Finite Group Databasebeta

← C131×#25089 #45710973

Subgroups — C131×#25089 #45710973

Order 33536.

1078 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#467×C131C211yesmaximal, characteristic, complemented
2C2×#464×C131C211yesmaximal, characteristic, complemented
3C2×#452×C131C211yesmaximal, characteristic
4C2×#416×C131C211yesmaximal, characteristic
5#2432×C131C211yesmaximal, characteristic
6#2362×C131C211yesmaximal, characteristic, complemented
7#2068×C131C211yesmaximal, characteristic, complemented
8#2055×C131C211yesmaximal, characteristic, complemented
9#2042×C131C211yesmaximal, characteristic, complemented
10#2016×C131C211yesmaximal, characteristic, complemented
11#1981×C131C211yesmaximal, characteristic, complemented
12#1925×C131C211yesmaximal, characteristic, complemented
13#1878×C131C211yesmaximal, characteristic, complemented
14#1873×C131C211yesmaximal, characteristic, complemented
15#1850×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C22×Q16×C131C2211yescharacteristic
18C22×Q16×C131C2211yescharacteristic
19C22×SD16×C131C2211yescharacteristic
20C23×C8×C131C2211yescharacteristic
21C2×C4⋊Q8×C131C2211yescharacteristic
22C2×#124×C131C2211yescharacteristic
23C2×C22⋊Q8×C131C2211yescharacteristic
24C2×C22⋊Q8×C131C2211yescharacteristic
25C2×C4×Q8×C131C2211yescharacteristic
26C2×#117×C131C2211yescharacteristic
27#467×C131—24no—
28#464×C131—24no—
29#452×C131—24no—
30C2×#107×C131C2211yescharacteristic
31C2×C4⋊C8×C131C2211yescharacteristic
32C2×C4⋊C8×C131C2211yescharacteristic
33#416×C131—24no—
34C2×#103×C131C2211yescharacteristic
35C2×#103×C131C2211yescharacteristic
36C2×#103×C131C2211yescharacteristic
37C2×#103×C131C2211yescharacteristic
38C2×#103×C131C2211yescharacteristic
39C2×#103×C131C2211yescharacteristic
40C2×#103×C131C2211yescharacteristic
41C2×#102×C131C2211yescharacteristic
42C2×#102×C131C2211yescharacteristic
43C2×#102×C131C2211yescharacteristic
44C2×C22⋊C8×C131C2211yescharacteristic
45#394×C131—21no—
46#394×C131—21no—
47#391×C131C2211yescharacteristic
48#391×C131C2211yescharacteristic
49#390×C131C2211yescharacteristic
50#389×C131C2211yescharacteristic
51#388×C131—21no—
52#388×C131—21no—
53#387×C131—21no—
54#385×C131—21no—
55#385×C131—21no—
56C4×C4⋊C4×C131—21no—
57C4×C4⋊C4×C131C2211yescharacteristic
58C4×C22⋊C4×C131C2211yescharacteristic
59#340×C131C2211yescharacteristic
60#340×C131C2211yescharacteristic
61#336×C131C2211yescharacteristic
62#336×C131C2211yescharacteristic
63C2×#41×C131—22no—
64C2×#41×C131—22no—
65C2×#41×C131—22no—
66C2×#41×C131—22no—
67C2×#41×C131—41no—
68C2×#41×C131—41no—
69C22×Q8×C131C2311yescharacteristic
70C22×Q8×C131C2311yescharacteristic
71C22×Q8×C131C2311yescharacteristic
72C22×D4×C131—21no—
73C22×D4×C131C2311yescharacteristic
74C23×C4×C131—21no—
75C23×C4×C131C2311yescharacteristic
76C2×Q16×C131—22no—
77C2×Q16×C131—22no—
78C2×Q16×C131—22no—
79C2×Q16×C131—22no—
80C2×Q16×C131—41no—
81C2×Q16×C131—41no—
82C2×SD16×C131—22no—
83C2×SD16×C131—22no—
84C2×SD16×C131—41no—
85C22×C8×C131—22no—
86C22×C8×C131—22no—
87C22×C8×C131—41no—
88C22×C8×C131C2311yescharacteristic
89C22×C8×C131C2311yescharacteristic
90C22×C8×C131C2311yescharacteristic
91C22×C8×C131C2311yescharacteristic
92C4⋊Q8×C131—22no—
93C4⋊Q8×C131—41no—
94#124×C131—22no—
95#124×C131—41no—
96C22⋊Q8×C131—22no—
97C22⋊Q8×C131—22no—
98C22⋊Q8×C131—22no—
99C22⋊Q8×C131D414yes—
100C4×Q8×C131—22no—
101C4×Q8×C131—41no—
102#117×C131—22no—
103#117×C131—41no—
104C2×C4⋊C4×C131—21no—
105C2×C4⋊C4×C131—21no—
106C2×C4⋊C4×C131—21no—
107C2×C4⋊C4×C131—21no—
108C2×C4⋊C4×C131—21no—
109C2×C4⋊C4×C131—21no—
110C2×C4⋊C4×C131C2311yescharacteristic
111C2×C4⋊C4×C131C2311yescharacteristic
112C2×C4⋊C4×C131C2311yescharacteristic
113C2×C4⋊C4×C131C2311yescharacteristic
114C2×C22⋊C4×C131—21no—
115C2×C22⋊C4×C131—21no—
116C2×C22⋊C4×C131—21no—
117C2×C22⋊C4×C131—21no—
118C2×C22⋊C4×C131—21no—
119C2×C22⋊C4×C131—21no—
120C2×C22⋊C4×C131—21no—
121C2×C22⋊C4×C131D411yescharacteristic
122C2×C22⋊C4×C131D411yescharacteristic
123C2×C42×C131—21no—
124C2×C42×C131—21no—
125C2×C42×C131—21no—
126C2×C42×C131C2311yescharacteristic
127C2×C42×C131C2311yescharacteristic
128#107×C131—22no—
129C4⋊C8×C131—22no—
130C4⋊C8×C131—41no—
131#103×C131—22no—
132#103×C131—22no—
133#103×C131—22no—
134#103×C131—22no—
135#103×C131—22no—
136#103×C131—22no—
137#103×C131—41no—
138#102×C131—22no—
139#102×C131—22no—
140#102×C131D414yes—
141C22⋊C8×C131—22no—
142#95×C131—21no—
143#95×C131—21no—
144#95×C131—21no—
145#95×C131—21no—
146#95×C131—21no—
147#95×C131—21no—
148#95×C131D411yescharacteristic
149#95×C131D411yescharacteristic
150C24×C131—21no—
151C24×C131C2×D411yescharacteristic
152#41×C131—28no—
153#41×C131—44no—
154#41×C131—44no—
155#41×C131—44no—
156C2×Q8×C131—21no—
157C2×Q8×C131—21no—
158C2×Q8×C131—21no—
159C2×Q8×C131—21no—
160C2×Q8×C131—21no—
161C2×Q8×C131—21no—
162C2×Q8×C131—21no—
163C2×Q8×C131—21no—
164C2×Q8×C131—21no—
165C2×Q8×C131—21no—
166C2×Q8×C131—21no—
167C2×Q8×C131—21no—
168C2×Q8×C131—21no—
169C2×Q8×C131—21no—
170C2×Q8×C131—21no—
171C2×Q8×C131—21no—
172C2×Q8×C131C2×D412yes—
173C2×Q8×C131#4112yes—
174C2×D4×C131—21no—
175C2×D4×C131—21no—
176C2×D4×C131—21no—
177C2×D4×C131—21no—
178C2×D4×C131—21no—
179C2×D4×C131—42no—
180C2×D4×C131—42no—
181C2×D4×C131—42no—
182C2×D4×C131C2×D412yes—
183C22×C4×C131—21no—
184C22×C4×C131—21no—
185C22×C4×C131—21no—
186C22×C4×C131—21no—
187C22×C4×C131—21no—
188C22×C4×C131—21no—
189C22×C4×C131—21no—
190C22×C4×C131—21no—
191C22×C4×C131—21no—
192C22×C4×C131—21no—
193C22×C4×C131—21no—
194C22×C4×C131—42no—
195C22×C4×C131—42no—
196C22×C4×C131—42no—
197C22×C4×C131C2×D411yescharacteristic
198C22×C4×C131C2×D411yescharacteristic
199C22×C4×C131C2×D411yescharacteristic
200C22×C4×C131C2×D411yescharacteristic
201C22×C4×C131C2×D412yes—
202C22×C4×C131C2×D411yescharacteristic
203C22×C4×C131#4112yes—
204C22×C4×C131C2411yescharacteristic
205Q16×C131—44no—
206Q16×C131—44no—
207SD16×C131—44no—
208C2×C8×C131—21no—
209C2×C8×C131—21no—
210C2×C8×C131—21no—
211C2×C8×C131—21no—
212C2×C8×C131—21no—
213C2×C8×C131—21no—
214C2×C8×C131—21no—
215C2×C8×C131—21no—
216C2×C8×C131—21no—
217C2×C8×C131—21no—
218C2×C8×C131—21no—
219C2×C8×C131—44no—
220C2×C8×C131C2×D412yes—
221C4⋊C4×C131—24no—
222C4⋊C4×C131—21no—
223C4⋊C4×C131—21no—
224C4⋊C4×C131—21no—
225C4⋊C4×C131—21no—
226C4⋊C4×C131—21no—
227C4⋊C4×C131—21no—
228C4⋊C4×C131—42no—
229C4⋊C4×C131—42no—
230C4⋊C4×C131—42no—
231C4⋊C4×C131—42no—
232C4⋊C4×C131—42no—
233C4⋊C4×C131C2×D412yes—
234C4⋊C4×C131C2×D412yes—
235C22⋊C4×C131—24no—
236C22⋊C4×C131—22no—
237C22⋊C4×C131—41no—
238C22⋊C4×C131—42no—
239C22⋊C4×C131—42no—
240C22⋊C4×C131—42no—
241C22⋊C4×C131—42no—
242C22⋊C4×C131—42no—
243C22⋊C4×C131—42no—
244C42×C131—21no—
245C42×C131—21no—
246C42×C131—21no—
247C42×C131—21no—
248C42×C131—42no—
249C42×C131—42no—
250C42×C131—42no—
251C23×C131—21no—
252C23×C131—21no—
253C23×C131—21no—
254C23×C131—21no—
255C23×C131—21no—
256C23×C131—21no—
257C23×C131—22no—
258C23×C131—41no—
259C23×C131—41no—
260C23×C131—41no—
261C23×C131—41no—
262C23×C131—41no—
263C23×C131—41no—
264C23×C131#12112yes—
265C23×C131C22×D411yescharacteristic
266Q8×C131—22no—
267Q8×C131—22no—
268Q8×C131—22no—
269Q8×C131—22no—
270Q8×C131—41no—
271Q8×C131—41no—
272Q8×C131—41no—
273Q8×C131—41no—
274Q8×C131—41no—
275Q8×C131—41no—
276Q8×C131—41no—
277Q8×C131—41no—
278D4×C131—22no—
279D4×C131—22no—
280D4×C131—48no—
281D4×C131—41no—
282D4×C131—41no—
283C2×C4×C131—21no—
284C2×C4×C131—21no—
285C2×C4×C131—21no—
286C2×C4×C131—21no—
287C2×C4×C131—22no—
288C2×C4×C131—22no—
289C2×C4×C131—22no—
290C2×C4×C131—22no—
291C2×C4×C131—22no—
292C2×C4×C131—22no—
293C2×C4×C131—21no—
294C2×C4×C131—21no—
295C2×C4×C131—22no—
296C2×C4×C131—21no—
297C2×C4×C131—22no—
298C2×C4×C131—21no—
299C2×C4×C131—21no—
300C2×C4×C131—21no—
301C2×C4×C131—21no—
302C2×C4×C131—21no—
303C2×C4×C131—21no—
304C2×C4×C131—48no—
305C2×C4×C131—41no—
306C2×C4×C131—41no—
307C2×C4×C131—41no—
308C2×C4×C131—41no—
309C2×C4×C131—41no—
310C2×C4×C131—41no—
311C2×C4×C131—41no—
312C2×C4×C131—41no—
313C2×C4×C131—41no—
314C2×C4×C131—41no—
315C2×C4×C131—41no—
316C2×C4×C131—41no—
317C2×C4×C131—41no—
318C2×C4×C131—41no—
319C2×C4×C131—41no—
320C2×C4×C131—41no—
321C2×C4×C131—41no—
322C2×C4×C131#12112yes—
323C2×C4×C131#13512yes—
324C2×C4×C131C22×D411yescharacteristic
325C2×C4×C131C22×D411yescharacteristic
326C2×C4×C131C2×#4111yescharacteristic
327C2×C4×C131C2×#4111yescharacteristic
328C2×C4×C131H(5,𝔽2)11yescharacteristic
329C2×C4×C131H(5,𝔽2)11yescharacteristic
330C8×C131—22no—
331C8×C131—41no—
332C8×C131—41no—
333C8×C131—41no—
334C22×C131—22no—
335C22×C131—22no—
336C22×C131—22no—
337C22×C131—41no—
338C22×C131—41no—
339C22×C131—41no—
340C22×C131—41no—
341C22×C131—42no—
342C22×C131—42no—
343C22×C131—42no—
344C22×C131—81no—
345C22×C131—81no—
346C22×C131—81no—
347C22×C131—81no—
348C22×C131C2×#12111yescharacteristic
349C22×C131D4211yescharacteristic
350C22×C131#54611yescharacteristic
351C22×C131C2×#13511yescharacteristic
352C22×C131#57511yescharacteristic
353C22×C131#57811yescharacteristic
354C22×C131#57811yescharacteristic
355C4×C131—22no—
356C4×C131—22no—
357C4×C131—42no—
358C4×C131—42no—
359C4×C131—41no—
360C4×C131—41no—
361C4×C131—42no—
362C4×C131—42no—
363C4×C131—41no—
364C4×C131—81no—
365C4×C131—81no—
366C4×C131—81no—
367C4×C131#52511yescharacteristic
368C4×C131#53811yescharacteristic
369C4×C131D4211yescharacteristic
370C4×C131#54611yescharacteristic
371C2×C131—42no—
372C2×C131—82no—
373C2×C131#242411yescharacteristic
374C2×C131#303511yescharacteristic
375C2×C131#304411yescharacteristic
376C2×C131#326911yescharacteristic
377C2×C131#328311yescharacteristic
378C2×C131#330011yescharacteristic
379C2×C131#331311yescharacteristic
380#25089C13111yesmaximal, characteristic, direct product factor, Sylow
381C131#2508911yescharacteristic, direct product factor, Sylow
382C2×#467C2×C13111yescharacteristic, complemented
383C2×#464C2×C13111yescharacteristic, complemented
384C2×#452C2×C13111yescharacteristic
385C2×#416C2×C13111yescharacteristic
386#2432C2×C13111yescharacteristic
387#2362C2×C13111yescharacteristic, complemented
388#2068C2×C13111yescharacteristic, complemented
389#2055C2×C13111yescharacteristic, complemented
390#2042C2×C13111yescharacteristic, complemented
391#2016C2×C13111yescharacteristic, complemented
392#1981C2×C13111yescharacteristic, complemented
393#1925C2×C13111yescharacteristic, complemented
394#1878C2×C13111yescharacteristic, complemented
395#1873C2×C13111yescharacteristic, complemented
396#1850C2×C13111yescharacteristic, complemented
397C22×#41C22×C13111yescharacteristic
398C22×Q16C22×C13111yescharacteristic
399C22×Q16C22×C13111yescharacteristic
400C22×SD16C22×C13111yescharacteristic
401C23×C8C22×C13111yescharacteristic
402C2×C4⋊Q8C22×C13111yescharacteristic
403C2×#124C22×C13111yescharacteristic
404C2×C22⋊Q8C22×C13111yescharacteristic
405C2×C22⋊Q8C22×C13111yescharacteristic
406C2×C4×Q8C22×C13111yescharacteristic
407C2×#117C22×C13111yescharacteristic
408#467—24no—
409#464—24no—
410#452—24no—
411C2×#107C22×C13111yescharacteristic
412C2×C4⋊C8C22×C13111yescharacteristic
413C2×C4⋊C8C22×C13111yescharacteristic
414#416—24no—
415C2×#103C22×C13111yescharacteristic
416C2×#103C22×C13111yescharacteristic
417C2×#103C22×C13111yescharacteristic
418C2×#103C22×C13111yescharacteristic
419C2×#103C22×C13111yescharacteristic
420C2×#103C22×C13111yescharacteristic
421C2×#103C22×C13111yescharacteristic
422C2×#102C22×C13111yescharacteristic
423C2×#102C22×C13111yescharacteristic
424C2×#102C22×C13111yescharacteristic
425C2×C22⋊C8C22×C13111yescharacteristic
426#394—21no—
427#394—21no—
428#391C22×C13111yescharacteristic
429#391C22×C13111yescharacteristic
430#390C22×C13111yescharacteristic
431#389C22×C13111yescharacteristic
432#388—21no—
433#388—21no—
434#387—21no—
435#385—21no—
436#385—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4C22×C13111yescharacteristic
439C4×C22⋊C4C22×C13111yescharacteristic
440#340C22×C13111yescharacteristic
441#340C22×C13111yescharacteristic
442#336C22×C13111yescharacteristic
443#336C22×C13111yescharacteristic
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—22no—
448C2×#41—41no—
449C2×#41—41no—
450C22×Q8C23×C13111yescharacteristic
451C22×Q8C23×C13111yescharacteristic
452C22×Q8C23×C13111yescharacteristic
453C22×D4—21no—
454C22×D4C23×C13111yescharacteristic
455C23×C4—21no—
456C23×C4C23×C13111yescharacteristic
457C2×Q16—22no—
458C2×Q16—22no—
459C2×Q16—22no—
460C2×Q16—22no—
461C2×Q16—41no—
462C2×Q16—41no—
463C2×SD16—22no—
464C2×SD16—22no—
465C2×SD16—41no—
466C22×C8—22no—
467C22×C8—22no—
468C22×C8—41no—
469C22×C8C23×C13111yescharacteristic
470C22×C8C23×C13111yescharacteristic
471C22×C8C23×C13111yescharacteristic
472C22×C8C23×C13111yescharacteristic
473C4⋊Q8—22no—
474C4⋊Q8—41no—
475#124—22no—
476#124—41no—
477C22⋊Q8—22no—
478C22⋊Q8—22no—
479C22⋊Q8—22no—
480C22⋊Q8D4×C13114yes—
481C4×Q8—22no—
482C4×Q8—41no—
483#117—22no—
484#117—41no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4C23×C13111yescharacteristic
492C2×C4⋊C4C23×C13111yescharacteristic
493C2×C4⋊C4C23×C13111yescharacteristic
494C2×C4⋊C4C23×C13111yescharacteristic
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4D4×C13111yescharacteristic
503C2×C22⋊C4D4×C13111yescharacteristic
504C2×C42—21no—
505C2×C42—21no—
506C2×C42—21no—
507C2×C42C23×C13111yescharacteristic
508C2×C42C23×C13111yescharacteristic
509#107—22no—
510C4⋊C8—22no—
511C4⋊C8—41no—
512#103—22no—
513#103—22no—
514#103—22no—
515#103—22no—
516#103—22no—
517#103—22no—
518#103—41no—
519#102—22no—
520#102—22no—
521#102D4×C13114yes—
522C22⋊C8—22no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95D4×C13111yescharacteristic
530#95D4×C13111yescharacteristic
531C24—21no—
532C24C2×D4×C13111yescharacteristic
533#41—28no—
534#41—44no—
535#41—44no—
536#41—44no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8C2×D4×C13112yes—
554C2×Q8#41×C13112yes—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4C2×D4×C13112yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4C2×D4×C13111yescharacteristic
579C22×C4C2×D4×C13111yescharacteristic
580C22×C4C2×D4×C13111yescharacteristic
581C22×C4C2×D4×C13111yescharacteristic
582C22×C4C2×D4×C13112yes—
583C22×C4C2×D4×C13111yescharacteristic
584C22×C4#41×C13112yes—
585C22×C4C24×C13111yescharacteristic
586Q16—44no—
587Q16—44no—
588SD16—44no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—44no—
601C2×C8C2×D4×C13112yes—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4C2×D4×C13112yes—
615C4⋊C4C2×D4×C13112yes—
616C22⋊C4—24no—
617C22⋊C4—22no—
618C22⋊C4—41no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—42no—
630C42—42no—
631C42—42no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23#121×C13112yes—
646C23C22×D4×C13111yescharacteristic
647Q8—22no—
648Q8—22no—
649Q8—22no—
650Q8—22no—
651Q8—41no—
652Q8—41no—
653Q8—41no—
654Q8—41no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659D4—22no—
660D4—22no—
661D4—48no—
662D4—41no—
663D4—41no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—48no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4#121×C13112yes—
704C2×C4#135×C13112yes—
705C2×C4C22×D4×C13111yescharacteristic
706C2×C4C22×D4×C13111yescharacteristic
707C2×C4C2×#41×C13111yescharacteristic
708C2×C4C2×#41×C13111yescharacteristic
709C2×C4H(5,𝔽2)×C13111yescharacteristic
710C2×C4H(5,𝔽2)×C13111yescharacteristic
711C8—22no—
712C8—41no—
713C8—41no—
714C8—41no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22C2×#121×C13111yescharacteristic
730C22D42×C13111yescharacteristic
731C22#546×C13111yescharacteristic
732C22C2×#135×C13111yescharacteristic
733C22#575×C13111yescharacteristic
734C22#578×C13111yescharacteristic
735C22#578×C13111yescharacteristic
736C4—22no—
737C4—22no—
738C4—41no—
739C4—41no—
740C4—42no—
741C4—42no—
742C4—41no—
743C4—42no—
744C4—42no—
745C4—81no—
746C4—81no—
747C4—81no—
748C4#525×C13111yescharacteristic
749C4#538×C13111yescharacteristic
750C4D42×C13111yescharacteristic
751C4#546×C13111yescharacteristic
752C2—42no—
753C2—82no—
754C2#2424×C13111yescharacteristic
755C2#3035×C13111yescharacteristic
756C2#3044×C13111yescharacteristic
757C2#3269×C13111yescharacteristic
758C2#3283×C13111yescharacteristic
759C2#3300×C13111yescharacteristic
760C2#3313×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC22×#41×C131C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C4×C22⋊C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#467×C131C2semidirect
2. C2×#464×C131C2semidirect
6. #2362×C131C2semidirect
7. #2068×C131C2semidirect
8. #2055×C131C2semidirect
9. #2042×C131C2semidirect
10. #2016×C131C2semidirect
11. #1981×C131C2semidirect
12. #1925×C131C2semidirect
13. #1878×C131C2semidirect
14. #1873×C131C2semidirect
15. #1850×C131C2semidirect
380. #25089C131direct (N × H)
381. C131#25089direct (N × H)
382. C2×#467C2×C131semidirect
383. C2×#464C2×C131semidirect
387. #2362C2×C131semidirect
388. #2068C2×C131semidirect
389. #2055C2×C131semidirect
390. #2042C2×C131semidirect
391. #2016C2×C131semidirect
392. #1981C2×C131semidirect
393. #1925C2×C131semidirect
394. #1878C2×C131semidirect
395. #1873C2×C131semidirect
396. #1850C2×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#467×C1312
C2×#464×C1312
C2×#452×C1312
C2×#416×C1312
#2432×C1312
#2362×C1312
#2068×C1312
#2055×C1312
#2042×C1312
#2016×C1312
#1981×C1312
#1925×C1312
#1878×C1312
#1873×C1312
#1850×C1312
#25089131