Finite Group Databasebeta

← #12963281

Subgroups — #12963281

Order 1280.

2756 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×D4×#41C211yesmaximal, characteristic
2C2×#66153C211yesmaximal, characteristic, complemented
3C22×#4094C211yesmaximal, characteristic, complemented
4#10615806C211yesmaximal, characteristic, complemented
5#10615806C211yesmaximal, characteristic, complemented
6#10615008C213yesmaximal, complemented
7#10615007C213yesmaximal, complemented
8#10614649C213yesmaximal, complemented
9#10614649C213yesmaximal, complemented
10#10614648C213yesmaximal, complemented
11#10614647C213yesmaximal, complemented
12#10614243C211yesmaximal, characteristic, complemented
13#10614242C211yesmaximal, characteristic, complemented
14D4×#681C213yesmaximal, complemented
15C2×#65300C213yesmaximal, complemented
16C22×C5×#41C2211yescharacteristic
17C22×C5×#41C2211yescharacteristic
18C5×#550C411yescharacteristic
19C5×D4×Q8C411yescharacteristic
20C5×#548C411yescharacteristic
21C5×#548C411yescharacteristic
22C5×#547C413yes—
23C5×#546C413yes—
24C5×#546C413yes—
25C5×D42C413yes—
26C5×#532C2213yes—
27C5×#525C2213yes—
28C5×#525C2213yes—
29C4×C5×#41C2211yescharacteristic
30C2×C4×C5×D4C2213yes—
31#66153—28no—
32C2×#4094—28no—
33C2×#4094C2211yescharacteristic
34C2×#4094C2211yescharacteristic
35C2×#4094C2211yescharacteristic
36C2×#4094C2211yescharacteristic
37C2×#4094C2213yescomplemented
38C2×#4094C2213yescomplemented
39C2×#4094C2213yescomplemented
40C2×#4094C2213yescomplemented
41C22×#681C2213yescomplemented
42C22×#681C2213yescomplemented
43C22×#681C2213yescomplemented
44C23×#168C2213yescomplemented
45#65523C2213yescomplemented
46#65523C2213yescomplemented
47#65523C2213yescomplemented
48#65523C2213yescomplemented
49#65496C2213yescomplemented
50#65496C2213yescomplemented
51C2×C22⋊#168C2213yescomplemented
52C2×C22⋊#168C2213yescomplemented
53#65301C2216yescomplemented
54#65301C2216yescomplemented
55#65300C2211yescharacteristic
56#65300C2213yes—
57#65300C2213yescomplemented
58#65300C2213yescomplemented
59#65300C2213yescomplemented
60#65300C2213yescomplemented
61#65300C2213yescomplemented
62#65300C2213yescomplemented
63#65300C2216yescomplemented
64#65300C2216yescomplemented
65#65300C2216yescomplemented
66D4×#168C2216yescomplemented
67D4×#168C2216yescomplemented
68#65288C2213yescomplemented
69#65288C2213yescomplemented
70#65286C2213yescomplemented
71#65286C2213yescomplemented
72#65213C2213yescomplemented
73C2×C4⋊#168C2213yescomplemented
74C4×#681C2213yescomplemented
75C2×#3935C2213yescomplemented
76#60146—51nomaximal, Sylow
77C2×C5×#41—24no—
78C2×C5×#41—24no—
79C2×C5×#41—24no—
80C2×C5×#41—24no—
81C2×C5×#41C2×C413yes—
82C2×C5×#41C2×C413yes—
83C2×C5×#41C2×C411yescharacteristic
84C2×C5×#41C2×C411yescharacteristic
85C2×C5×#41C2313yes—
86C2×C5×#41C2313yes—
87C2×C5×#41C2311yescharacteristic
88C22×C5×Q8C2×C411yescharacteristic
89C22×C5×Q8C2×C411yescharacteristic
90C22×C5×D4C2×C413yes—
91C22×C5×D4C2×C413yes—
92C22×C5×D4C2×C413yes—
93C23×C4×C5C2313yes—
94C23×C4×C5C2313yes—
95C5×C4⋊Q8C2×C413yes—
96C5×#127C2×C413yes—
97C5×#124C2×C413yes—
98C5×#124C2×C413yes—
99C5×#123C2×C416yes—
100C5×#123C2×C416yes—
101C5×C22⋊Q8C2×C413yes—
102C5×C22⋊Q8C2×C413yes—
103C5×C22⋊Q8C2×C413yes—
104C5×C22⋊Q8C2×C413yes—
105C5×#121C2×C413yes—
106C5×#121C2×C413yes—
107C5×#121C2×C413yes—
108C5×#121C2×C413yes—
109C5×#121C2×C416yes—
110C5×#121C2×C416yes—
111C5×#120C2×C416yes—
112C5×#120C2×C416yes—
113C4×C5×Q8C2×C411yescharacteristic
114C4×C5×Q8C2×C411yescharacteristic
115C4×C5×D4C2×C413yes—
116C4×C5×D4C2×C413yes—
117C4×C5×D4C2×C413yes—
118C4×C5×D4C2×C413yes—
119C4×C5×D4C2×C413yes—
120C4×C5×D4C2×C413yes—
121C4×C5×D4C2313yes—
122C4×C5×D4C2316yes—
123C4×C5×D4C2311yescharacteristic
124C4×C5×D4C2313yes—
125C4×C5×D4C2313yes—
126C5×#117C2313yes—
127C2×C5×C4⋊C4C2×C413yes—
128C2×C5×C22⋊C4C2×C413yes—
129C2×C5×C22⋊C4C2×C413yes—
130C2×C42×C5C2313yes—
131#4094—24no—
132#4094—24no—
133#4094—24no—
134#4094—212no—
135#4094—212no—
136#4094—212no—
137#4094—212no—
138#4094D418yescomplemented
139C2×#681—212no—
140C2×#681—212no—
141C2×#681—212no—
142C2×#681C2313yes—
143C2×#681C2313yes—
144C2×#681C2313yes—
145C2×#681C2311yescharacteristic
146C2×#681C2313yes—
147C2×#681C2313yes—
148C2×#681C2313yes—
149C2×#681C2316yes—
150C2×#681C2313yes—
151C22×#168—212no—
152C22×#168C2313yes—
153C22×#168C2313yes—
154C22×#168C2313yes—
155C22×#168C2313yes—
156C22×#168C2313yes—
157C22×#168C2316yes—
158C22×#168C2311yescharacteristic
159C22×#168C2313yes—
160C22×#168C2313yes—
161C22⋊#168C2313yes—
162C22⋊#168C2313yes—
163C22⋊#168C2316yes—
164C22⋊#168C2316yes—
165C22⋊#168C2311yescharacteristic
166C22⋊#168C2311yescharacteristic
167C22⋊#168C2313yes—
168C22⋊#168C2313yes—
169C22⋊#168C2313yes—
170C22⋊#168C2313yes—
171C4⋊#168C2313yes—
172C4⋊#168C2316yes—
173C4⋊#168C2313yes—
174C4⋊#168C2311yescharacteristic
175C4⋊#168C2313yes—
176#3935C2313yes—
177#3935C2313yes—
178#3935C2311yescharacteristic
179#3935C2313yes—
180C4×#168C2316yes—
181C2×#568—51no—
182C22×#131—51no—
183D4×#41D511yescharacteristic
184#2935—53no—
185D4×M16—53no—
186#2933—53no—
187#2933—53no—
188#2932—53no—
189#2930—53no—
190#2929—53no—
191C2×#435—53no—
192#2906—51no—
193#2880—51no—
194#2880—51no—
195#2875—51no—
196C24×C5C22×C413yes—
197C24×C5C22×C413yes—
198C5×#41—24no—
199C5×#41—24no—
200C5×#41—212no—
201C5×#41—212no—
202C5×#41—26no—
203C5×#41—26no—
204C5×#41—26no—
205C5×#41—26no—
206C5×#41C2×D414yes—
207C5×#41#4114yes—
208C2×C5×Q8—24no—
209C2×C5×Q8—24no—
210C2×C5×Q8C22×C413yes—
211C2×C5×Q8C22×C413yes—
212C2×C5×Q8C22×C411yescharacteristic
213C2×C5×D4—212no—
214C2×C5×D4—212no—
215C2×C5×D4—46no—
216C2×C5×D4C22×C411yescharacteristic
217C2×C5×D4C22×C413yes—
218C2×C5×D4C22×C416yes—
219C2×C5×D4C22×C416yes—
220C2×C5×D4C22×C413yes—
221C2×C5×D4C22×C413yes—
222C2×C5×D4C22×C413yes—
223C2×C5×D4C22×C413yes—
224C2×C5×D4C22×C416yes—
225C2×C5×D4C22×C413yes—
226C22×C4×C5—26no—
227C22×C4×C5—26no—
228C22×C4×C5—26no—
229C22×C4×C5—26no—
230C22×C4×C5C22×C413yes—
231C22×C4×C5C22×C413yes—
232C22×C4×C5C22×C413yes—
233C22×C4×C5C22×C413yes—
234C22×C4×C5C22×C413yes—
235C22×C4×C5C22×C413yes—
236C22×C4×C5C22×C413yes—
237C22×C4×C5C22×C413yes—
238C22×C4×C5C2411yescharacteristic
239C22×C4×C5C2411yescharacteristic
240C22×C4×C5C2413yes—
241C22×C4×C5C2413yes—
242C22×C4×C5C2413yes—
243C5×C4⋊C4C22×C411yescharacteristic
244C5×C4⋊C4C22×C413yes—
245C5×C4⋊C4C22×C413yes—
246C5×C4⋊C4C22×C413yes—
247C5×C4⋊C4C22×C413yes—
248C5×C4⋊C4C22×C413yes—
249C5×C4⋊C4C22×C416yes—
250C5×C22⋊C4C22×C411yescharacteristic
251C5×C22⋊C4C22×C411yescharacteristic
252C5×C22⋊C4C22×C413yes—
253C5×C22⋊C4C22×C413yes—
254C5×C22⋊C4C22×C413yes—
255C5×C22⋊C4C22×C413yes—
256C5×C22⋊C4C22×C413yes—
257C5×C22⋊C4C22×C413yes—
258C5×C22⋊C4C22×C416yes—
259C5×C22⋊C4C22×C416yes—
260C5×C22⋊C4C22×C416yes—
261C42×C5C22×C413yes—
262C42×C5C22×C413yes—
263C42×C5C2411yescharacteristic
264C42×C5C2413yes—
265#681—26no—
266#681—26no—
267#681—26no—
268#681—22no—
269#681—26no—
270#681—26no—
271#681—212no—
272#681—26no—
273#681C2×D4112yescomplemented
274C2×#168—26no—
275C2×#168—26no—
276C2×#168—26no—
277C2×#168—22no—
278C2×#168—26no—
279C2×#168—26no—
280C2×#168—26no—
281C2×#168—212no—
282C2×#168C2×D4112yescomplemented
283C2×#168C2413yes—
284C2×#168C2411yescharacteristic
285C2×#168C2411yescharacteristic
286C2×#168C2413yes—
287C2×#168C2413yes—
288C2×#168C2411yescharacteristic
289C2×#168C2413yes—
290C2×#168C2411yescharacteristic
291C22×#41C2×D511yescharacteristic
292C22×#41C2×D511yescharacteristic
293#568—108no—
294C2×#131—51no—
295C2×#131—51no—
296C2×#131—51no—
297C2×#131—51no—
298C2×#131—53no—
299C2×#131—53no—
300C2×#131—53no—
301C2×#131—53no—
302C2×#131—108no—
303C22×M16—53no—
304C22×M16—53no—
305C22×M16—53no—
306C23×C8—53no—
307#550Dic511yescharacteristic
308D4×Q8Dic511yescharacteristic
309#548Dic511yescharacteristic
310#548Dic511yescharacteristic
311#547Dic513yes—
312#546Dic513yes—
313#546Dic513yes—
314D42Dic513yes—
315#532C2×D513yes—
316#525C2×D513yes—
317#525C2×D513yes—
318C4×#41C2×D511yescharacteristic
319C2×C4×D4C2×D513yes—
320#436—56no—
321#436—56no—
322#435—51no—
323#435—53no—
324#435—53no—
325#435—53no—
326#435—53no—
327#435—53no—
328#435—53no—
329#435—53no—
330#435—56no—
331#435—56no—
332#435—56no—
333C8×D4—56no—
334C8×D4—56no—
335#424—53no—
336#424—53no—
337#423—53no—
338C2×C4⋊C8—53no—
339#408—53no—
340#408—53no—
341#408—53no—
342#408—53no—
343#407—53no—
344#407—53no—
345C2×C22⋊C8—53no—
346C2×C22⋊C8—53no—
347#405—53no—
348#405—53no—
349C4×M16—53no—
350C2×#97—53no—
351C23×C5—26no—
352C23×C5—26no—
353C23×C5—26no—
354C23×C5—43no—
355C23×C5—43no—
356C23×C5—43no—
357C23×C5C23×C411yescharacteristic
358C23×C5C23×C413yes—
359C23×C5C23×C413yes—
360C23×C5C23×C413yes—
361C23×C5C23×C411yescharacteristic
362C5×Q8—26no—
363C5×Q8—26no—
364C5×Q8C4×D414yes—
365C5×D4—212no—
366C5×D4—212no—
367C5×D4—22no—
368C5×D4—26no—
369C5×D4—26no—
370C5×D4—26no—
371C5×D4—43no—
372C5×D4—43no—
373C5×D4—46no—
374C5×D4C4×D4112yes—
375C2×C4×C5—26no—
376C2×C4×C5—26no—
377C2×C4×C5—26no—
378C2×C4×C5—26no—
379C2×C4×C5—26no—
380C2×C4×C5—26no—
381C2×C4×C5—21no—
382C2×C4×C5—23no—
383C2×C4×C5—23no—
384C2×C4×C5—21no—
385C2×C4×C5—21no—
386C2×C4×C5—21no—
387C2×C4×C5—23no—
388C2×C4×C5—23no—
389C2×C4×C5—43no—
390C2×C4×C5—43no—
391C2×C4×C5C23×C411yescharacteristic
392C2×C4×C5C23×C411yescharacteristic
393C2×C4×C5C23×C413yes—
394C2×C4×C5C23×C413yes—
395C2×C4×C5C23×C411yescharacteristic
396C2×C4×C5C23×C411yescharacteristic
397C2×C4×C5C23×C413yes—
398C2×C4×C5C23×C413yes—
399C2×C4×C5C23×C413yes—
400C2×C4×C5C22×D416yes—
401C2×C4×C5C2×#4116yes—
402C2×C4×C5C2511yescharacteristic
403#168—21no—
404#168—23no—
405#168—21no—
406#168—23no—
407#168—21no—
408#168—23no—
409#168C22×D412yes—
410#168C22×D416yes—
411C2×#41—24no—
412C2×#41—24no—
413C2×#41—24no—
414C2×#41—24no—
415C2×#41C2×Dic513yes—
416C2×#41C2×Dic513yes—
417C2×#41C2×Dic511yescharacteristic
418C2×#41C2×Dic511yescharacteristic
419C2×#41C22×D513yes—
420C2×#41C22×D513yes—
421C2×#41C22×D511yescharacteristic
422C22×Q8C2×Dic511yescharacteristic
423C22×Q8C2×Dic511yescharacteristic
424C22×D4C2×Dic513yes—
425C22×D4C2×Dic513yes—
426C22×D4C2×Dic513yes—
427C23×C4C22×D513yes—
428C23×C4C22×D513yes—
429#131—58no—
430#131—1012no—
431#131—1012no—
432#131—1012no—
433#131—1012no—
434#131—104no—
435#131—104no—
436#131—104no—
437C2×M16—53no—
438C2×M16—51no—
439C2×M16—53no—
440C2×M16—53no—
441C2×M16—53no—
442C2×M16—53no—
443C2×M16—53no—
444C2×M16—56no—
445C2×M16—53no—
446C2×M16—1012no—
447C2×M16—1012no—
448C2×M16—1012no—
449C22×C8—53no—
450C22×C8—51no—
451C22×C8—53no—
452C22×C8—53no—
453C22×C8—53no—
454C22×C8—53no—
455C22×C8—53no—
456C22×C8—56no—
457C22×C8—53no—
458C22×C8—1012no—
459C4⋊Q8C2×Dic513yes—
460#127C2×Dic513yes—
461#124C2×Dic513yes—
462#124C2×Dic513yes—
463#123C2×Dic516yes—
464#123C2×Dic516yes—
465C22⋊Q8C2×Dic513yes—
466C22⋊Q8C2×Dic513yes—
467C22⋊Q8C2×Dic513yes—
468C22⋊Q8C2×Dic513yes—
469#121C2×Dic513yes—
470#121C2×Dic513yes—
471#121C2×Dic513yes—
472#121C2×Dic513yes—
473#121C2×Dic516yes—
474#121C2×Dic516yes—
475#120C2×Dic516yes—
476#120C2×Dic516yes—
477C4×Q8C2×Dic511yescharacteristic
478C4×Q8C2×Dic511yescharacteristic
479C4×D4C2×Dic513yes—
480C4×D4C2×Dic513yes—
481C4×D4C2×Dic513yes—
482C4×D4C2×Dic513yes—
483C4×D4C2×Dic513yes—
484C4×D4C2×Dic513yes—
485C4×D4C22×D511yescharacteristic
486C4×D4C22×D513yes—
487C4×D4C22×D513yes—
488C4×D4C22×D513yes—
489C4×D4C22×D516yes—
490#117C22×D513yes—
491C2×C4⋊C4C2×Dic513yes—
492C2×C22⋊C4C2×Dic513yes—
493C2×C22⋊C4C2×Dic513yes—
494C2×C42C22×D513yes—
495C4⋊C8—51no—
496C4⋊C8—53no—
497C4⋊C8—53no—
498C4⋊C8—53no—
499C4⋊C8—56no—
500C22⋊C8—51no—
501C22⋊C8—51no—
502C22⋊C8—53no—
503C22⋊C8—53no—
504C22⋊C8—53no—
505C22⋊C8—53no—
506C22⋊C8—53no—
507C22⋊C8—53no—
508C22⋊C8—56no—
509C22⋊C8—56no—
510#97—51no—
511#97—53no—
512#97—53no—
513#97—53no—
514C4×C8—56no—
515C22×C5—21no—
516C22×C5—23no—
517C22×C5—23no—
518C22×C5—21no—
519C22×C5—21no—
520C22×C5—23no—
521C22×C5—23no—
522C22×C5—21no—
523C22×C5—23no—
524C22×C5—23no—
525C22×C5—23no—
526C22×C5—23no—
527C22×C5—21no—
528C22×C5—412no—
529C22×C5—86no—
530C22×C5C2×C4×D416yes—
531C22×C5#56812yescomplemented
532C22×C5C24×C411yescharacteristic
533C4×C5—21no—
534C4×C5—21no—
535C4×C5—23no—
536C4×C5—23no—
537C4×C5—21no—
538C4×C5—23no—
539C4×C5—21no—
540C4×C5—23no—
541C4×C5C2×C4×D416yes—
542C4×C5C23×D411yescharacteristic
543C4×C5C22×#4111yescharacteristic
544C24C22×Dic513yes—
545C24C22×Dic513yes—
546#41—24no—
547#41—24no—
548#41—212no—
549#41—212no—
550#41—26no—
551#41—26no—
552#41—26no—
553#41—26no—
554#41D4×D514yes—
555#41#71114yes—
556C2×Q8—24no—
557C2×Q8—24no—
558C2×Q8C22×Dic513yes—
559C2×Q8C22×Dic513yes—
560C2×Q8C22×Dic511yescharacteristic
561C2×D4—212no—
562C2×D4—212no—
563C2×D4—46no—
564C2×D4C22×Dic511yescharacteristic
565C2×D4C22×Dic513yes—
566C2×D4C22×Dic516yes—
567C2×D4C22×Dic516yes—
568C2×D4C22×Dic513yes—
569C2×D4C22×Dic513yes—
570C2×D4C22×Dic513yes—
571C2×D4C22×Dic513yes—
572C2×D4C22×Dic516yes—
573C2×D4C22×Dic513yes—
574C22×C4—26no—
575C22×C4—26no—
576C22×C4—26no—
577C22×C4—26no—
578C22×C4C22×Dic513yes—
579C22×C4C22×Dic513yes—
580C22×C4C22×Dic513yes—
581C22×C4C22×Dic513yes—
582C22×C4C22×Dic513yes—
583C22×C4C22×Dic513yes—
584C22×C4C22×Dic513yes—
585C22×C4C22×Dic513yes—
586C22×C4C23×D511yescharacteristic
587C22×C4C23×D513yes—
588C22×C4C23×D513yes—
589C22×C4C23×D511yescharacteristic
590C22×C4C23×D513yes—
591M16—512no—
592M16—102no—
593M16—106no—
594M16—106no—
595M16—106no—
596M16—1012no—
597M16—106no—
598M16—106no—
599M16—106no—
600C2×C8—512no—
601C2×C8—53no—
602C2×C8—51no—
603C2×C8—53no—
604C2×C8—51no—
605C2×C8—51no—
606C2×C8—51no—
607C2×C8—53no—
608C2×C8—53no—
609C2×C8—102no—
610C2×C8—106no—
611C2×C8—106no—
612C2×C8—106no—
613C2×C8—1012no—
614C2×C8—106no—
615C2×C8—106no—
616C2×C8—106no—
617C4⋊C4C22×Dic511yescharacteristic
618C4⋊C4C22×Dic513yes—
619C4⋊C4C22×Dic513yes—
620C4⋊C4C22×Dic513yes—
621C4⋊C4C22×Dic513yes—
622C4⋊C4C22×Dic513yes—
623C4⋊C4C22×Dic516yes—
624C22⋊C4C22×Dic511yescharacteristic
625C22⋊C4C22×Dic511yescharacteristic
626C22⋊C4C22×Dic513yes—
627C22⋊C4C22×Dic513yes—
628C22⋊C4C22×Dic513yes—
629C22⋊C4C22×Dic513yes—
630C22⋊C4C22×Dic513yes—
631C22⋊C4C22×Dic513yes—
632C22⋊C4C22×Dic516yes—
633C22⋊C4C22×Dic516yes—
634C22⋊C4C22×Dic516yes—
635C42C22×Dic513yes—
636C42C22×Dic513yes—
637C42C23×D513yes—
638C42C23×D511yescharacteristic
639C2×C5—22no—
640C2×C5—26no—
641C2×C5—43no—
642C2×C5—43no—
643C2×C5—41no—
644C2×C5C22×C4×D411yescharacteristic
645C2×C5C2×#56811yescharacteristic
646C2×C5#357311yescharacteristic
647C23—26no—
648C23—26no—
649C23—26no—
650C23—43no—
651C23—43no—
652C23—43no—
653C23C23×Dic511yescharacteristic
654C23C23×Dic513yes—
655C23C23×Dic513yes—
656C23C23×Dic513yes—
657C23C23×Dic511yescharacteristic
658Q8—26no—
659Q8—26no—
660Q8D4×Dic514yes—
661D4—212no—
662D4—212no—
663D4—22no—
664D4—26no—
665D4—26no—
666D4—26no—
667D4—43no—
668D4—43no—
669D4—46no—
670D4D4×Dic5112yes—
671C2×C4—26no—
672C2×C4—26no—
673C2×C4—26no—
674C2×C4—26no—
675C2×C4—26no—
676C2×C4—26no—
677C2×C4—21no—
678C2×C4—23no—
679C2×C4—23no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—23no—
684C2×C4—23no—
685C2×C4—43no—
686C2×C4—43no—
687C2×C4C2×D4×D516yes—
688C2×C4C2×#71116yes—
689C2×C4C23×Dic511yescharacteristic
690C2×C4C23×Dic511yescharacteristic
691C2×C4C23×Dic513yes—
692C2×C4C23×Dic513yes—
693C2×C4C23×Dic511yescharacteristic
694C2×C4C23×Dic511yescharacteristic
695C2×C4C23×Dic513yes—
696C2×C4C23×Dic513yes—
697C2×C4C23×Dic513yes—
698C2×C4C24×D511yescharacteristic
699C8—52no—
700C8—56no—
701C8—101no—
702C8—103no—
703C8—103no—
704C8—101no—
705C8—101no—
706C8—103no—
707C5#6014611yescharacteristic, complemented, Sylow
708C22—23no—
709C22—23no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—23no—
714C22—23no—
715C22—23no—
716C22—23no—
717C22—21no—
718C22—21no—
719C22—23no—
720C22—23no—
721C22—412no—
722C22—86no—
723C22C2×D4×Dic516yes—
724C22#6615312yescomplemented
725C22C24×Dic511yescharacteristic
726C4—21no—
727C4—23no—
728C4—21no—
729C4—23no—
730C4—21no—
731C4—21no—
732C4—23no—
733C4—23no—
734C4C2×D4×Dic516yes—
735C4C22×D4×D511yescharacteristic
736C4C22×#71111yescharacteristic
737C2—22no—
738C2—26no—
739C2—43no—
740C2—41no—
741C2—43no—
742C2C22×D4×Dic511yescharacteristic
743C2C2×#6615311yescharacteristic
744C2#1061919711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D5
commutator, socleC22×C5C24×C4
Fitting, prime radicalC5×D4×#41C2
cosocleC2×C4×C5C25
hypercenterD4×#41D5
hypocenterC5#60146
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
2. C2×#66153C2semidirect
3. C22×#4094C2semidirect
4. #10615806C2semidirect
5. #10615806C2semidirect
6. #10615008C2semidirect
7. #10615007C2semidirect
8. #10614649C2semidirect
9. #10614649C2semidirect
10. #10614648C2semidirect
11. #10614647C2semidirect
12. #10614243C2semidirect
13. #10614242C2semidirect
14. D4×#681C2semidirect
15. C2×#65300C2semidirect
37. C2×#4094C22semidirect
38. C2×#4094C22semidirect
39. C2×#4094C22semidirect
40. C2×#4094C22semidirect
41. C22×#681C22semidirect
42. C22×#681C22semidirect
43. C22×#681C22semidirect
44. C23×#168C22semidirect
45. #65523C22semidirect
46. #65523C22semidirect
47. #65523C22semidirect
48. #65523C22semidirect
49. #65496C22semidirect
50. #65496C22semidirect
51. C2×C22⋊#168C22semidirect
52. C2×C22⋊#168C22semidirect
53. #65301C22semidirect
54. #65301C22semidirect
57. #65300C22semidirect
58. #65300C22semidirect
59. #65300C22semidirect
60. #65300C22semidirect
61. #65300C22semidirect
62. #65300C22semidirect
63. #65300C22semidirect
64. #65300C22semidirect
65. #65300C22semidirect
66. D4×#168C22semidirect
67. D4×#168C22semidirect
68. #65288C22semidirect
69. #65288C22semidirect
70. #65286C22semidirect
71. #65286C22semidirect
72. #65213C22semidirect
73. C2×C4⋊#168C22semidirect
74. C4×#681C22semidirect
75. C2×#3935C22semidirect
138. #4094D4semidirect
273. #681C2×D4semidirect
282. C2×#168C2×D4semidirect
531. C22×C5#568semidirect
707. C5#60146semidirect
724. C22#66153semidirect

Maximal subgroups

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

subgroupindex
C5×D4×#412
C2×#661532
C22×#40942
#106158062
#106150082
#106150072
#106146492
#106146482
#106146472
#106142432
#106142422
D4×#6812
C2×#653002
#601465