Finite Group Databasebeta

← C4×#16810517 #27305249

Subgroups — C4×#16810517 #27305249

Order 13568.

2134 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810517C212yesmaximal
2C2×C4×#11719919C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Dic53C211yesmaximal, characteristic
4C2×C4×C22⋊Dic53C211yesmaximal, characteristic
5C2×C42×Dic53C211yesmaximal, characteristic, complemented
6#20272952C212yesmaximal
7#20272950C212yesmaximal, complemented
8#20272941C212yesmaximal, complemented
9C4×#13133124C211yesmaximal, characteristic, complemented
10C4×#13133124C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C53C211yesmaximal, characteristic
12C22×#11719919C2212yes—
13C22×C22⋊Dic53C2211yescharacteristic
14C22×C22⋊Dic53C2212yes—
15C22×C22⋊Dic53C2211yescharacteristic
16C22×C4×Dic53C2211yescharacteristic
17C22×C4×Dic53C2212yes—
18C22×C4×Dic53C2211yescharacteristic
19C22×C4×Dic53C2211yescharacteristic
20C22×C4×Dic53C2212yes—
21C22×C4×Dic53C2211yescharacteristic
22#16810517C4116yesdirect product factor
23C4×#11719919—24no—
24C4×C22⋊Dic53—24no—
25C4×C22⋊Dic53C418yescomplemented
26C2×#13133124C2212yes—
27C2×#13133124C2212yes—
28C2×#13133124C2212yes—
29C2×#13133124C2212yes—
30C2×#13133124C2211yescharacteristic
31C2×#13133124C2211yescharacteristic
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C42×Dic53—24no—
35C24×C4×C53C2211yescharacteristic
36C22×C22⋊C4×C53C2212yes—
37C22×C42×C53C2211yescharacteristic
38C22×C42×C53C2211yescharacteristic
39C4×C22⋊C4×C53—24no—
40C2×#95×C53C2212yes—
41C23×Dic53C2312yes—
42C23×Dic53C2311yescharacteristic
43C23×Dic53C2311yescharacteristic
44C23×Dic53C2311yescharacteristic
45C23×Dic53C2312yes—
46C23×Dic53C2311yescharacteristic
47C2×#11719919—24no—
48C2×#11719919—24no—
49C2×#11719919C2×C418yescomplemented
50C2×C22⋊Dic53—24no—
51C2×C22⋊Dic53—24no—
52C2×C22⋊Dic53—24no—
53C2×C22⋊Dic53C2×C418yes—
54C2×C22⋊Dic53C2×C414yes—
55C2×C22⋊Dic53C2×C418yes—
56C2×C22⋊Dic53C2×C414yes—
57C2×C4×Dic53—22no—
58C2×C4×Dic53—22no—
59C2×C4×Dic53—22no—
60C2×C4×Dic53—22no—
61C2×C4×Dic53—24no—
62C2×C4×Dic53—22no—
63C2×C4×Dic53—22no—
64C2×C4×Dic53—22no—
65C2×C4×Dic53—22no—
66C2×C4×Dic53—22no—
67C2×C4×Dic53—24no—
68C2×C4×Dic53—24no—
69C2×C4×Dic53—24no—
70C2×C4×Dic53—24no—
71C2×C4×Dic53C2×C414yes—
72C2×C4×Dic53C2×C414yes—
73C2×C4×Dic53C2×C418yescomplemented
74C2×C4×Dic53D414yes—
75#13133124—24no—
76#13133124—24no—
77#13133124—24no—
78#13133124—24no—
79#13133124C2×C414yes—
80#13133124C2×C414yes—
81#13133124C2×C418yescomplemented
82#13133124C2×C418yescomplemented
83C25×C53C2311yescharacteristic
84C23×C4×C53—22no—
85C23×C4×C53—22no—
86C23×C4×C53—22no—
87C23×C4×C53—22no—
88C23×C4×C53—22no—
89C23×C4×C53—22no—
90C23×C4×C53C2×C414yes—
91C23×C4×C53C2312yes—
92C23×C4×C53C2311yescharacteristic
93C23×C4×C53C2312yes—
94C23×C4×C53C2311yescharacteristic
95C2×C22⋊C4×C53—24no—
96C2×C22⋊C4×C53—24no—
97C2×C22⋊C4×C53C2×C418yes—
98C2×C42×C53—22no—
99C2×C42×C53—22no—
100C2×C42×C53—22no—
101C2×C42×C53—22no—
102C2×C42×C53—22no—
103C2×C42×C53D414yes—
104#95×C53—24no—
105C24×C53—21no—
106C24×C53—21no—
107C24×C53—22no—
108C24×C53—21no—
109C24×C53—21no—
110C24×C53—21no—
111C24×C53—21no—
112C24×C53—22no—
113C24×C53—22no—
114C24×C53C22×C414yes—
115C24×C53C22×C412yes—
116C24×C53C2411yescharacteristic
117C22×C4×C53—22no—
118C22×C4×C53—22no—
119C22×C4×C53—22no—
120C22×C4×C53—22no—
121C22×C4×C53—21no—
122C22×C4×C53—22no—
123C22×C4×C53—21no—
124C22×C4×C53—22no—
125C22×C4×C53—22no—
126C22×C4×C53—22no—
127C22×C4×C53—21no—
128C22×C4×C53—21no—
129C22×C4×C53—21no—
130C22×C4×C53—21no—
131C22×C4×C53—22no—
132C22×C4×C53—22no—
133C22×C4×C53—28no—
134C22×C4×C53—28no—
135C22×C4×C53—28no—
136C22×C4×C53—44no—
137C22×C4×C53—44no—
138C22×C4×C53—44no—
139C22×C4×C53—44no—
140C22×C4×C53C22×C414yes—
141C22×C4×C53C22×C412yes—
142C22×C4×C53C22×C414yes—
143C22×C4×C53C22×C412yes—
144C22×C4×C53C2×D414yes—
145C22×C4×C53C2×D412yes—
146C22×C4×C53C2×D412yes—
147C22×C4×C53#4114yes—
148C22×C4×C53#4112yes—
149C22×C4×C53#4112yes—
150C22×C4×C53#4112yes—
151C22×C4×C53#4112yes—
152C22×Dic53—21no—
153C22×Dic53—21no—
154C22×Dic53—21no—
155C22×Dic53—22no—
156C22×Dic53—21no—
157C22×Dic53—21no—
158C22×Dic53—21no—
159C22×Dic53—22no—
160C22×Dic53—22no—
161C22×Dic53—22no—
162C22×Dic53—22no—
163C22×Dic53—22no—
164C22×Dic53—22no—
165C22×Dic53—21no—
166C22×Dic53—22no—
167C22×Dic53—22no—
168C22×Dic53—22no—
169C22×Dic53—22no—
170C22×Dic53—21no—
171C22×Dic53—22no—
172C22×Dic53—22no—
173C22×Dic53—22no—
174C22×Dic53—22no—
175C22×Dic53C22×C412yes—
176C22×Dic53C22×C414yes—
177C22×Dic53C22×C412yes—
178C22×Dic53C22×C412yes—
179C22×Dic53C22×C414yes—
180C22×Dic53C22×C414yes—
181C22×Dic53C22×C412yes—
182C22×Dic53C22×C414yes—
183C22×Dic53C2×D414yes—
184C22×Dic53#4114yes—
185C22×Dic53#4114yes—
186C22⋊C4×C53—216no—
187C42×C53—28no—
188C42×C53—44no—
189C22⋊Dic53—28no—
190C22⋊Dic53—216no—
191C22⋊Dic53C42116yescomplemented
192#11719919—216no—
193C4×Dic53—216no—
194C4×Dic53—28no—
195C4×Dic53—28no—
196C4×Dic53—28no—
197C4×Dic53—216no—
198C4×Dic53—44no—
199C23×C53—22no—
200C23×C53—22no—
201C23×C53—22no—
202C23×C53—22no—
203C23×C53—24no—
204C23×C53—24no—
205C23×C53—24no—
206C23×C53—24no—
207C23×C53—24no—
208C23×C53—22no—
209C23×C53—24no—
210C23×C53—22no—
211C23×C53—41no—
212C23×C53—41no—
213C23×C53—42no—
214C23×C53—41no—
215C23×C53—41no—
216C23×C53—42no—
217C23×C53—42no—
218C23×C53—42no—
219C23×C53—42no—
220C23×C53—42no—
221C23×C53C2×C4214yes—
222C23×C53C23×C411yescharacteristic
223C23×C53C23×C412yes—
224C23×C53C22×D411yescharacteristic
225C23×C53C22×D411yescharacteristic
226C23×C53C2×#4112yes—
227C23×C53C2×#4112yes—
228C23×C53C2×#4111yescharacteristic
229C23×C53C2×#4111yescharacteristic
230C23×C53C2×#4111yescharacteristic
231C23×C53C2×#4111yescharacteristic
232C23×C53C2×#4112yes—
233C2×C4×C53—24no—
234C2×C4×C53—24no—
235C2×C4×C53—24no—
236C2×C4×C53—24no—
237C2×C4×C53—24no—
238C2×C4×C53—24no—
239C2×C4×C53—22no—
240C2×C4×C53—22no—
241C2×C4×C53—22no—
242C2×C4×C53—24no—
243C2×C4×C53—24no—
244C2×C4×C53—24no—
245C2×C4×C53—41no—
246C2×C4×C53—41no—
247C2×C4×C53—41no—
248C2×C4×C53—42no—
249C2×C4×C53—41no—
250C2×C4×C53—42no—
251C2×C4×C53—42no—
252C2×C4×C53—42no—
253C2×C4×C53—416no—
254C2×C4×C53#11714yes—
255C2×C4×C53C4×D414yes—
256C2×C4×C53C4×D418yes—
257C2×C4×C53C4×D414yes—
258C2×C4×C53#12114yes—
259C2×C4×C53#12314yes—
260C2×C4×C53#12414yes—
261C2×C4×C53#12614yes—
262C2×Dic53—24no—
263C2×Dic53—22no—
264C2×Dic53—22no—
265C2×Dic53—22no—
266C2×Dic53—24no—
267C2×Dic53—24no—
268C2×Dic53—24no—
269C2×Dic53—22no—
270C2×Dic53—24no—
271C2×Dic53—22no—
272C2×Dic53—22no—
273C2×Dic53—24no—
274C2×Dic53—24no—
275C2×Dic53—24no—
276C2×Dic53—24no—
277C2×Dic53—24no—
278C2×Dic53—24no—
279C2×Dic53—24no—
280C2×Dic53—22no—
281C2×Dic53—22no—
282C2×Dic53—24no—
283C2×Dic53—24no—
284C2×Dic53—24no—
285C2×Dic53—22no—
286C2×Dic53—42no—
287C2×Dic53—42no—
288C2×Dic53—42no—
289C2×Dic53—42no—
290C2×Dic53—42no—
291C2×Dic53—42no—
292C2×Dic53C2×C4214yes—
293C2×Dic53C2×C4214yes—
294C2×Dic53#11714yes—
295C2×Dic53C4×D418yes—
296C4×#388—531nomaximal, Sylow
297C22×C53—24no—
298C22×C53—24no—
299C22×C53—24no—
300C22×C53—44no—
301C22×C53—42no—
302C22×C53—42no—
303C22×C53—42no—
304C22×C53—42no—
305C22×C53—44no—
306C22×C53—44no—
307C22×C53—44no—
308C22×C53C22×C4211yescharacteristic
309C22×C53C2×#11711yescharacteristic
310C22×C53C2×#11711yescharacteristic
311C22×C53C2×C4×D412yes—
312C22×C53C2×C4×D411yescharacteristic
313C22×C53C2×C4×D411yescharacteristic
314C22×C53C2×C4×D412yes—
315C22×C53C4×#4112yes—
316C22×C53C4×#4112yes—
317C22×C53C4×#4112yes—
318C22×C53C4×#4111yescharacteristic
319C22×C53C4×#4112yes—
320C22×C53C4×#4111yescharacteristic
321C22×C53C2×#12111yescharacteristic
322C22×C53C2×#12311yescharacteristic
323C22×C53#52512yes—
324C22×C53C2×#12411yescharacteristic
325C22×C53C2×#12611yescharacteristic
326C22×C53#52912yes—
327C22×C53#52912yes—
328C22×C53#52912yes—
329C22×C53#52912yes—
330C22×C53#53212yes—
331C4×C53—28no—
332C4×C53—42no—
333C4×C53—44no—
334C4×C53#38818yescomplemented
335Dic53—24no—
336Dic53—24no—
337Dic53—24no—
338Dic53—28no—
339Dic53—42no—
340Dic53—44no—
341C2×#388—532no—
342C2×C4×C4⋊C4—531no—
343C2×C4×C22⋊C4—531no—
344C2×C4×C22⋊C4—531no—
345C2×C4×C22⋊C4D5311yescharacteristic
346C2×C43—531no—
347#1437—532no—
348#1436—532no—
349#1434—532no—
350C4×#95—531no—
351C4×#95—531no—
352C2×C53—44no—
353C2×C53C4×#11711yescharacteristic
354C2×C53C42×D411yescharacteristic
355C2×C53C42×D411yescharacteristic
356C2×C53C2×#38811yescharacteristic
357C2×C53#229011yescharacteristic
358C2×C53#229311yescharacteristic
359C2×C53#229811yescharacteristic
360C2×C53C4×#12112yes—
361C2×C53C4×#12312yes—
362C2×C53C4×#12412yes—
363C2×C53C4×#12612yes—
364C24×C4C2×D5311yescharacteristic
365C22×C4⋊C4—532no—
366C22×C22⋊C4—531no—
367C22×C22⋊C4—531no—
368C22×C22⋊C4—532no—
369C22×C22⋊C4C2×D5312yes—
370C22×C42—532no—
371C22×C42—531no—
372C22×C42—531no—
373C22×C42—531no—
374C22×C42—532no—
375C22×C42—531no—
376C22×C42C2×D5311yescharacteristic
377C22×C42C2×D5311yescharacteristic
378#388—5316no—
379C4×C4⋊C4—1064no—
380C4×C22⋊C4—24no—
381C4×C22⋊C4—538no—
382C4×C22⋊C4—1064no—
383C2×#95—532no—
384C2×#95—532no—
385C2×#95—531no—
386C2×#95—531no—
387C2×#95—532no—
388C2×#95—532no—
389C2×#95—532no—
390C2×#95—532no—
391C2×#95C2×D5312yes—
392C43—1064no—
393C53C4×#38811yescharacteristic, complemented, Sylow
394C25C22×D5311yescharacteristic
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—531no—
402C23×C4—531no—
403C23×C4—532no—
404C23×C4—531no—
405C23×C4—532no—
406C23×C4—531no—
407C23×C4C4×D5314yes—
408C23×C4C22×D5312yes—
409C23×C4C22×D5311yescharacteristic
410C23×C4C22×D5312yes—
411C23×C4C22×D5311yescharacteristic
412C2×C4⋊C4—538no—
413C2×C4⋊C4—1064no—
414C2×C4⋊C4—1064no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—534no—
418C2×C22⋊C4—538no—
419C2×C22⋊C4—534no—
420C2×C22⋊C4—538no—
421C2×C22⋊C4—1064no—
422C2×C22⋊C4—1064no—
423C2×C22⋊C4—1064no—
424C2×C22⋊C4C4×D5318yes—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—534no—
431C2×C42—534no—
432C2×C42—538no—
433C2×C42—534no—
434C2×C42—1064no—
435C2×C42—1064no—
436C2×C42—1064no—
437C2×C42—1064no—
438C2×C42—1064no—
439C2×C42—1062no—
440C2×C42—1062no—
441C2×C42—1062no—
442C2×C42—1062no—
443C2×C42—1062no—
444C2×C42—1062no—
445C2×C42—1062no—
446C2×C42—1062no—
447C2×C42—1062no—
448C2×C42C22⋊D5314yes—
449#95—24no—
450#95—534no—
451#95—534no—
452#95—538no—
453#95—538no—
454#95—1064no—
455#95—1064no—
456#95—1064no—
457#95—1064no—
458C24—21no—
459C24—21no—
460C24—22no—
461C24—22no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—22no—
466C24—21no—
467C24C2×C4×D5314yes—
468C24C2×C4×D5312yes—
469C24C23×D5311yescharacteristic
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—28no—
487C22×C4—28no—
488C22×C4—28no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—44no—
492C22×C4—44no—
493C22×C4—534no—
494C22×C4—532no—
495C22×C4—532no—
496C22×C4—532no—
497C22×C4—534no—
498C22×C4—534no—
499C22×C4—534no—
500C22×C4—534no—
501C22×C4—534no—
502C22×C4—532no—
503C22×C4—534no—
504C22×C4—1061no—
505C22×C4—1061no—
506C22×C4—1061no—
507C22×C4—1062no—
508C22×C4—1062no—
509C22×C4—1061no—
510C22×C4—1061no—
511C22×C4—1062no—
512C22×C4—1061no—
513C22×C4—1062no—
514C22×C4—1062no—
515C22×C4—1062no—
516C22×C4—1062no—
517C22×C4—1062no—
518C22×C4—1061no—
519C22×C4—1062no—
520C22×C4—1062no—
521C22×C4—1062no—
522C22×C4—1062no—
523C22×C4—1062no—
524C22×C4—1062no—
525C22×C4—1061no—
526C22×C4—1062no—
527C22×C4C2×C4×D5314yes—
528C22×C4C2×C4×D5312yes—
529C22×C4C2×C4×D5314yes—
530C22×C4C2×C4×D5312yes—
531C22×C4#1171994514yes—
532C22×C4#1171994512yes—
533C22×C4D4×D5312yes—
534C22×C4#1171994712yes—
535C22×C4#1171994712yes—
536C22×C4#1171994712yes—
537C22×C4C2×C22⋊D5314yes—
538C22×C4C2×C22⋊D5312yes—
539C4⋊C4—10616no—
540C22⋊C4—216no—
541C22⋊C4—5316no—
542C22⋊C4—1068no—
543C22⋊C4—10616no—
544C42—28no—
545C42—44no—
546C42—10616no—
547C42—10616no—
548C42—1068no—
549C42—1068no—
550C42—1068no—
551C42—2124no—
552C23—22no—
553C23—22no—
554C23—24no—
555C23—22no—
556C23—24no—
557C23—22no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—22no—
562C23—24no—
563C23—22no—
564C23—41no—
565C23—41no—
566C23—42no—
567C23—41no—
568C23—41no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23C42×D5314yes—
575C23C22×C4×D5311yescharacteristic
576C23C22×C4×D5312yes—
577C23C2×D4×D5311yescharacteristic
578C23C22×C22⋊D5311yescharacteristic
579C23#41×D5312yes—
580C23#41×D5312yes—
581C23C2×#1171994711yescharacteristic
582C23C2×#1171994711yescharacteristic
583C23C2×#1171994711yescharacteristic
584C23C2×#1171994511yescharacteristic
585C23C2×#1171994512yes—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—22no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—416no—
607C2×C4—534no—
608C2×C4—534no—
609C2×C4—534no—
610C2×C4—538no—
611C2×C4—1064no—
612C2×C4—1062no—
613C2×C4—1062no—
614C2×C4—1062no—
615C2×C4—1064no—
616C2×C4—1064no—
617C2×C4—1064no—
618C2×C4—1062no—
619C2×C4—1064no—
620C2×C4—1062no—
621C2×C4—1062no—
622C2×C4—1064no—
623C2×C4—1064no—
624C2×C4—1064no—
625C2×C4—1064no—
626C2×C4—1064no—
627C2×C4—1064no—
628C2×C4—1064no—
629C2×C4—1062no—
630C2×C4—1064no—
631C2×C4—1062no—
632C2×C4—1064no—
633C2×C4—1064no—
634C2×C4—1062no—
635C2×C4—2122no—
636C2×C4—2122no—
637C2×C4—2122no—
638C2×C4—2122no—
639C2×C4—2122no—
640C2×C4—2122no—
641C2×C4#1313317314yes—
642C2×C4#1313317714yes—
643C2×C4C4×C22⋊D5318yes—
644C2×C4C4×C22⋊D5314yes—
645C2×C4#1313318914yes—
646C2×C4#1313319914yes—
647C2×C4#1313320414yes—
648C2×C4#1313321014yes—
649C22—24no—
650C22—24no—
651C22—24no—
652C22—44no—
653C22—44no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—44no—
659C22—44no—
660C22C2×C42×D5311yescharacteristic
661C22#117×D5311yescharacteristic
662C22C2×#1313317311yescharacteristic
663C22C4×D4×D5312yes—
664C22C2×#1313317711yescharacteristic
665C22C2×C4×C22⋊D5312yes—
666C22C2×C4×C22⋊D5311yescharacteristic
667C22C4×#1171994712yes—
668C22C4×#1171994712yes—
669C22C4×#1171994712yes—
670C22#1681109111yescharacteristic
671C22C4×#1171994512yes—
672C22C4×#1171994511yescharacteristic
673C22C2×#1313318911yescharacteristic
674C22C2×#1313319911yescharacteristic
675C22#1681113212yes—
676C22C2×#1313320411yescharacteristic
677C22C2×#1313321011yescharacteristic
678C22#1681115112yes—
679C22#1681115312yes—
680C22#1681115512yes—
681C22#1681115512yes—
682C22#1681116912yes—
683C4—28no—
684C4—44no—
685C4—42no—
686C4—1064no—
687C4—1064no—
688C4—1064no—
689C4—1068no—
690C4—2122no—
691C4—2124no—
692C4#1681051718yesdirect product factor
693C2—44no—
694C2C4×#1313317311yescharacteristic
695C2C4×#1313317711yescharacteristic
696C2C42×C22⋊D5311yescharacteristic
697C2C2×#1681051711yescharacteristic
698C2#2027716111yescharacteristic
699C2#2027717411yescharacteristic
700C2#2027721111yescharacteristic
701C2C4×#1313318912yes—
702C2C4×#1313319912yes—
703C2C4×#1313320412yes—
704C2C4×#1313321012yes—
subgroupG/H
centerC23×C4C22×D53
commutatorC22×C53C22×C42
FrattiniC24C23×D53
FittingC2×C4×C22⋊C4×C53C2
socle, cosocleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×C4×C22⋊C4D53
hypocenterC53C4×#388
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11719919C2semidirect
5. C2×C42×Dic53C2semidirect
7. #20272950C2semidirect
8. #20272941C2semidirect
9. C4×#13133124C2semidirect
10. C4×#13133124C2semidirect
22. #16810517C4direct (N × H)
25. C4×C22⋊Dic53C4semidirect
49. C2×#11719919C2×C4semidirect
73. C2×C4×Dic53C2×C4semidirect
81. #13133124C2×C4semidirect
82. #13133124C2×C4semidirect
191. C22⋊Dic53C42semidirect
334. C4×C53#388semidirect
393. C53C4×#388semidirect
692. C4#16810517direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168105172
C2×C4×#117199192
C2×C4×C22⋊Dic532
C2×C42×Dic532
#202729522
#202729502
#202729412
C4×#131331242
C2×C4×C22⋊C4×C532
C4×#38853