Finite Group Databasebeta

← C2×#20280732 #27550770

Subgroups — C2×#20280732 #27550770

Order 13568.

2026 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20280732C2116yesmaximal, direct product factor
2C2×#16810565C211yesmaximal, characteristic, complemented
3C2×#16810562C211yesmaximal, characteristic, complemented
4C2×#16810552C211yesmaximal, characteristic
5C2×#16810550C211yesmaximal, characteristic
6C2×#16810545C211yesmaximal, characteristic
7C2×#16810544C211yesmaximal, characteristic, complemented
8C2×#16810536C211yesmaximal, characteristic
9C2×#16810528C211yesmaximal, characteristic, complemented
10C2×#16810515C211yesmaximal, characteristic
11C2×#16810513C211yesmaximal, characteristic
12C2×#16810512C211yesmaximal, characteristic
13C2×#16810510C211yesmaximal, characteristic, complemented
14C2×#16810506C211yesmaximal, characteristic, complemented
15C2×#16810474C211yesmaximal, characteristic, complemented
16C2×C53×#400C211yesmaximal, characteristic, complemented
17C23×Dic106C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20C22×C4⋊Dic53C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×#11719921C2211yescharacteristic
25C22×#11719921C2211yescharacteristic
26C22×#11719921C2211yescharacteristic
27C22×#11719921C2211yescharacteristic
28C22×#11719921C2211yescharacteristic
29C22×#11719921C2211yescharacteristic
30C22×#11719921C2211yescharacteristic
31C22×C4×Dic53C2211yescharacteristic
32C22×C4×Dic53C2211yescharacteristic
33C22×C4×Dic53C2211yescharacteristic
34#16810565C2218yescomplemented
35#16810562C2218yescomplemented
36#16810552C2218yes—
37#16810550C2218yes—
38#16810545C2218yes—
39#16810544C2218yescomplemented
40#16810536C2218yes—
41#16810528C2218yescomplemented
42#16810515C2218yes—
43#16810513C2218yes—
44#16810512C2218yes—
45#16810510C2218yescomplemented
46#16810506C2218yescomplemented
47#16810474C2218yescomplemented
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C2×#13133124C2211yescharacteristic
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
68C22×Dic106—24no—
69C22×Dic106—42no—
70C22×Dic106—42no—
71C22×Dic106C2314yes—
72C23×Dic53C2311yescharacteristic
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C2×C4⋊Dic53—24no—
80C2×C4⋊Dic53—42no—
81C2×C4⋊Dic53—42no—
82C2×C4⋊Dic53C2314yes—
83C2×C4⋊Dic53C2314yes—
84C2×C4⋊Dic53C2314yes—
85C2×#11719919—24no—
86C2×#11719919—24no—
87C2×#11719919—24no—
88C2×#11719919C2314yes—
89C2×#11719919C2314yes—
90C2×#11719919C2314yes—
91C2×#11719921—24no—
92C2×#11719921—24no—
93C2×#11719921—24no—
94C2×#11719921—42no—
95C2×#11719921—42no—
96C2×#11719921—42no—
97C2×#11719921—42no—
98C2×#11719921C2314yes—
99C2×#11719921C2314yes—
100C2×#11719921C2314yes—
101C2×#11719921C2314yes—
102C2×#11719921C2314yes—
103C2×#11719921C2314yes—
104C2×#11719921C2314yes—
105C2×C4×Dic53—24no—
106C2×C4×Dic53—42no—
107C2×C4×Dic53—42no—
108C2×C4×Dic53C2314yes—
109C2×C4×Dic53C2314yes—
110C2×C4×Dic53C2314yes—
111#13133124C2314yes—
112#13133124C2314yes—
113#13133124C2314yes—
114#13133124C2314yes—
115#13133124C2314yes—
116#13133124C2314yes—
117#13133124C2314yes—
118#13133124C2314yes—
119#13133124C2314yes—
120#13133124C2314yes—
121#13133124C2314yes—
122C23×C4×C53C2311yescharacteristic
123C23×C4×C53C2311yescharacteristic
124C23×C4×C53C2311yescharacteristic
125C23×C4×C53C2311yescharacteristic
126C23×C4×C53C2311yescharacteristic
127C23×C4×C53C2311yescharacteristic
128C23×C4×C53C2311yescharacteristic
129C2×C4⋊C4×C53—42no—
130C2×C4⋊C4×C53—42no—
131C2×C4⋊C4×C53C2314yes—
132C2×C4⋊C4×C53C2314yes—
133#95×C53C2314yes—
134#95×C53C2314yes—
135#95×C53C2314yes—
136#95×C53C2314yes—
137#95×C53C2314yes—
138C24×C53C2411yescharacteristic
139C23×D53—22no—
140C23×D53—22no—
141C23×D53—22no—
142C23×D53—22no—
143C23×D53—22no—
144C23×D53—22no—
145C23×D53—22no—
146C23×D53C2412yes—
147C22×C4×C53—22no—
148C22×C4×C53—22no—
149C22×C4×C53—22no—
150C22×C4×C53—22no—
151C22×C4×C53—22no—
152C22×C4×C53—22no—
153C22×C4×C53—22no—
154C22×C4×C53—22no—
155C22×C4×C53—22no—
156C22×C4×C53—22no—
157C22×C4×C53—22no—
158C22×C4×C53—22no—
159C22×C4×C53—22no—
160C22×C4×C53—22no—
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#4114yes—
168C22×C4×C53C2412yes—
169C22×C4×C53C2412yes—
170C22×C4×C53C2412yes—
171C22×C4×C53C2412yes—
172C22×C4×C53C2412yes—
173C22×C4×C53C2412yes—
174C22×C4×C53C2412yes—
175C22×Dic53—22no—
176C22×Dic53—22no—
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—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53#4114yes—
195C22×Dic53#4114yes—
196C22×Dic53C2412yes—
197C22×Dic53C2412yes—
198C22×Dic53C2412yes—
199C22×Dic53C2412yes—
200C22×Dic53C2412yes—
201C22×Dic53C2412yes—
202C22×Dic53C2412yes—
203C2×Dic106—28no—
204C2×Dic106—44no—
205C2×Dic106—44no—
206C2×Dic106—416no—
207C4⋊C4×C53—44no—
208C4⋊C4×C53—44no—
209#11719921—28no—
210#11719921—28no—
211#11719921—28no—
212#11719921—44no—
213#11719921—44no—
214#11719921—44no—
215#11719921—44no—
216C4⋊Dic53—28no—
217C4⋊Dic53—44no—
218C4⋊Dic53—44no—
219#11719919—28no—
220#11719919—28no—
221#11719919—28no—
222C4×Dic53—28no—
223C4×Dic53—44no—
224C4×Dic53—44no—
225C23×C53C2×#4112yes—
226C23×C53C2×#4112yes—
227C23×C53C2×#4112yes—
228C23×C53H(5,𝔽2)12yes—
229C23×C53H(5,𝔽2)12yes—
230C23×C532−1+412yes—
231C23×C532−1+412yes—
232C23×C53C2511yescharacteristic
233C22×D53—22no—
234C22×D53—22no—
235C22×D53—22no—
236C22×D53—22no—
237C22×D53—22no—
238C22×D53—22no—
239C22×D53—22no—
240C22×D53—44no—
241C22×D53—44no—
242C22×D53—44no—
243C22×D53—44no—
244C22×D53—44no—
245C22×D53—44no—
246C22×D53—44no—
247C2×C4×C53—28no—
248C2×C4×C53—22no—
249C2×C4×C53—22no—
250C2×C4×C53—22no—
251C2×C4×C53—22no—
252C2×C4×C53—22no—
253C2×C4×C53—22no—
254C2×C4×C53—22no—
255C2×C4×C53—22no—
256C2×C4×C53—22no—
257C2×C4×C53—22no—
258C2×C4×C53—22no—
259C2×C4×C53—22no—
260C2×C4×C53—22no—
261C2×C4×C53—22no—
262C2×C4×C53—22no—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—22no—
266C2×C4×C53—22no—
267C2×C4×C53—22no—
268C2×C4×C53—44no—
269C2×C4×C53—44no—
270C2×C4×C53—44no—
271C2×C4×C53—44no—
272C2×C4×C53—44no—
273C2×C4×C53—44no—
274C2×C4×C53C2×#4114yes—
275C2×Dic53—28no—
276C2×Dic53—28no—
277C2×Dic53—22no—
278C2×Dic53—22no—
279C2×Dic53—22no—
280C2×Dic53—22no—
281C2×Dic53—22no—
282C2×Dic53—22no—
283C2×Dic53—22no—
284C2×Dic53—22no—
285C2×Dic53—22no—
286C2×Dic53—22no—
287C2×Dic53—22no—
288C2×Dic53—22no—
289C2×Dic53—22no—
290C2×Dic53—22no—
291C2×Dic53—22no—
292C2×Dic53—22no—
293C2×Dic53—22no—
294C2×Dic53—22no—
295C2×Dic53—22no—
296C2×Dic53—44no—
297C2×Dic53—44no—
298C2×Dic53—44no—
299C2×Dic53—44no—
300C2×Dic53—44no—
301C2×Dic53C2×#4114yes—
302C2×Dic53C2×#4114yes—
303Dic106—416no—
304C2×#2650—531nomaximal, Sylow
305C22×C53#52914yes—
306C22×C53#53814yes—
307C22×C53#53914yes—
308C22×C53#54114yes—
309C22×C53#54214yes—
310C22×C53#54214yes—
311C22×C53#54214yes—
312C22×C53C22×#4111yescharacteristic
313C22×C53C22×#4111yescharacteristic
314C22×C53C22×#4111yescharacteristic
315C22×C53C2×H(5,𝔽2)11yescharacteristic
316C22×C53C2×H(5,𝔽2)11yescharacteristic
317C22×C53C2×2−1+411yescharacteristic
318C22×C53C2×2−1+411yescharacteristic
319C2×D53—42no—
320C2×D53—42no—
321C2×D53—42no—
322C2×D53—42no—
323C2×D53—42no—
324C2×D53—42no—
325C2×D53—42no—
326C2×D53—88no—
327C4×C53—24no—
328C4×C53—42no—
329C4×C53—42no—
330C4×C53—42no—
331C4×C53—42no—
332C4×C53—42no—
333C4×C53—42no—
334Dic53—24no—
335Dic53—24no—
336Dic53—42no—
337Dic53—42no—
338Dic53—42no—
339Dic53—42no—
340Dic53—42no—
341#2650—5316no—
342C2×#400—531no—
343C2×#400—531no—
344C2×#400D5311yescharacteristic, complemented
345C2×#397—531no—
346C2×#397—531no—
347C2×#396—531no—
348C2×#395—531no—
349C2×#393—531no—
350C2×#391—531no—
351C2×#388—531no—
352C2×#388—531no—
353C2×#388—531no—
354C2×#387—531no—
355C2×#387—531no—
356C2×C4×C4⋊C4—531no—
357C2×C53#265018yescomplemented
358C2×C53C2×#52911yescharacteristic
359C2×C53C2×#53811yescharacteristic
360C2×C53C2×#53911yescharacteristic
361C2×C53C2×#54111yescharacteristic
362C2×C53C2×#54211yescharacteristic
363C2×C53C2×#54211yescharacteristic
364C2×C53C2×#54211yescharacteristic
365D53—82no—
366C23×Q8—531no—
367C22×C4⋊C4—531no—
368C22×C4⋊C4—531no—
369C22×C4⋊C4—531no—
370C22×C4⋊C4—531no—
371C22×C4⋊C4—531no—
372C22×C4⋊C4—531no—
373C22×C4⋊C4C2×D5311yescharacteristic
374C22×C4⋊C4C2×D5311yescharacteristic
375C22×C22⋊C4—531no—
376C22×C22⋊C4—531no—
377C22×C22⋊C4—531no—
378C22×C22⋊C4—531no—
379C22×C22⋊C4—531no—
380C22×C22⋊C4—531no—
381C22×C22⋊C4—531no—
382C22×C42—531no—
383C22×C42—531no—
384C22×C42—531no—
385#400—538no—
386#400—538no—
387#400C2×D5318yescomplemented
388#397—538no—
389#397—538no—
390#396—538no—
391#395—538no—
392#393—538no—
393#391—538no—
394#388—538no—
395#388—538no—
396#388—538no—
397#387—538no—
398#387—538no—
399C4×C4⋊C4—538no—
400C2×#95—531no—
401C2×#95—531no—
402C2×#95—531no—
403C2×#95—531no—
404C2×#95—531no—
405C2×#95—531no—
406C2×#95—531no—
407C2×#95—531no—
408C2×#95—531no—
409C2×#95—531no—
410C2×#95—531no—
411C2×#95C2×D5311yescharacteristic
412C2×#95C2×D5311yescharacteristic
413C2×#95C2×D5311yescharacteristic
414C2×#95C2×D5311yescharacteristic
415C2×#95C2×D5311yescharacteristic
416C53C2×#265011yescharacteristic, complemented, Sylow
417C25—531no—
418C22×Q8—534no—
419C22×Q8—1064no—
420C22×Q8—2122no—
421C22×Q8—2122no—
422C23×C4—531no—
423C23×C4—531no—
424C23×C4—531no—
425C23×C4—531no—
426C23×C4—531no—
427C23×C4—531no—
428C23×C4—531no—
429C23×C4C22×D5311yescharacteristic
430C23×C4C22×D5311yescharacteristic
431C23×C4C22×D5311yescharacteristic
432C23×C4C22×D5311yescharacteristic
433C23×C4C22×D5311yescharacteristic
434C23×C4C22×D5311yescharacteristic
435C23×C4C22×D5311yescharacteristic
436C2×C4⋊C4—42no—
437C2×C4⋊C4—42no—
438C2×C4⋊C4—534no—
439C2×C4⋊C4—534no—
440C2×C4⋊C4—534no—
441C2×C4⋊C4—534no—
442C2×C4⋊C4—534no—
443C2×C4⋊C4—534no—
444C2×C4⋊C4—1064no—
445C2×C4⋊C4—1064no—
446C2×C4⋊C4—1064no—
447C2×C4⋊C4—1064no—
448C2×C4⋊C4—2122no—
449C2×C4⋊C4—2122no—
450C2×C4⋊C4C22×D5314yes—
451C2×C4⋊C4C22×D5314yes—
452C2×C22⋊C4—534no—
453C2×C22⋊C4—534no—
454C2×C22⋊C4—534no—
455C2×C22⋊C4—534no—
456C2×C22⋊C4—534no—
457C2×C22⋊C4—534no—
458C2×C22⋊C4—534no—
459C2×C22⋊C4—1064no—
460C2×C22⋊C4—1064no—
461C2×C22⋊C4—1064no—
462C2×C22⋊C4—2122no—
463C2×C22⋊C4—2122no—
464C2×C22⋊C4—2122no—
465C2×C22⋊C4—2122no—
466C2×C42—534no—
467C2×C42—534no—
468C2×C42—534no—
469C2×C42—1064no—
470C2×C42—2122no—
471C2×C42—2122no—
472#95—534no—
473#95—534no—
474#95—534no—
475#95—534no—
476#95—534no—
477#95—534no—
478#95—534no—
479#95—534no—
480#95—534no—
481#95—534no—
482#95—534no—
483#95C22×D5314yes—
484#95C22×D5314yes—
485#95C22×D5314yes—
486#95C22×D5314yes—
487#95C22×D5314yes—
488C24—532no—
489C24—1062no—
490C24—1062no—
491C24—1062no—
492C24—1062no—
493C24—1062no—
494C24—1062no—
495C24—1062no—
496C24C23×D5311yescharacteristic
497C2×Q8—1068no—
498C2×Q8—2124no—
499C2×Q8—2124no—
500C2×Q8—21216no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—534no—
522C22×C4—534no—
523C22×C4—532no—
524C22×C4—532no—
525C22×C4—532no—
526C22×C4—532no—
527C22×C4—532no—
528C22×C4—532no—
529C22×C4—532no—
530C22×C4—1062no—
531C22×C4—1062no—
532C22×C4—1062no—
533C22×C4—1062no—
534C22×C4—1062no—
535C22×C4—1062no—
536C22×C4—1062no—
537C22×C4—1062no—
538C22×C4—1062no—
539C22×C4—1062no—
540C22×C4—1062no—
541C22×C4—1062no—
542C22×C4—1062no—
543C22×C4—1062no—
544C22×C4—1062no—
545C22×C4—1062no—
546C22×C4—1062no—
547C22×C4—1062no—
548C22×C4—1062no—
549C22×C4#1171994914yes—
550C22×C4C23×D5312yes—
551C22×C4C23×D5312yes—
552C22×C4C23×D5312yes—
553C22×C4C23×D5312yes—
554C22×C4C23×D5312yes—
555C22×C4C23×D5312yes—
556C22×C4C23×D5312yes—
557C4⋊C4—44no—
558C4⋊C4—44no—
559C4⋊C4—1068no—
560C4⋊C4—1068no—
561C4⋊C4—1068no—
562C4⋊C4—1068no—
563C4⋊C4—2124no—
564C4⋊C4—2124no—
565C22⋊C4—1068no—
566C22⋊C4—1068no—
567C22⋊C4—1068no—
568C22⋊C4—2124no—
569C22⋊C4—2124no—
570C22⋊C4—2124no—
571C22⋊C4—2124no—
572C42—1068no—
573C42—2124no—
574C42—2124no—
575C23—1062no—
576C23—1062no—
577C23—1062no—
578C23—1062no—
579C23—1062no—
580C23—1062no—
581C23—1062no—
582C23—2124no—
583C23—2124no—
584C23—2124no—
585C23—2124no—
586C23—2124no—
587C23—2124no—
588C23—2124no—
589C23#41×D5312yes—
590C23#41×D5312yes—
591C23C2×#1171994912yes—
592C23#1313326212yes—
593C23#1313326312yes—
594C23#1313326412yes—
595C23#1313326412yes—
596C23C24×D5311yescharacteristic
597Q8—21216no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—28no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—44no—
620C2×C4—44no—
621C2×C4—44no—
622C2×C4—44no—
623C2×C4—44no—
624C2×C4—44no—
625C2×C4—534no—
626C2×C4—534no—
627C2×C4—1068no—
628C2×C4—1062no—
629C2×C4—1062no—
630C2×C4—1062no—
631C2×C4—1062no—
632C2×C4—1068no—
633C2×C4—1062no—
634C2×C4—1062no—
635C2×C4—1062no—
636C2×C4—1062no—
637C2×C4—1062no—
638C2×C4—1062no—
639C2×C4—1062no—
640C2×C4—1062no—
641C2×C4—1062no—
642C2×C4—1062no—
643C2×C4—1062no—
644C2×C4—1062no—
645C2×C4—1062no—
646C2×C4—1062no—
647C2×C4—1062no—
648C2×C4—2124no—
649C2×C4—2124no—
650C2×C4—2124no—
651C2×C4—2124no—
652C2×C4—2124no—
653C2×C4C2×#1171994914yes—
654C22—4248no—
655C22—2122no—
656C22—2122no—
657C22—2122no—
658C22—2122no—
659C22—2122no—
660C22—2122no—
661C22—2122no—
662C22#1681115814yes—
663C22#1681121314yes—
664C22#1681121414yes—
665C22#1681123614yes—
666C22#1681123714yes—
667C22#1681123914yes—
668C22#1681124114yes—
669C22C2×#41×D5311yescharacteristic
670C22C2×#41×D5311yescharacteristic
671C22C22×#1171994911yescharacteristic
672C22C2×#1313326211yescharacteristic
673C22C2×#1313326311yescharacteristic
674C22C2×#1313326411yescharacteristic
675C22C2×#1313326411yescharacteristic
676C4—24no—
677C4—42no—
678C4—42no—
679C4—42no—
680C4—42no—
681C4—42no—
682C4—42no—
683C4—1064no—
684C4—1064no—
685C4—2122no—
686C4—2122no—
687C4—2122no—
688C4—2122no—
689C4—2122no—
690C2—4242no—
691C2#2028073218yesdirect product factor
692C2C2×#1681115811yescharacteristic
693C2C2×#1681121311yescharacteristic
694C2C2×#1681121411yescharacteristic
695C2C2×#1681123611yescharacteristic
696C2C2×#1681123711yescharacteristic
697C2C2×#1681123911yescharacteristic
698C2C2×#1681124111yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#400C2
socleC24×C53C24
prime radicalC24×D53C23
hypercenterC2×#400D53
hypocenterC53C2×#2650
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. #20280732C2direct (N × H)
2. C2×#16810565C2semidirect
3. C2×#16810562C2semidirect
7. C2×#16810544C2semidirect
9. C2×#16810528C2semidirect
13. C2×#16810510C2semidirect
14. C2×#16810506C2semidirect
15. C2×#16810474C2semidirect
16. C2×C53×#400C2semidirect
34. #16810565C22semidirect
35. #16810562C22semidirect
39. #16810544C22semidirect
41. #16810528C22semidirect
45. #16810510C22semidirect
46. #16810506C22semidirect
47. #16810474C22semidirect
61. C53×#400C22semidirect
344. C2×#400D53semidirect
357. C2×C53#2650semidirect
387. #400C2×D53semidirect
416. C53C2×#2650semidirect
691. C2#20280732direct (N × H)

Maximal subgroups

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

subgroupindex
#202807322
C2×#168105652
C2×#168105622
C2×#168105522
C2×#168105502
C2×#168105452
C2×#168105442
C2×#168105362
C2×#168105282
C2×#168105152
C2×#168105132
C2×#168105122
C2×#168105102
C2×#168105062
C2×#168104742
C2×C53×#4002
C2×#265053