Finite Group Databasebeta

← C31×#25565 #21482324

Subgroups — C31×#25565 #21482324

Order 7936.

1312 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3490C211yesmaximal, characteristic
2C31×#2483C211yesmaximal, characteristic, complemented
3C31×#2412C212yesmaximal, complemented
4C31×#2062C211yesmaximal, characteristic, complemented
5C31×#2044C211yesmaximal, characteristic, complemented
6C31×#2030C211yesmaximal, characteristic, complemented
7C31×#2022C211yesmaximal, characteristic, complemented
8C31×#1898C212yesmaximal, complemented
9C31×#1890C212yesmaximal, complemented
10C31×#1867C212yesmaximal, complemented
11C2×C31×#342C211yesmaximal, characteristic, complemented
12C31×#551—22no—
13C31×#551—22no—
14C31×#546—22no—
15C31×#546—22no—
16C31×#543C2211yescharacteristic
17C31×#538—21no—
18C31×#538—21no—
19C31×#534C2211yescharacteristic
20C31×#525—21no—
21C31×#525—21no—
22C2×C31×#123C2212yes—
23C2×C31×#120C2212yes—
24C31×#518C2212yes—
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2212yes—
28C2×C31×#99C2212yes—
29C2×C31×#99C2212yes—
30C31×#397—22no—
31C31×#397—21no—
32C31×#397—21no—
33C31×#394—22no—
34C31×#386—22no—
35C31×#386C2212yes—
36C31×#385—21no—
37C31×#385C2212yes—
38C31×#385C2211yescharacteristic
39C31×#385C2211yescharacteristic
40C31×#381—21no—
41C31×#381C2211yescharacteristic
42C31×#381C2212yes—
43C31×#381C2211yescharacteristic
44C31×#380—22no—
45C31×#379C2211yescharacteristic
46C31×#342C2212yes—
47C31×#342C2211yescharacteristic
48C31×#342C2212yes—
49C31×#342C2212yes—
50C31×#342C2211yescharacteristic
51C25×C31C2311yescharacteristic
52C2×#41×C31—21no—
53C2×#41×C31—21no—
54C22×D4×C31D412yes—
55C22×D4×C31D412yes—
56C22×D4×C31C2312yes—
57C23×C4×C31—22no—
58C23×C4×C31D411yescharacteristic
59C23×C4×C31D411yescharacteristic
60C23×C4×C31C2311yescharacteristic
61C23×C4×C31C2311yescharacteristic
62C31×#126—22no—
63C31×#126—22no—
64C31×#124—22no—
65C31×#124—22no—
66C31×#123—22no—
67C31×#123—22no—
68C31×#123—22no—
69C31×#123—22no—
70C31×#123—22no—
71C31×#123—24no—
72C31×#123—42no—
73C31×C22⋊Q8—21no—
74C31×C22⋊Q8—21no—
75C31×C22⋊Q8—21no—
76C31×C22⋊Q8—21no—
77C31×C22⋊Q8—22no—
78C31×C22⋊Q8—22no—
79C31×#121—21no—
80C31×#121—21no—
81C31×#121—22no—
82C31×#121—22no—
83C31×#121—21no—
84C31×#121—21no—
85C31×#120—22no—
86C31×#120—22no—
87C31×#120—22no—
88C31×#120—22no—
89C31×#120—22no—
90C4×D4×C31—22no—
91C4×D4×C31—22no—
92C4×D4×C31—22no—
93C4×D4×C31—22no—
94C4×D4×C31—22no—
95C4×D4×C31—22no—
96C31×#117—21no—
97C31×#117—21no—
98C31×#117—22no—
99C2×C4⋊C4×C31—22no—
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31—21no—
102C2×C4⋊C4×C31—22no—
103C2×C22⋊C4×C31—22no—
104C2×C22⋊C4×C31—22no—
105C2×C22⋊C4×C31—22no—
106C2×C22⋊C4×C31—24no—
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31—22no—
109C2×C22⋊C4×C31—22no—
110C2×C22⋊C4×C31—22no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—22no—
113C2×C22⋊C4×C31—21no—
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—22no—
116C2×C22⋊C4×C31—42no—
117C2×C22⋊C4×C31D411yescharacteristic
118C2×C22⋊C4×C31D411yescharacteristic
119C2×C22⋊C4×C31D412yes—
120C2×C22⋊C4×C31D412yes—
121C2×C22⋊C4×C31C2311yescharacteristic
122C2×C22⋊C4×C31C2311yescharacteristic
123C2×C22⋊C4×C31C2312yes—
124C2×C22⋊C4×C31C2311yescharacteristic
125C2×C22⋊C4×C31C2311yescharacteristic
126C2×C22⋊C4×C31C2312yes—
127C2×C22⋊C4×C31C2312yes—
128C31×#99—24no—
129C31×#99—42no—
130C31×#95—22no—
131C31×#95—21no—
132C31×#95—21no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95—22no—
138C31×#95—22no—
139C31×#95—22no—
140C24×C31—22no—
141C24×C31—21no—
142C24×C31—21no—
143C24×C31—42no—
144C24×C31—81no—
145C24×C31C2×D412yes—
146C24×C31C2×D411yescharacteristic
147C24×C31C2×D412yes—
148C24×C31C2×D412yes—
149C24×C31C2×D411yescharacteristic
150C24×C31C2411yescharacteristic
151#41×C31—82no—
152#41×C31—82no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×D4×C31—22no—
156C2×D4×C31—22no—
157C2×D4×C31—22no—
158C2×D4×C31—22no—
159C2×D4×C31—22no—
160C2×D4×C31—22no—
161C2×D4×C31—22no—
162C2×D4×C31—22no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—22no—
166C2×D4×C31—22no—
167C2×D4×C31—44no—
168C2×D4×C31—82no—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—22no—
180C22×C4×C31—22no—
181C22×C4×C31—22no—
182C22×C4×C31—21no—
183C22×C4×C31—22no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—44no—
187C22×C4×C31—42no—
188C22×C4×C31—44no—
189C22×C4×C31—81no—
190C22×C4×C31—81no—
191C22×C4×C31—82no—
192C22×C4×C31C2×D412yes—
193C22×C4×C31C2×D411yescharacteristic
194C22×C4×C31C2×D412yes—
195C22×C4×C31C2×D411yescharacteristic
196C22×C4×C31C2×D411yescharacteristic
197C22×C4×C31C2×D412yes—
198C22×C4×C31C2×D411yescharacteristic
199C4⋊C4×C31—22no—
200C4⋊C4×C31—22no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—22no—
206C4⋊C4×C31—22no—
207C4⋊C4×C31—44no—
208C4⋊C4×C31—82no—
209C4⋊C4×C31—81no—
210C4⋊C4×C31—81no—
211C22⋊C4×C31—22no—
212C22⋊C4×C31—22no—
213C22⋊C4×C31—22no—
214C22⋊C4×C31—22no—
215C22⋊C4×C31—22no—
216C22⋊C4×C31—22no—
217C22⋊C4×C31—22no—
218C22⋊C4×C31—22no—
219C22⋊C4×C31—22no—
220C22⋊C4×C31—22no—
221C22⋊C4×C31—22no—
222C22⋊C4×C31—22no—
223C22⋊C4×C31—22no—
224C22⋊C4×C31—22no—
225C22⋊C4×C31—22no—
226C22⋊C4×C31—22no—
227C22⋊C4×C31—22no—
228C22⋊C4×C31—21no—
229C22⋊C4×C31—22no—
230C22⋊C4×C31—21no—
231C22⋊C4×C31—44no—
232C22⋊C4×C31—44no—
233C22⋊C4×C31—42no—
234C22⋊C4×C31—42no—
235C22⋊C4×C31—41no—
236C22⋊C4×C31—41no—
237C22⋊C4×C31—81no—
238C22⋊C4×C31—82no—
239C22⋊C4×C31#4114yescomplemented
240C42×C31—22no—
241C42×C31—22no—
242#25565C3111yesmaximal, characteristic, direct product factor, Sylow
243C23×C31—21no—
244C23×C31—21no—
245C23×C31—22no—
246C23×C31—22no—
247C23×C31—22no—
248C23×C31—24no—
249C23×C31—21no—
250C23×C31—21no—
251C23×C31—22no—
252C23×C31—22no—
253C23×C31—22no—
254C23×C31—22no—
255C23×C31—22no—
256C23×C31—41no—
257C23×C31—42no—
258C23×C31—41no—
259C23×C31—41no—
260C23×C31—41no—
261C23×C31—42no—
262C23×C31—41no—
263C23×C31—42no—
264C23×C31—42no—
265C23×C31—42no—
266C23×C31—84no—
267C23×C31—82no—
268C23×C31—82no—
269C23×C31#12012yes—
270C23×C31#12011yescharacteristic
271C23×C31#12011yescharacteristic
272C23×C31C22×D411yescharacteristic
273C23×C31C22×D412yes—
274C23×C31C2×#4112yes—
275C23×C31H(5,𝔽2)11yescharacteristic
276C23×C312−1+411yescharacteristic
277Q8×C31—81no—
278Q8×C31—81no—
279D4×C31—44no—
280D4×C31—42no—
281D4×C31—42no—
282D4×C31—42no—
283D4×C31—42no—
284D4×C31—44no—
285D4×C31—82no—
286D4×C31—82no—
287D4×C31—81no—
288D4×C31—81no—
289C2×C4×C31—22no—
290C2×C4×C31—21no—
291C2×C4×C31—21no—
292C2×C4×C31—22no—
293C2×C4×C31—22no—
294C2×C4×C31—21no—
295C2×C4×C31—21no—
296C2×C4×C31—24no—
297C2×C4×C31—22no—
298C2×C4×C31—22no—
299C2×C4×C31—42no—
300C2×C4×C31—42no—
301C2×C4×C31—42no—
302C2×C4×C31—42no—
303C2×C4×C31—41no—
304C2×C4×C31—41no—
305C2×C4×C31—42no—
306C2×C4×C31—41no—
307C2×C4×C31—41no—
308C2×C4×C31—42no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—41no—
312C2×C4×C31—41no—
313C2×C4×C31—42no—
314C2×C4×C31—42no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—42no—
318C2×C4×C31—42no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—42no—
326C2×C4×C31—42no—
327C2×C4×C31—42no—
328C2×C4×C31—81no—
329C2×C4×C31—81no—
330C2×C4×C31—82no—
331C2×C4×C31—82no—
332C2×C4×C31—88no—
333#3490C2×C3111yescharacteristic
334#2483C2×C3111yescharacteristic, complemented
335#2412C2×C3112yescomplemented
336#2062C2×C3111yescharacteristic, complemented
337#2044C2×C3111yescharacteristic, complemented
338#2030C2×C3111yescharacteristic, complemented
339#2022C2×C3111yescharacteristic, complemented
340#1898C2×C3112yescomplemented
341#1890C2×C3112yescomplemented
342#1867C2×C3112yescomplemented
343C2×#342C2×C3111yescharacteristic, complemented
344C22×C31—21no—
345C22×C31—21no—
346C22×C31—22no—
347C22×C31—21no—
348C22×C31—22no—
349C22×C31—21no—
350C22×C31—21no—
351C22×C31—22no—
352C22×C31—21no—
353C22×C31—22no—
354C22×C31—21no—
355C22×C31—22no—
356C22×C31—42no—
357C22×C31—41no—
358C22×C31—41no—
359C22×C31—44no—
360C22×C31—42no—
361C22×C31—42no—
362C22×C31—44no—
363C22×C31—42no—
364C22×C31—42no—
365C22×C31—42no—
366C22×C31—82no—
367C22×C31—81no—
368C22×C31—81no—
369C22×C31—82no—
370C22×C31—82no—
371C22×C31—82no—
372C22×C31#45812yes—
373C22×C31C2×#12011yescharacteristic
374C22×C31#53211yescharacteristic
375C22×C31#53711yescharacteristic
376C22×C31#54612yes—
377C22×C31#54712yes—
378C4×C31—44no—
379C4×C31—42no—
380C4×C31—41no—
381C4×C31—41no—
382C4×C31—42no—
383C4×C31—41no—
384C4×C31—41no—
385C4×C31—42no—
386C4×C31—81no—
387C4×C31—81no—
388C4×C31—82no—
389C4×C31—81no—
390C4×C31—81no—
391#551—22no—
392#551—22no—
393#546—22no—
394#546—22no—
395#543C22×C3111yescharacteristic
396#538—21no—
397#538—21no—
398#534C22×C3111yescharacteristic
399#525—21no—
400#525—21no—
401C2×#123C22×C3112yes—
402C2×#120C22×C3112yes—
403#518C22×C3112yes—
404C22×C22⋊C4C22×C3111yescharacteristic
405C22×C22⋊C4C22×C3111yescharacteristic
406C22×C22⋊C4C22×C3112yes—
407C2×#99C22×C3112yes—
408C2×#99C22×C3112yes—
409#397—22no—
410#397—21no—
411#397—21no—
412#394—22no—
413#386—22no—
414#386C22×C3112yes—
415#385—21no—
416#385C22×C3112yes—
417#385C22×C3111yescharacteristic
418#385C22×C3111yescharacteristic
419#381—21no—
420#381C22×C3111yescharacteristic
421#381C22×C3112yes—
422#381C22×C3111yescharacteristic
423#380—22no—
424#379C22×C3111yescharacteristic
425#342C22×C3112yes—
426#342C22×C3111yescharacteristic
427#342C22×C3112yes—
428#342C22×C3112yes—
429#342C22×C3111yescharacteristic
430C2×C31—22no—
431C2×C31—21no—
432C2×C31—21no—
433C2×C31—22no—
434C2×C31—22no—
435C2×C31—41no—
436C2×C31—42no—
437C2×C31—82no—
438C2×C31#243011yescharacteristic
439C2×C31C2×#45811yescharacteristic
440C2×C31#302611yescharacteristic
441C25C23×C3111yescharacteristic
442C2×#41—21no—
443C2×#41—21no—
444C22×D4D4×C3112yes—
445C22×D4D4×C3112yes—
446C22×D4C23×C3112yes—
447C23×C4—22no—
448C23×C4D4×C3111yescharacteristic
449C23×C4D4×C3111yescharacteristic
450C23×C4C23×C3111yescharacteristic
451C23×C4C23×C3111yescharacteristic
452#126—22no—
453#126—22no—
454#124—22no—
455#124—22no—
456#123—22no—
457#123—22no—
458#123—22no—
459#123—22no—
460#123—22no—
461#123—24no—
462#123—42no—
463C22⋊Q8—21no—
464C22⋊Q8—21no—
465C22⋊Q8—21no—
466C22⋊Q8—21no—
467C22⋊Q8—22no—
468C22⋊Q8—22no—
469#121—21no—
470#121—21no—
471#121—22no—
472#121—22no—
473#121—21no—
474#121—21no—
475#120—22no—
476#120—22no—
477#120—22no—
478#120—22no—
479#120—22no—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—22no—
486#117—21no—
487#117—21no—
488#117—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4D4×C3111yescharacteristic
508C2×C22⋊C4D4×C3111yescharacteristic
509C2×C22⋊C4D4×C3112yes—
510C2×C22⋊C4D4×C3112yes—
511C2×C22⋊C4C23×C3112yes—
512C2×C22⋊C4C23×C3111yescharacteristic
513C2×C22⋊C4C23×C3111yescharacteristic
514C2×C22⋊C4C23×C3111yescharacteristic
515C2×C22⋊C4C23×C3111yescharacteristic
516C2×C22⋊C4C23×C3112yes—
517C2×C22⋊C4C23×C3112yes—
518#99—24no—
519#99—42no—
520#95—22no—
521#95—22no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—22no—
529#95—22no—
530C31#2556511yescharacteristic, direct product factor, Sylow
531C24—22no—
532C24—21no—
533C24—21no—
534C24—42no—
535C24—81no—
536C24C2×D4×C3112yes—
537C24C2×D4×C3111yescharacteristic
538C24C2×D4×C3112yes—
539C24C2×D4×C3112yes—
540C24C2×D4×C3111yescharacteristic
541C24C24×C3111yescharacteristic
542#41—82no—
543#41—82no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—44no—
559C2×D4—82no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—44no—
578C22×C4—42no—
579C22×C4—44no—
580C22×C4—81no—
581C22×C4—81no—
582C22×C4—82no—
583C22×C4C2×D4×C3112yes—
584C22×C4C2×D4×C3111yescharacteristic
585C22×C4C2×D4×C3112yes—
586C22×C4C2×D4×C3111yescharacteristic
587C22×C4C2×D4×C3111yescharacteristic
588C22×C4C2×D4×C3112yes—
589C22×C4C2×D4×C3111yescharacteristic
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—44no—
599C4⋊C4—82no—
600C4⋊C4—81no—
601C4⋊C4—81no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—41no—
627C22⋊C4—41no—
628C22⋊C4—81no—
629C22⋊C4—82no—
630C22⋊C4#41×C3114yescomplemented
631C42—22no—
632C42—22no—
633C23—22no—
634C23—24no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—22no—
639C23—21no—
640C23—21no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—41no—
647C23—42no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—42no—
652C23—41no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—84no—
657C23—82no—
658C23—82no—
659C23C31×#12012yes—
660C23C31×#12011yescharacteristic
661C23C31×#12011yescharacteristic
662C23C22×D4×C3111yescharacteristic
663C23C22×D4×C3112yes—
664C23C2×#41×C3112yes—
665C23C31×H(5,𝔽2)11yescharacteristic
666C23C31×2−1+411yescharacteristic
667Q8—81no—
668Q8—81no—
669D4—44no—
670D4—44no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—42no—
675D4—82no—
676D4—82no—
677D4—81no—
678D4—81no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4—88no—
723C22—21no—
724C22—21no—
725C22—22no—
726C22—21no—
727C22—22no—
728C22—21no—
729C22—21no—
730C22—22no—
731C22—21no—
732C22—22no—
733C22—21no—
734C22—22no—
735C22—42no—
736C22—41no—
737C22—41no—
738C22—44no—
739C22—42no—
740C22—42no—
741C22—44no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—82no—
746C22—81no—
747C22—81no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22C31×#45812yes—
752C22C2×C31×#12011yescharacteristic
753C22C31×#53211yescharacteristic
754C22C31×#53711yescharacteristic
755C22C31×#54612yes—
756C22C31×#54712yes—
757C4—44no—
758C4—42no—
759C4—41no—
760C4—41no—
761C4—42no—
762C4—41no—
763C4—41no—
764C4—42no—
765C4—82no—
766C4—81no—
767C4—81no—
768C4—81no—
769C4—81no—
770C2—22no—
771C2—21no—
772C2—21no—
773C2—22no—
774C2—22no—
775C2—41no—
776C2—42no—
777C2—82no—
778C2C31×#243011yescharacteristic
779C2C2×C31×#45811yescharacteristic
780C2C31×#302611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC24C24×C31
prime radicalC31×#3490C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2483C2semidirect
3. C31×#2412C2semidirect
4. C31×#2062C2semidirect
5. C31×#2044C2semidirect
6. C31×#2030C2semidirect
7. C31×#2022C2semidirect
8. C31×#1898C2semidirect
9. C31×#1890C2semidirect
10. C31×#1867C2semidirect
11. C2×C31×#342C2semidirect
239. C22⋊C4×C31#41semidirect
242. #25565C31direct (N × H)
334. #2483C2×C31semidirect
335. #2412C2×C31semidirect
336. #2062C2×C31semidirect
337. #2044C2×C31semidirect
338. #2030C2×C31semidirect
339. #2022C2×C31semidirect
340. #1898C2×C31semidirect
341. #1890C2×C31semidirect
342. #1867C2×C31semidirect
343. C2×#342C2×C31semidirect
530. C31#25565direct (N × H)
630. C22⋊C4#41×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#34902
C31×#24832
C31×#24122
C31×#20622
C31×#20442
C31×#20302
C31×#20222
C31×#18982
C31×#18902
C31×#18672
C2×C31×#3422
#2556531