Finite Group Databasebeta

← C131×#23580 #45709464

Subgroups — C131×#23580 #45709464

Order 33536.

1242 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#540×C131C211yesmaximal, characteristic, complemented
2C2×#442×C131C211yesmaximal, characteristic, complemented
3C2×C4×D8×C131C211yesmaximal, characteristic, complemented
4#2324×C131C211yesmaximal, characteristic, complemented
5#2059×C131C211yesmaximal, characteristic, complemented
6#2041×C131C211yesmaximal, characteristic, complemented
7#2034×C131C211yesmaximal, characteristic, complemented
8#2033×C131C211yesmaximal, characteristic, complemented
9#2025×C131C211yesmaximal, characteristic, complemented
10#2011×C131C211yesmaximal, characteristic, complemented
11#1999×C131C211yesmaximal, characteristic, complemented
12#1999×C131C211yesmaximal, characteristic, complemented
13#1762×C131C211yesmaximal, characteristic, complemented
14C4×#102×C131C211yesmaximal, characteristic, complemented
15#1750×C131C211yesmaximal, characteristic, complemented
16C22×D8×C131C2211yescharacteristic
17C22×D8×C131C2211yescharacteristic
18#540×C131—24no—
19#540×C131—24no—
20C2×#127×C131C2211yescharacteristic
21C2×#125×C131C2211yescharacteristic
22C2×#123×C131—21no—
23C2×#123×C131—21no—
24C2×#121×C131—21no—
25C2×#121×C131—21no—
26C2×#121×C131C2211yescharacteristic
27C2×#121×C131C2211yescharacteristic
28C2×#121×C131C2211yescharacteristic
29C2×C4×D4×C131C2211yescharacteristic
30C2×C4×D4×C131C2211yescharacteristic
31C2×C4×D4×C131C2211yescharacteristic
32C2×#117×C131C2211yescharacteristic
33#442×C131—24no—
34C4×D8×C131—24no—
35C2×#107×C131C2211yescharacteristic
36C2×#106×C131C2211yescharacteristic
37C2×#102×C131C2211yescharacteristic
38C2×#102×C131C2211yescharacteristic
39C2×#102×C131C2211yescharacteristic
40C2×#102×C131C2211yescharacteristic
41C2×#102×C131C2211yescharacteristic
42C2×#102×C131C2211yescharacteristic
43C2×#102×C131C2211yescharacteristic
44C2×#102×C131C2211yescharacteristic
45C2×C22⋊C8×C131C2211yescharacteristic
46C2×C22⋊C8×C131C2211yescharacteristic
47C2×#97×C131C2211yescharacteristic
48C2×C4×C8×C131C2211yescharacteristic
49#390×C131—21no—
50#390×C131C2211yescharacteristic
51#389×C131C2211yescharacteristic
52#388×C131—21no—
53#386×C131—21no—
54#385×C131—21no—
55#380×C131C2211yescharacteristic
56C4×C4⋊C4×C131C2211yescharacteristic
57#340×C131C2211yescharacteristic
58#340×C131C2211yescharacteristic
59#340×C131C2211yescharacteristic
60#340×C131C2211yescharacteristic
61#336×C131C2211yescharacteristic
62#336×C131C2211yescharacteristic
63C22×D4×C131—21no—
64C22×D4×C131—21no—
65C22×D4×C131—21no—
66C22×D4×C131—21no—
67C22×D4×C131—21no—
68C22×D4×C131C2311yescharacteristic
69C22×D4×C131C2311yescharacteristic
70C22×D4×C131C2311yescharacteristic
71C23×C4×C131—21no—
72C23×C4×C131—21no—
73C23×C4×C131—21no—
74C23×C4×C131C2311yescharacteristic
75C2×D8×C131—22no—
76C2×D8×C131—22no—
77C2×D8×C131—22no—
78C2×D8×C131—22no—
79C2×D8×C131—22no—
80C2×D8×C131—22no—
81C22×C8×C131C2311yescharacteristic
82C22×C8×C131C2311yescharacteristic
83C22×C8×C131C2311yescharacteristic
84C22×C8×C131C2311yescharacteristic
85#127×C131—22no—
86#127×C131—22no—
87#125×C131—22no—
88#125×C131—22no—
89#123×C131—28no—
90#123×C131—28no—
91#121×C131—28no—
92#121×C131—28no—
93#121×C131—22no—
94#121×C131—22no—
95#121×C131—22no—
96#121×C131—22no—
97#121×C131—22no—
98#121×C131—22no—
99C4×D4×C131—22no—
100C4×D4×C131—22no—
101C4×D4×C131—22no—
102C4×D4×C131—22no—
103C4×D4×C131D414yescomplemented
104C4×D4×C131D414yescomplemented
105#117×C131—22no—
106#117×C131—22no—
107C2×C4⋊C4×C131—21no—
108C2×C4⋊C4×C131—21no—
109C2×C4⋊C4×C131—21no—
110C2×C4⋊C4×C131D411yescharacteristic
111C2×C4⋊C4×C131D411yescharacteristic
112C2×C4⋊C4×C131C2311yescharacteristic
113C2×C4⋊C4×C131C2311yescharacteristic
114C2×C4⋊C4×C131C2311yescharacteristic
115C2×C4⋊C4×C131C2311yescharacteristic
116C2×C4⋊C4×C131C2311yescharacteristic
117C2×C22⋊C4×C131—21no—
118C2×C22⋊C4×C131—21no—
119C2×C22⋊C4×C131—21no—
120C2×C22⋊C4×C131—21no—
121C2×C22⋊C4×C131—21no—
122C2×C22⋊C4×C131—21no—
123C2×C22⋊C4×C131—21no—
124C2×C22⋊C4×C131—21no—
125C2×C22⋊C4×C131—21no—
126C2×C22⋊C4×C131D411yescharacteristic
127C2×C22⋊C4×C131D411yescharacteristic
128C2×C42×C131—21no—
129C2×C42×C131C2311yescharacteristic
130C2×C42×C131C2311yescharacteristic
131#107×C131—22no—
132#106×C131—22no—
133#102×C131—22no—
134#102×C131—22no—
135#102×C131—22no—
136#102×C131—22no—
137#102×C131—22no—
138#102×C131—22no—
139#102×C131—22no—
140#102×C131—22no—
141C22⋊C8×C131—22no—
142C22⋊C8×C131—22no—
143#97×C131—22no—
144C4×C8×C131—22no—
145#95×C131—21no—
146#95×C131—21no—
147#95×C131—21no—
148C24×C131—21no—
149C24×C131—21no—
150C24×C131—21no—
151C24×C131C2×D411yescharacteristic
152C2×D4×C131—24no—
153C2×D4×C131—24no—
154C2×D4×C131—24no—
155C2×D4×C131—24no—
156C2×D4×C131—24no—
157C2×D4×C131—21no—
158C2×D4×C131—21no—
159C2×D4×C131—21no—
160C2×D4×C131—21no—
161C2×D4×C131—21no—
162C2×D4×C131—21no—
163C2×D4×C131—21no—
164C2×D4×C131—21no—
165C2×D4×C131—21no—
166C2×D4×C131—21no—
167C2×D4×C131—21no—
168C2×D4×C131—21no—
169C2×D4×C131—21no—
170C2×D4×C131—21no—
171C2×D4×C131—21no—
172C2×D4×C131—81no—
173C2×D4×C131—81no—
174C2×D4×C131—81no—
175C2×D4×C131—81no—
176C2×D4×C131—81no—
177C2×D4×C131—81no—
178C2×D4×C131—81no—
179C2×D4×C131—81no—
180C2×D4×C131—81no—
181C2×D4×C131—81no—
182C2×D4×C131C2×D412yes—
183C2×D4×C131C2×D412yes—
184C2×D4×C131#4112yes—
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—24no—
195C22×C4×C131—24no—
196C22×C4×C131—21no—
197C22×C4×C131—21no—
198C22×C4×C131—42no—
199C22×C4×C131—81no—
200C22×C4×C131—81no—
201C22×C4×C131—81no—
202C22×C4×C131—81no—
203C22×C4×C131—81no—
204C22×C4×C131—81no—
205C22×C4×C131C2×D411yescharacteristic
206C22×C4×C131C2×D411yescharacteristic
207C22×C4×C131C2×D411yescharacteristic
208C22×C4×C131C2×D411yescharacteristic
209C22×C4×C131C2×D411yescharacteristic
210C22×C4×C131C2411yescharacteristic
211D8×C131—28no—
212D8×C131—28no—
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—21no—
220C2×C8×C131—21no—
221C2×C8×C131—21no—
222C2×C8×C131—21no—
223C2×C8×C131#4112yes—
224C2×C8×C131#4112yes—
225C4⋊C4×C131—24no—
226C4⋊C4×C131—24no—
227C4⋊C4×C131—22no—
228C4⋊C4×C131—22no—
229C4⋊C4×C131—21no—
230C4⋊C4×C131—21no—
231C4⋊C4×C131—21no—
232C4⋊C4×C131—21no—
233C4⋊C4×C131—21no—
234C4⋊C4×C131—21no—
235C4⋊C4×C131—21no—
236C4⋊C4×C131—81no—
237C4⋊C4×C131C2×D412yes—
238C4⋊C4×C131C2×D412yes—
239C4⋊C4×C131#4112yes—
240C22⋊C4×C131—24no—
241C22⋊C4×C131—24no—
242C22⋊C4×C131—24no—
243C22⋊C4×C131—24no—
244C22⋊C4×C131—24no—
245C22⋊C4×C131—22no—
246C22⋊C4×C131—22no—
247C22⋊C4×C131—42no—
248C22⋊C4×C131—81no—
249C22⋊C4×C131—81no—
250C22⋊C4×C131—81no—
251C42×C131—21no—
252C42×C131—21no—
253C42×C131—81no—
254C42×C131C2×D412yes—
255C42×C131C2×D412yes—
256C23×C131—21no—
257C23×C131—22no—
258C23×C131—22no—
259C23×C131—22no—
260C23×C131—21no—
261C23×C131—21no—
262C23×C131—21no—
263C23×C131—21no—
264C23×C131—21no—
265C23×C131—21no—
266C23×C131—41no—
267C23×C131—41no—
268C23×C131—41no—
269C23×C131—41no—
270C23×C131—41no—
271C23×C131—41no—
272C23×C131—41no—
273C23×C131—41no—
274C23×C131—41no—
275C23×C131—41no—
276C23×C131—41no—
277C23×C131—41no—
278C23×C131—41no—
279C23×C131—41no—
280C23×C131—41no—
281C23×C131—41no—
282C23×C131—41no—
283C23×C131—41no—
284C23×C131C22×D411yescharacteristic
285D4×C131—22no—
286D4×C131—22no—
287D4×C131—22no—
288D4×C131—22no—
289D4×C131—22no—
290D4×C131—22no—
291D4×C131—41no—
292D4×C131—41no—
293D4×C131—41no—
294D4×C131—41no—
295D4×C131—41no—
296D4×C131—41no—
297D4×C131—84no—
298D4×C131—84no—
299D4×C131—84no—
300D4×C131—84no—
301D4×C131—84no—
302C2×C4×C131—21no—
303C2×C4×C131—21no—
304C2×C4×C131—21no—
305C2×C4×C131—21no—
306C2×C4×C131—21no—
307C2×C4×C131—21no—
308C2×C4×C131—21no—
309C2×C4×C131—22no—
310C2×C4×C131—22no—
311C2×C4×C131—21no—
312C2×C4×C131—22no—
313C2×C4×C131—21no—
314C2×C4×C131—21no—
315C2×C4×C131—21no—
316C2×C4×C131—21no—
317C2×C4×C131—21no—
318C2×C4×C131—41no—
319C2×C4×C131—41no—
320C2×C4×C131—41no—
321C2×C4×C131—41no—
322C2×C4×C131—41no—
323C2×C4×C131—41no—
324C2×C4×C131—41no—
325C2×C4×C131—41no—
326C2×C4×C131—41no—
327C2×C4×C131—41no—
328C2×C4×C131—41no—
329C2×C4×C131—41no—
330C2×C4×C131—41no—
331C2×C4×C131—41no—
332C2×C4×C131—41no—
333C2×C4×C131—41no—
334C2×C4×C131—84no—
335C2×C4×C131—84no—
336C2×C4×C131—84no—
337C2×C4×C131#12012yes—
338C2×C4×C131#12012yes—
339C2×C4×C131C22×D411yescharacteristic
340C2×C4×C131C22×D411yescharacteristic
341C2×C4×C131C2×#4111yescharacteristic
342C2×C4×C131C2×#4111yescharacteristic
343C2×C4×C131C2×#4111yescharacteristic
344C2×C4×C131C2×#4111yescharacteristic
345C8×C131—22no—
346C8×C131—22no—
347C8×C131—41no—
348C8×C131—41no—
349C22×C131—41no—
350C22×C131—42no—
351C22×C131—41no—
352C22×C131—42no—
353C22×C131—41no—
354C22×C131—42no—
355C22×C131—42no—
356C22×C131—42no—
357C22×C131—41no—
358C22×C131—41no—
359C22×C131—42no—
360C22×C131—41no—
361C22×C131—42no—
362C22×C131—42no—
363C22×C131—41no—
364C22×C131—42no—
365C22×C131—81no—
366C22×C131—81no—
367C22×C131—81no—
368C22×C131—81no—
369C22×C131—81no—
370C22×C131—81no—
371C22×C131—81no—
372C22×C131—81no—
373C22×C131—81no—
374C22×C131—81no—
375C22×C131—81no—
376C22×C131—81no—
377C22×C131C2×#12011yescharacteristic
378C22×C131#52511yescharacteristic
379C22×C131#53211yescharacteristic
380C22×C131#57611yescharacteristic
381C22×C131#57611yescharacteristic
382C22×C131#57611yescharacteristic
383C22×C131#57711yescharacteristic
384C4×C131—22no—
385C4×C131—22no—
386C4×C131—42no—
387C4×C131—41no—
388C4×C131—41no—
389C4×C131—42no—
390C4×C131—41no—
391C4×C131—42no—
392C4×C131—81no—
393C4×C131—81no—
394C4×C131#52511yescharacteristic
395C4×C131#52511yescharacteristic
396C4×C131#53211yescharacteristic
397C4×C131#53211yescharacteristic
398C2×C131—81no—
399C2×C131—82no—
400C2×C131—82no—
401C2×C131—82no—
402C2×C131#238811yescharacteristic
403C2×C131#300811yescharacteristic
404C2×C131#301211yescharacteristic
405C2×C131#311911yescharacteristic
406C2×C131#312211yescharacteristic
407C2×C131#317611yescharacteristic
408C2×C131#317911yescharacteristic
409#23580C13111yesmaximal, characteristic, direct product factor, Sylow
410C131#2358011yescharacteristic, direct product factor, Sylow
411C2×#540C2×C13111yescharacteristic, complemented
412C2×#442C2×C13111yescharacteristic, complemented
413C2×C4×D8C2×C13111yescharacteristic, complemented
414#2324C2×C13111yescharacteristic, complemented
415#2059C2×C13111yescharacteristic, complemented
416#2041C2×C13111yescharacteristic, complemented
417#2034C2×C13111yescharacteristic, complemented
418#2033C2×C13111yescharacteristic, complemented
419#2025C2×C13111yescharacteristic, complemented
420#2011C2×C13111yescharacteristic, complemented
421#1999C2×C13111yescharacteristic, complemented
422#1999C2×C13111yescharacteristic, complemented
423#1762C2×C13111yescharacteristic, complemented
424C4×#102C2×C13111yescharacteristic, complemented
425#1750C2×C13111yescharacteristic, complemented
426C22×D8C22×C13111yescharacteristic
427C22×D8C22×C13111yescharacteristic
428#540—24no—
429#540—24no—
430C2×#127C22×C13111yescharacteristic
431C2×#125C22×C13111yescharacteristic
432C2×#123—21no—
433C2×#123—21no—
434C2×#121—21no—
435C2×#121—21no—
436C2×#121C22×C13111yescharacteristic
437C2×#121C22×C13111yescharacteristic
438C2×#121C22×C13111yescharacteristic
439C2×C4×D4C22×C13111yescharacteristic
440C2×C4×D4C22×C13111yescharacteristic
441C2×C4×D4C22×C13111yescharacteristic
442C2×#117C22×C13111yescharacteristic
443#442—24no—
444C4×D8—24no—
445C2×#107C22×C13111yescharacteristic
446C2×#106C22×C13111yescharacteristic
447C2×#102C22×C13111yescharacteristic
448C2×#102C22×C13111yescharacteristic
449C2×#102C22×C13111yescharacteristic
450C2×#102C22×C13111yescharacteristic
451C2×#102C22×C13111yescharacteristic
452C2×#102C22×C13111yescharacteristic
453C2×#102C22×C13111yescharacteristic
454C2×#102C22×C13111yescharacteristic
455C2×C22⋊C8C22×C13111yescharacteristic
456C2×C22⋊C8C22×C13111yescharacteristic
457C2×#97C22×C13111yescharacteristic
458C2×C4×C8C22×C13111yescharacteristic
459#390—21no—
460#390C22×C13111yescharacteristic
461#389C22×C13111yescharacteristic
462#388—21no—
463#386—21no—
464#385—21no—
465#380C22×C13111yescharacteristic
466C4×C4⋊C4C22×C13111yescharacteristic
467#340C22×C13111yescharacteristic
468#340C22×C13111yescharacteristic
469#340C22×C13111yescharacteristic
470#340C22×C13111yescharacteristic
471#336C22×C13111yescharacteristic
472#336C22×C13111yescharacteristic
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4C23×C13111yescharacteristic
479C22×D4C23×C13111yescharacteristic
480C22×D4C23×C13111yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C13111yescharacteristic
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—22no—
490C2×D8—22no—
491C22×C8C23×C13111yescharacteristic
492C22×C8C23×C13111yescharacteristic
493C22×C8C23×C13111yescharacteristic
494C22×C8C23×C13111yescharacteristic
495#127—22no—
496#127—22no—
497#125—22no—
498#125—22no—
499#123—28no—
500#123—28no—
501#121—28no—
502#121—28no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4D4×C13114yescomplemented
514C4×D4D4×C13114yescomplemented
515#117—22no—
516#117—22no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4D4×C13111yescharacteristic
521C2×C4⋊C4D4×C13111yescharacteristic
522C2×C4⋊C4C23×C13111yescharacteristic
523C2×C4⋊C4C23×C13111yescharacteristic
524C2×C4⋊C4C23×C13111yescharacteristic
525C2×C4⋊C4C23×C13111yescharacteristic
526C2×C4⋊C4C23×C13111yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4D4×C13111yescharacteristic
537C2×C22⋊C4D4×C13111yescharacteristic
538C2×C42—21no—
539C2×C42C23×C13111yescharacteristic
540C2×C42C23×C13111yescharacteristic
541#107—22no—
542#106—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553#97—22no—
554C4×C8—22no—
555#95—21no—
556#95—21no—
557#95—21no—
558C24—21no—
559C24—21no—
560C24—21no—
561C24C2×D4×C13111yescharacteristic
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C2×D4×C13112yes—
593C2×D4C2×D4×C13112yes—
594C2×D4#41×C13112yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C2×D4×C13111yescharacteristic
616C22×C4C2×D4×C13111yescharacteristic
617C22×C4C2×D4×C13111yescharacteristic
618C22×C4C2×D4×C13111yescharacteristic
619C22×C4C2×D4×C13111yescharacteristic
620C22×C4C24×C13111yescharacteristic
621D8—28no—
622D8—28no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8#41×C13112yes—
634C2×C8#41×C13112yes—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C2×D4×C13112yes—
648C4⋊C4C2×D4×C13112yes—
649C4⋊C4#41×C13112yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—81no—
664C42C2×D4×C13112yes—
665C42C2×D4×C13112yes—
666C23—21no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23C22×D4×C13111yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4#120×C13112yes—
748C2×C4#120×C13112yes—
749C2×C4C22×D4×C13111yescharacteristic
750C2×C4C22×D4×C13111yescharacteristic
751C2×C4C2×#41×C13111yescharacteristic
752C2×C4C2×#41×C13111yescharacteristic
753C2×C4C2×#41×C13111yescharacteristic
754C2×C4C2×#41×C13111yescharacteristic
755C8—22no—
756C8—22no—
757C8—41no—
758C8—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—42no—
769C22—41no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22C2×#120×C13111yescharacteristic
788C22#525×C13111yescharacteristic
789C22#532×C13111yescharacteristic
790C22#576×C13111yescharacteristic
791C22#576×C13111yescharacteristic
792C22#576×C13111yescharacteristic
793C22#577×C13111yescharacteristic
794C4—22no—
795C4—22no—
796C4—41no—
797C4—42no—
798C4—41no—
799C4—42no—
800C4—42no—
801C4—41no—
802C4—81no—
803C4—81no—
804C4#525×C13111yescharacteristic
805C4#525×C13111yescharacteristic
806C4#532×C13111yescharacteristic
807C4#532×C13111yescharacteristic
808C2—81no—
809C2—82no—
810C2—82no—
811C2—82no—
812C2#2388×C13111yescharacteristic
813C2#3008×C13111yescharacteristic
814C2#3012×C13111yescharacteristic
815C2#3119×C13111yescharacteristic
816C2#3122×C13111yescharacteristic
817C2#3176×C13111yescharacteristic
818C2#3179×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×#117×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#540×C131C2semidirect
2. C2×#442×C131C2semidirect
3. C2×C4×D8×C131C2semidirect
4. #2324×C131C2semidirect
5. #2059×C131C2semidirect
6. #2041×C131C2semidirect
7. #2034×C131C2semidirect
8. #2033×C131C2semidirect
9. #2025×C131C2semidirect
10. #2011×C131C2semidirect
11. #1999×C131C2semidirect
12. #1999×C131C2semidirect
13. #1762×C131C2semidirect
14. C4×#102×C131C2semidirect
15. #1750×C131C2semidirect
103. C4×D4×C131D4semidirect
104. C4×D4×C131D4semidirect
409. #23580C131direct (N × H)
410. C131#23580direct (N × H)
411. C2×#540C2×C131semidirect
412. C2×#442C2×C131semidirect
413. C2×C4×D8C2×C131semidirect
414. #2324C2×C131semidirect
415. #2059C2×C131semidirect
416. #2041C2×C131semidirect
417. #2034C2×C131semidirect
418. #2033C2×C131semidirect
419. #2025C2×C131semidirect
420. #2011C2×C131semidirect
421. #1999C2×C131semidirect
422. #1999C2×C131semidirect
423. #1762C2×C131semidirect
424. C4×#102C2×C131semidirect
425. #1750C2×C131semidirect
513. C4×D4D4×C131semidirect
514. C4×D4D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#540×C1312
C2×#442×C1312
C2×C4×D8×C1312
#2324×C1312
#2059×C1312
#2041×C1312
#2034×C1312
#2033×C1312
#2025×C1312
#2011×C1312
#1999×C1312
#1762×C1312
C4×#102×C1312
#1750×C1312
#23580131