
504C2×C22⋊C4—1064no—
505C2×C22⋊C4—1064no—
506C2×C22⋊C4—2122no—
507C2×C22⋊C4—2122no—
508C2×C22⋊C4—2122no—
509C2×C22⋊C4—2122no—
510C2×C22⋊C4—2122no—
511C2×C22⋊C4—2122no—
512C2×C22⋊C4—2122no—
513C2×C22⋊C4—2122no—
514C2×C22⋊C4—2122no—
515C2×C22⋊C4—2122no—
516C2×C42—534no—
517C2×C42—2122no—
518#95—534no—
519#95—534no—
520#95—534no—
521#95—534no—
522#95—534no—
523#95C22×D5314yes—
524#95C22×D5314yes—
525#95C22×D5314yes—
526#95C22×D5314yes—
527#95C22×D5314yes—
528C24—532no—
529C24—532no—
530C24—1062no—
531C24—1062no—
532C24—1062no—
533C24—1062no—
534C24—1062no—
535C24—1062no—
536C24—1062no—
537C24—1062no—
538C24—1062no—
539C24—1062no—
540C24—1062no—
541C24—1062no—
542C24—1062no—
543C24—1062no—
544C24C23×D5311yescharacteristic
545C2×D4—2124no—
546C2×D4—2124no—
547C2×D4—2124no—
548C2×D4—21216no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—534no—
571C22×C4—532no—
572C22×C4—532no—
573C22×C4—532no—
574C22×C4—532no—
575C22×C4—532no—
576C22×C4—532no—
577C22×C4—1062no—
578C22×C4—1062no—
579C22×C4—1062no—
580C22×C4—1062no—
581C22×C4—1062no—
582C22×C4—1062no—
583C22×C4—1062no—
584C22×C4—1062no—
585C22×C4—1062no—
586C22×C4—1062no—
587C22×C4—1062no—
588C22×C4—1062no—
589C22×C4—1062no—
590C22×C4—1062no—
591C22×C4—1062no—
592C22×C4—1062no—
593C22×C4—1062no—
594C22×C4C23×D5312yes—
595C22×C4C23×D5312yes—
596C22×C4C23×D5312yes—
597C22×C4C23×D5312yes—
598C22×C4C23×D5312yes—
599C22×C4C23×D5312yes—
600C22×C4C23×D5312yes—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—1068no—
604C4⋊C4—2124no—
605C4⋊C4—2124no—
606C4⋊C4—2124no—
607C4⋊C4—2124no—
608C4⋊C4—2124no—
609C4⋊C4—2124no—
610C4⋊C4—2124no—
611C4⋊C4—2124no—
612C22⋊C4—1068no—
613C22⋊C4—1068no—
614C22⋊C4—2124no—
615C22⋊C4—2124no—
616C22⋊C4—2124no—
617C22⋊C4—2124no—
618C22⋊C4—2124no—
619C22⋊C4—2124no—
620C22⋊C4—2124no—
621C22⋊C4—2124no—
622C22⋊C4—2124no—
623C22⋊C4—2124no—
624C42—2124no—
625C23—1062no—
626C23—1062no—
627C23—1062no—
628C23—1062no—
629C23—1062no—
630C23—1062no—
631C23—1062no—
632C23—1062no—
633C23—1062no—
634C23—1062no—
635C23—1062no—
636C23—1062no—
637C23—1062no—
638C23—1062no—
639C23—2124no—
640C23—2124no—
641C23—2124no—
642C23—2124no—
643C23—2124no—
644C23—2124no—
645C23—2124no—
646C23—2124no—
647C23—2124no—
648C23—2124no—
649C23—2124no—
650C23—2124no—
651C23—2124no—
652C23—2124no—
653C23#41×D5312yes—
654C23#1313326212yes—
655C23#1313326312yes—
656C23#1313326312yes—
657C23#1313326312yes—
658C23#1313326412yes—
659C23#1313326512yes—
660C23C24×D5311yescharacteristic
661D4—21216no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—534no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—1068no—
694C2×C4—1062no—
695C2×C4—1062no—
696C2×C4—1062no—
697C2×C4—1062no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—1062no—
707C2×C4—1062no—
708C2×C4—1062no—
709C2×C4—2124no—
710C2×C4—2124no—
711C2×C4—2124no—
712C2×C4—2124no—
713C2×C4—2124no—
714C22—4248no—
715C22—4248no—
716C22—2122no—
717C22—2122no—
718C22—2122no—
719C22—2122no—
720C22—2122no—
721C22—2122no—
722C22—2122no—
723C22—2122no—
724C22—2122no—
725C22—2122no—
726C22—2122no—
727C22—2122no—
728C22—2122no—
729C22—2122no—
730C22#1681122114yes—
731C22#1681122514yes—
732C22#1681123914yes—
733C22#1681136414yes—
734C22#1681136714yes—
735C22#1681136914yes—
736C22#1681137714yes—
737C22C2×#41×D5311yescharacteristic
738C22C2×#1313326211yescharacteristic
739C22C2×#1313326311yescharacteristic
740C22C2×#1313326311yescharacteristic
741C22C2×#1313326311yescharacteristic
742C22C2×#1313326411yescharacteristic
743C22C2×#1313326511yescharacteristic
744C4—42no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—1064no—
752C4—2122no—
753C4—2122no—
754C4—2122no—
755C4—2122no—
756C4—2122no—
757C2—4242no—
758C2—4242no—
759C2#2028293618yesdirect product factor
760C2C2×#1681122111yescharacteristic
761C2C2×#1681122511yescharacteristic
762C2C2×#1681123911yescharacteristic
763C2C2×#1681136411yescharacteristic
764C2C2×#1681136711yescharacteristic
765C2C2×#1681136911yescharacteristic
766C2C2×#1681137711yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#400C2
socleC24×C53C24
prime radicalC23×D212C22
hypercenterC2×#400D53
hypocenterC53C2×#2837
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. #20282936C2direct (N × H)
2. C2×#16810560C2semidirect
3. C2×#16810558C2semidirect
4. C2×#16810557C2semidirect
5. C2×#16810557C2semidirect
6. C2×#16810552C2semidirect
7. C2×#16810552C2semidirect
8. C2×#16810545C2semidirect
9. C2×#16810545C2semidirect
13. C2×#16810520C2semidirect
14. C2×#16810515C2semidirect
15. C2×#16810513C2semidirect
16. C2×C53×#400C2semidirect
40. #16810560C22semidirect
41. #16810558C22semidirect
42. #16810557C22semidirect
43. #16810557C22semidirect
44. #16810552C22semidirect
45. #16810552C22semidirect
46. #16810545C22semidirect
47. #16810545C22semidirect
51. #16810520C22semidirect
52. #16810515C22semidirect
53. #16810513C22semidirect
61. C53×#400C22semidirect
375. C2×#400D53semidirect
390. C2×C53#2837semidirect
425. #400C2×D53semidirect
450. C53C2×#2837semidirect
759. C2#20282936direct (N × H)

Maximal subgroups

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

subgroupindex
#202829362
C2×#168105602
C2×#168105582
C2×#168105572
C2×#168105522
C2×#168105452
C2×#168105412
C2×#168105202
C2×#168105152
C2×#168105132
C2×C53×#4002
C2×#283753