Finite Group Databasebeta

← C131×#25585 #45711469

Subgroups — C131×#25585 #45711469

Order 33536.

1636 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3505×C131C211yesmaximal, characteristic, complemented
2#2435×C131C211yesmaximal, characteristic, complemented
3#2433×C131C211yesmaximal, characteristic, complemented
4#2408×C131C211yesmaximal, characteristic, complemented
5#2021×C131C214yesmaximal, complemented
6#1996×C131C211yesmaximal, characteristic, complemented
7#1964×C131C211yesmaximal, characteristic, complemented
8#1889×C131C214yesmaximal, complemented
9C4×#99×C131C211yesmaximal, characteristic, complemented
10C23×D4×C131C2211yescharacteristic
11#553×C131—21no—
12#553×C131—22no—
13#552×C131—21no—
14#551×C131—22no—
15#548×C131—21no—
16#546×C131—21no—
17#539×C131—21no—
18#538×C131—21no—
19#534×C131C2212yes—
20C2×#127×C131—21no—
21#529×C131—21no—
22C2×#124×C131—21no—
23#525×C131—21no—
24C2×C22⋊Q8×C131C2211yescharacteristic
25C2×#121×C131—21no—
26C2×#121×C131C2211yescharacteristic
27C2×#120×C131C2214yes—
28C2×#120×C131C2212yes—
29#518×C131C2212yes—
30C2×C4×D4×C131C2211yescharacteristic
31C2×#99×C131C2212yes—
32C2×#99×C131C2214yes—
33#394×C131—21no—
34#394×C131—22no—
35#392×C131—21no—
36#392×C131—22no—
37#390×C131—21no—
38#390×C131—21no—
39#390×C131—21no—
40#380×C131C2211yescharacteristic
41#379×C131C2214yes—
42#379×C131C2212yes—
43C4×C22⋊C4×C131C2211yescharacteristic
44C4×C22⋊C4×C131C2211yescharacteristic
45#342×C131C2214yes—
46#342×C131C2212yes—
47C25×C131C2312yes—
48C2×#41×C131—21no—
49C22×Q8×C131D411yescharacteristic, complemented
50C22×D4×C131—22no—
51C22×D4×C131—24no—
52C22×D4×C131—21no—
53C22×D4×C131—21no—
54C22×D4×C131—21no—
55C22×D4×C131—21no—
56C22×D4×C131—21no—
57C22×D4×C131—21no—
58C22×D4×C131—44no—
59C22×D4×C131D411yescharacteristic, complemented
60C22×D4×C131C2311yescharacteristic
61C22×D4×C131C2312yes—
62C23×C4×C131D411yescharacteristic, complemented
63C23×C4×C131C2311yescharacteristic
64#127×C131—44no—
65#126×C131—22no—
66#126×C131—22no—
67#126×C131—22no—
68#125×C131—21no—
69#125×C131—22no—
70#124×C131—21no—
71#124×C131—22no—
72#124×C131—44no—
73#123×C131—22no—
74#123×C131—22no—
75#123×C131—22no—
76#123×C131—22no—
77#123×C131—22no—
78C22⋊Q8×C131—21no—
79C22⋊Q8×C131—22no—
80C22⋊Q8×C131—21no—
81C22⋊Q8×C131—21no—
82C22⋊Q8×C131—21no—
83C22⋊Q8×C131—21no—
84#121×C131—21no—
85#121×C131—22no—
86#121×C131—21no—
87#121×C131—21no—
88#121×C131—21no—
89#121×C131—21no—
90#121×C131—22no—
91#121×C131—22no—
92#121×C131—44no—
93#120×C131—22no—
94#120×C131—22no—
95#120×C131—28no—
96#120×C131—44no—
97#120×C131—44no—
98C4×Q8×C131—21no—
99C4×D4×C131—22no—
100C4×D4×C131—21no—
101C4×D4×C131—21no—
102C4×D4×C131—21no—
103C4×D4×C131—21no—
104C4×D4×C131—21no—
105C4×D4×C131—22no—
106C4×D4×C131—22no—
107C4×D4×C131—22no—
108C4×D4×C131—22no—
109#117×C131—21no—
110#117×C131—22no—
111#117×C131—22no—
112C2×C4⋊C4×C131—21no—
113C2×C4⋊C4×C131D411yescharacteristic, complemented
114C2×C4⋊C4×C131D411yescharacteristic, complemented
115C2×C4⋊C4×C131D411yescharacteristic, complemented
116C2×C4⋊C4×C131D412yescomplemented
117C2×C22⋊C4×C131—22no—
118C2×C22⋊C4×C131—24no—
119C2×C22⋊C4×C131—22no—
120C2×C22⋊C4×C131—22no—
121C2×C22⋊C4×C131—24no—
122C2×C22⋊C4×C131—22no—
123C2×C22⋊C4×C131—24no—
124C2×C22⋊C4×C131D411yescharacteristic, complemented
125C2×C22⋊C4×C131D412yescomplemented
126C2×C22⋊C4×C131C2312yes—
127C2×C22⋊C4×C131C2312yes—
128C2×C22⋊C4×C131C2311yescharacteristic
129C2×C22⋊C4×C131C2312yes—
130C2×C22⋊C4×C131C2312yes—
131C2×C42×C131—21no—
132C2×C42×C131—21no—
133C2×C42×C131D411yescharacteristic, complemented
134#99×C131—24no—
135#99×C131—44no—
136#95×C131—21no—
137#95×C131—21no—
138#95×C131—21no—
139C24×C131—22no—
140C24×C131—22no—
141C24×C131—22no—
142C24×C131—24no—
143C24×C131—24no—
144C24×C131—44no—
145C24×C131—82no—
146C24×C131C2×D412yes—
147C24×C131C2×D411yescharacteristic
148C24×C131C2411yescharacteristic
149#41×C131—82no—
150C2×Q8×C131—21no—
151C2×Q8×C131—21no—
152C2×Q8×C131—42no—
153C2×D4×C131—24no—
154C2×D4×C131—24no—
155C2×D4×C131—24no—
156C2×D4×C131—21no—
157C2×D4×C131—22no—
158C2×D4×C131—21no—
159C2×D4×C131—22no—
160C2×D4×C131—22no—
161C2×D4×C131—24no—
162C2×D4×C131—24no—
163C2×D4×C131—22no—
164C2×D4×C131—22no—
165C2×D4×C131—22no—
166C2×D4×C131—21no—
167C2×D4×C131—21no—
168C2×D4×C131—42no—
169C2×D4×C131—42no—
170C2×D4×C131—42no—
171C2×D4×C131—42no—
172C2×D4×C131—48no—
173C2×D4×C131—44no—
174C2×D4×C131—44no—
175C2×D4×C131—44no—
176C2×D4×C131—44no—
177C2×D4×C131—44no—
178C2×D4×C131—48no—
179C2×D4×C131—41no—
180C2×D4×C131—41no—
181C2×D4×C131—41no—
182C2×D4×C131—41no—
183C2×D4×C131—84no—
184C2×D4×C131—82no—
185C22×C4×C131—22no—
186C22×C4×C131—22no—
187C22×C4×C131—22no—
188C22×C4×C131—21no—
189C22×C4×C131—21no—
190C22×C4×C131—22no—
191C22×C4×C131—22no—
192C22×C4×C131—42no—
193C22×C4×C131—42no—
194C22×C4×C131C2×D411yescharacteristic
195C22×C4×C131C2×D412yes—
196C22×C4×C131C2×D411yescharacteristic
197C22×C4×C131C2×D411yescharacteristic
198C22×C4×C131C2×D411yescharacteristic
199C22×C4×C131C2×D411yescharacteristic
200C22×C4×C131C2×D412yes—
201C22×C4×C131C2×D411yescharacteristic
202C22×C4×C131C2×D412yes—
203C22×C4×C131C2×D411yescharacteristic
204C22×C4×C131C2×D411yescharacteristic
205C22×C4×C131C2×D411yescharacteristic
206C4⋊C4×C131—22no—
207C4⋊C4×C131—22no—
208C4⋊C4×C131—22no—
209C4⋊C4×C131—22no—
210C4⋊C4×C131—21no—
211C4⋊C4×C131—22no—
212C4⋊C4×C131—21no—
213C4⋊C4×C131—21no—
214C4⋊C4×C131—21no—
215C4⋊C4×C131—21no—
216C4⋊C4×C131—22no—
217C4⋊C4×C131—21no—
218C4⋊C4×C131—42no—
219C22⋊C4×C131—22no—
220C22⋊C4×C131—22no—
221C22⋊C4×C131—22no—
222C22⋊C4×C131—22no—
223C22⋊C4×C131—22no—
224C22⋊C4×C131—22no—
225C22⋊C4×C131—21no—
226C22⋊C4×C131—22no—
227C22⋊C4×C131—21no—
228C22⋊C4×C131—22no—
229C22⋊C4×C131—22no—
230C22⋊C4×C131—22no—
231C22⋊C4×C131—21no—
232C22⋊C4×C131—21no—
233C22⋊C4×C131—22no—
234C22⋊C4×C131—22no—
235C22⋊C4×C131—22no—
236C22⋊C4×C131—24no—
237C22⋊C4×C131—48no—
238C22⋊C4×C131—44no—
239C22⋊C4×C131—44no—
240C22⋊C4×C131—48no—
241C22⋊C4×C131—84no—
242C22⋊C4×C131—82no—
243C22⋊C4×C131#4114yescomplemented
244C42×C131—22no—
245C42×C131—22no—
246C42×C131—21no—
247C42×C131—21no—
248C42×C131—42no—
249C42×C131—42no—
250C23×C131—24no—
251C23×C131—24no—
252C23×C131—24no—
253C23×C131—21no—
254C23×C131—22no—
255C23×C131—21no—
256C23×C131—21no—
257C23×C131—24no—
258C23×C131—41no—
259C23×C131—41no—
260C23×C131—41no—
261C23×C131—41no—
262C23×C131—44no—
263C23×C131—42no—
264C23×C131—42no—
265C23×C131—42no—
266C23×C131—42no—
267C23×C131—42no—
268C23×C131—44no—
269C23×C131—42no—
270C23×C131—42no—
271C23×C131—42no—
272C23×C131—42no—
273C23×C131—42no—
274C23×C131—44no—
275C23×C131—44no—
276C23×C131—88no—
277C23×C131—88no—
278C23×C131C22×D411yescharacteristic
279C23×C131C22×D411yescharacteristic
280C23×C131C22×D411yescharacteristic
281C23×C131C2×#4112yes—
282C23×C131H(5,𝔽2)12yes—
283Q8×C131—42no—
284Q8×C131—81no—
285D4×C131—44no—
286D4×C131—44no—
287D4×C131—44no—
288D4×C131—42no—
289D4×C131—42no—
290D4×C131—42no—
291D4×C131—42no—
292D4×C131—44no—
293D4×C131—44no—
294D4×C131—42no—
295D4×C131—81no—
296D4×C131—82no—
297D4×C131—82no—
298D4×C131—816no—
299D4×C131—88no—
300C2×C4×C131—22no—
301C2×C4×C131—22no—
302C2×C4×C131—22no—
303C2×C4×C131—21no—
304C2×C4×C131—22no—
305C2×C4×C131—21no—
306C2×C4×C131—21no—
307C2×C4×C131—22no—
308C2×C4×C131—22no—
309C2×C4×C131—21no—
310C2×C4×C131—21no—
311C2×C4×C131—24no—
312C2×C4×C131—24no—
313C2×C4×C131—41no—
314C2×C4×C131—41no—
315C2×C4×C131—41no—
316C2×C4×C131—42no—
317C2×C4×C131—42no—
318C2×C4×C131—42no—
319C2×C4×C131—41no—
320C2×C4×C131—42no—
321C2×C4×C131—41no—
322C2×C4×C131—42no—
323C2×C4×C131—42no—
324C2×C4×C131—42no—
325C2×C4×C131—42no—
326C2×C4×C131—42no—
327C2×C4×C131—42no—
328C2×C4×C131—42no—
329C2×C4×C131—81no—
330C2×C4×C131—82no—
331C2×C4×C131—82no—
332C2×C4×C131#12011yescharacteristic
333C2×C4×C131#12011yescharacteristic
334C2×C4×C131#12011yescharacteristic
335C2×C4×C131#12011yescharacteristic
336C22×C131—21no—
337C22×C131—21no—
338C22×C131—21no—
339C22×C131—21no—
340C22×C131—21no—
341C22×C131—21no—
342C22×C131—42no—
343C22×C131—42no—
344C22×C131—42no—
345C22×C131—48no—
346C22×C131—44no—
347C22×C131—48no—
348C22×C131—44no—
349C22×C131—41no—
350C22×C131—42no—
351C22×C131—41no—
352C22×C131—42no—
353C22×C131—44no—
354C22×C131—42no—
355C22×C131—41no—
356C22×C131—84no—
357C22×C131—81no—
358C22×C131—84no—
359C22×C131—82no—
360C22×C131—84no—
361C22×C131—82no—
362C22×C131—82no—
363C22×C131—82no—
364C22×C131C2×#12011yescharacteristic
365C22×C131#53211yescharacteristic
366C22×C131#53511yescharacteristic
367C22×C131#54612yes—
368C22×C131#55012yes—
369C4×C131—21no—
370C4×C131—21no—
371C4×C131—21no—
372C4×C131—44no—
373C4×C131—41no—
374C4×C131—42no—
375C4×C131—41no—
376C4×C131—42no—
377C4×C131—41no—
378C4×C131—42no—
379C4×C131—82no—
380C4×C131—82no—
381C4×C131B(4,𝔽2)12yes—
382C2×C131—22no—
383C2×C131—21no—
384C2×C131—22no—
385C2×C131—21no—
386C2×C131—84no—
387C2×C131—81no—
388C2×C131—82no—
389C2×C131#243111yescharacteristic
390C2×C131C2×B(4,𝔽2)11yescharacteristic
391C2×C131#302711yescharacteristic
392#25585C13111yesmaximal, characteristic, direct product factor, Sylow
393C131#2558511yescharacteristic, direct product factor, Sylow
394#3505C2×C13111yescharacteristic, complemented
395#2435C2×C13111yescharacteristic, complemented
396#2433C2×C13111yescharacteristic, complemented
397#2408C2×C13111yescharacteristic, complemented
398#2021C2×C13114yescomplemented
399#1996C2×C13111yescharacteristic, complemented
400#1964C2×C13111yescharacteristic, complemented
401#1889C2×C13114yescomplemented
402C4×#99C2×C13111yescharacteristic, complemented
403C23×D4C22×C13111yescharacteristic
404#553—21no—
405#553—22no—
406#552—21no—
407#551—22no—
408#548—21no—
409#546—21no—
410#539—21no—
411#538—21no—
412#534C22×C13112yes—
413C2×#127—21no—
414#529—21no—
415C2×#124—21no—
416#525—21no—
417C2×C22⋊Q8C22×C13111yescharacteristic
418C2×#121—21no—
419C2×#121C22×C13111yescharacteristic
420C2×#120C22×C13114yes—
421C2×#120C22×C13112yes—
422#518C22×C13112yes—
423C2×C4×D4C22×C13111yescharacteristic
424C2×#99C22×C13112yes—
425C2×#99C22×C13114yes—
426#394—21no—
427#394—22no—
428#392—21no—
429#392—22no—
430#390—21no—
431#390—21no—
432#390—21no—
433#380C22×C13111yescharacteristic
434#379C22×C13112yes—
435#379C22×C13114yes—
436C4×C22⋊C4C22×C13111yescharacteristic
437C4×C22⋊C4C22×C13111yescharacteristic
438#342C22×C13112yes—
439#342C22×C13114yes—
440C25C23×C13112yes—
441C2×#41—21no—
442C22×Q8D4×C13111yescharacteristic, complemented
443C22×D4—22no—
444C22×D4—24no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—44no—
452C22×D4D4×C13111yescharacteristic, complemented
453C22×D4C23×C13111yescharacteristic
454C22×D4C23×C13112yes—
455C23×C4D4×C13111yescharacteristic, complemented
456C23×C4C23×C13111yescharacteristic
457#127—44no—
458#126—22no—
459#126—22no—
460#126—22no—
461#125—21no—
462#125—22no—
463#124—21no—
464#124—22no—
465#124—44no—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—22no—
470#123—22no—
471C22⋊Q8—21no—
472C22⋊Q8—22no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477#121—21no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—21no—
483#121—22no—
484#121—22no—
485#121—44no—
486#120—22no—
487#120—22no—
488#120—28no—
489#120—44no—
490#120—44no—
491C4×Q8—21no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—21no—
503#117—22no—
504#117—22no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4D4×C13111yescharacteristic, complemented
507C2×C4⋊C4D4×C13111yescharacteristic, complemented
508C2×C4⋊C4D4×C13111yescharacteristic, complemented
509C2×C4⋊C4D4×C13112yescomplemented
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4D4×C13111yescharacteristic, complemented
518C2×C22⋊C4D4×C13112yescomplemented
519C2×C22⋊C4C23×C13112yes—
520C2×C22⋊C4C23×C13112yes—
521C2×C22⋊C4C23×C13111yescharacteristic
522C2×C22⋊C4C23×C13112yes—
523C2×C22⋊C4C23×C13112yes—
524C2×C42—21no—
525C2×C42—21no—
526C2×C42D4×C13111yescharacteristic, complemented
527#99—24no—
528#99—44no—
529#95—21no—
530#95—21no—
531#95—21no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—24no—
536C24—24no—
537C24—44no—
538C24—82no—
539C24C2×D4×C13112yes—
540C24C2×D4×C13111yescharacteristic
541C24C24×C13111yescharacteristic
542#41—82no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—42no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—48no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—48no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—84no—
577C2×D4—82no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4C2×D4×C13111yescharacteristic
588C22×C4C2×D4×C13112yes—
589C22×C4C2×D4×C13111yescharacteristic
590C22×C4C2×D4×C13111yescharacteristic
591C22×C4C2×D4×C13111yescharacteristic
592C22×C4C2×D4×C13111yescharacteristic
593C22×C4C2×D4×C13112yes—
594C22×C4C2×D4×C13111yescharacteristic
595C22×C4C2×D4×C13112yes—
596C22×C4C2×D4×C13111yescharacteristic
597C22×C4C2×D4×C13111yescharacteristic
598C22×C4C2×D4×C13111yescharacteristic
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—21no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—24no—
630C22⋊C4—48no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—48no—
634C22⋊C4—84no—
635C22⋊C4—82no—
636C22⋊C4#41×C13114yescomplemented
637C42—22no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—42no—
642C42—42no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—44no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—44no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—44no—
669C23—88no—
670C23—88no—
671C23C22×D4×C13111yescharacteristic
672C23C22×D4×C13111yescharacteristic
673C23C22×D4×C13111yescharacteristic
674C23C2×#41×C13112yes—
675C23H(5,𝔽2)×C13112yes—
676Q8—42no—
677Q8—81no—
678D4—44no—
679D4—44no—
680D4—44no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—42no—
685D4—44no—
686D4—44no—
687D4—42no—
688D4—81no—
689D4—82no—
690D4—82no—
691D4—816no—
692D4—88no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—81no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4#120×C13111yescharacteristic
726C2×C4#120×C13111yescharacteristic
727C2×C4#120×C13111yescharacteristic
728C2×C4#120×C13111yescharacteristic
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—48no—
739C22—44no—
740C22—48no—
741C22—44no—
742C22—41no—
743C22—42no—
744C22—44no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—84no—
750C22—81no—
751C22—84no—
752C22—82no—
753C22—84no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22C2×#120×C13111yescharacteristic
758C22#532×C13111yescharacteristic
759C22#535×C13111yescharacteristic
760C22#546×C13112yes—
761C22#550×C13112yes—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—44no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—42no—
770C4—41no—
771C4—42no—
772C4—82no—
773C4—82no—
774C4B(4,𝔽2)×C13112yes—
775C2—22no—
776C2—21no—
777C2—22no—
778C2—21no—
779C2—84no—
780C2—81no—
781C2—82no—
782C2#2431×C13111yescharacteristic
783C2C2×B(4,𝔽2)×C13111yescharacteristic
784C2#3027×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC24C24×C131
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3505×C131C2semidirect
2. #2435×C131C2semidirect
3. #2433×C131C2semidirect
4. #2408×C131C2semidirect
5. #2021×C131C2semidirect
6. #1996×C131C2semidirect
7. #1964×C131C2semidirect
8. #1889×C131C2semidirect
9. C4×#99×C131C2semidirect
49. C22×Q8×C131D4semidirect
59. C22×D4×C131D4semidirect
62. C23×C4×C131D4semidirect
113. C2×C4⋊C4×C131D4semidirect
114. C2×C4⋊C4×C131D4semidirect
115. C2×C4⋊C4×C131D4semidirect
116. C2×C4⋊C4×C131D4semidirect
124. C2×C22⋊C4×C131D4semidirect
125. C2×C22⋊C4×C131D4semidirect
133. C2×C42×C131D4semidirect
243. C22⋊C4×C131#41semidirect
392. #25585C131direct (N × H)
393. C131#25585direct (N × H)
394. #3505C2×C131semidirect
395. #2435C2×C131semidirect
396. #2433C2×C131semidirect
397. #2408C2×C131semidirect
398. #2021C2×C131semidirect
399. #1996C2×C131semidirect
400. #1964C2×C131semidirect
401. #1889C2×C131semidirect
402. C4×#99C2×C131semidirect
442. C22×Q8D4×C131semidirect
452. C22×D4D4×C131semidirect
455. C23×C4D4×C131semidirect
506. C2×C4⋊C4D4×C131semidirect
507. C2×C4⋊C4D4×C131semidirect
508. C2×C4⋊C4D4×C131semidirect
509. C2×C4⋊C4D4×C131semidirect
517. C2×C22⋊C4D4×C131semidirect
518. C2×C22⋊C4D4×C131semidirect
526. C2×C42D4×C131semidirect
636. C22⋊C4#41×C131semidirect

Maximal subgroups

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

subgroupindex
#3505×C1312
#2435×C1312
#2433×C1312
#2408×C1312
#2021×C1312
#1996×C1312
#1964×C1312
#1889×C1312
C4×#99×C1312
#25585131