Finite Group Databasebeta

← C131×#14456 #45700340

Subgroups — C131×#14456 #45700340

Order 33536.

1450 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#385×C131C211yesmaximal, characteristic
2#1445×C131C211yesmaximal, characteristic, complemented
3#1443×C131C211yesmaximal, characteristic, complemented
4#1441×C131C211yesmaximal, characteristic, complemented
5#1441×C131C211yesmaximal, characteristic, complemented
6#1439×C131C211yesmaximal, characteristic
7#1439×C131C211yesmaximal, characteristic
8#1437×C131C211yesmaximal, characteristic
9#1437×C131C211yesmaximal, characteristic
10#1436×C131C211yesmaximal, characteristic, complemented
11C4⋊#95×C131C211yesmaximal, characteristic, complemented
12#1434×C131C211yesmaximal, characteristic, complemented
13#1434×C131C211yesmaximal, characteristic, complemented
14C22⋊#95×C131C211yesmaximal, characteristic
15C22⋊#95×C131C211yesmaximal, characteristic
16C24×C4×C131C2211yescharacteristic
17C22×C4⋊C4×C131C2211yescharacteristic
18C22×C4⋊C4×C131C2211yescharacteristic
19C22×C4⋊C4×C131C2211yescharacteristic
20C22×C4⋊C4×C131C2211yescharacteristic
21C22×C22⋊C4×C131C2211yescharacteristic
22C22×C22⋊C4×C131C2211yescharacteristic
23C22×C22⋊C4×C131C2211yescharacteristic
24C22×C22⋊C4×C131C2211yescharacteristic
25C22×C22⋊C4×C131C2211yescharacteristic
26C22×C22⋊C4×C131C2211yescharacteristic
27C22×C42×C131C2211yescharacteristic
28C22×C42×C131C2211yescharacteristic
29#385×C131C418yescomplemented
30C2×#95×C131C2211yescharacteristic
31C2×#95×C131C2211yescharacteristic
32C2×#95×C131C2211yescharacteristic
33C2×#95×C131C2211yescharacteristic
34C2×#95×C131C2211yescharacteristic
35C2×#95×C131C2211yescharacteristic
36C2×#95×C131C2211yescharacteristic
37C2×#95×C131C2211yescharacteristic
38C2×#95×C131C2211yescharacteristic
39C2×#95×C131C2211yescharacteristic
40C2×#95×C131C2211yescharacteristic
41C2×#95×C131C2211yescharacteristic
42C2×#95×C131C2211yescharacteristic
43C2×#95×C131C2211yescharacteristic
44C2×#95×C131C2211yescharacteristic
45C2×#95×C131C2211yescharacteristic
46C2×#95×C131C2211yescharacteristic
47C2×#95×C131C2211yescharacteristic
48C2×#95×C131C2211yescharacteristic
49C2×#95×C131C2211yescharacteristic
50C2×#95×C131C2211yescharacteristic
51C2×#95×C131C2211yescharacteristic
52C25×C131C2311yescharacteristic
53C23×C4×C131—41no—
54C23×C4×C131—41no—
55C23×C4×C131—41no—
56C23×C4×C131—41no—
57C23×C4×C131—41no—
58C23×C4×C131—41no—
59C23×C4×C131C2×C414yes—
60C23×C4×C131C2311yescharacteristic
61C23×C4×C131C2311yescharacteristic
62C23×C4×C131C2311yescharacteristic
63C23×C4×C131C2311yescharacteristic
64C23×C4×C131C2311yescharacteristic
65C23×C4×C131C2311yescharacteristic
66C23×C4×C131C2311yescharacteristic
67C23×C4×C131C2311yescharacteristic
68C23×C4×C131C2311yescharacteristic
69C23×C4×C131C2311yescharacteristic
70C23×C4×C131C2311yescharacteristic
71C23×C4×C131C2311yescharacteristic
72C23×C4×C131C2311yescharacteristic
73C23×C4×C131C2311yescharacteristic
74C2×C4⋊C4×C131—22no—
75C2×C4⋊C4×C131—22no—
76C2×C4⋊C4×C131—41no—
77C2×C4⋊C4×C131—41no—
78C2×C4⋊C4×C131—41no—
79C2×C4⋊C4×C131—41no—
80C2×C4⋊C4×C131—41no—
81C2×C4⋊C4×C131—41no—
82C2×C4⋊C4×C131—41no—
83C2×C4⋊C4×C131—41no—
84C2×C4⋊C4×C131C2×C414yes—
85C2×C4⋊C4×C131C2×C414yes—
86C2×C22⋊C4×C131—22no—
87C2×C22⋊C4×C131—22no—
88C2×C22⋊C4×C131—22no—
89C2×C22⋊C4×C131—22no—
90C2×C22⋊C4×C131—22no—
91C2×C22⋊C4×C131—22no—
92C2×C22⋊C4×C131—22no—
93C2×C22⋊C4×C131—41no—
94C2×C22⋊C4×C131—41no—
95C2×C22⋊C4×C131—41no—
96C2×C22⋊C4×C131—41no—
97C2×C22⋊C4×C131—41no—
98C2×C22⋊C4×C131—41no—
99C2×C22⋊C4×C131—41no—
100C2×C22⋊C4×C131—41no—
101C2×C22⋊C4×C131C2×C414yes—
102C2×C22⋊C4×C131C2×C414yes—
103C2×C22⋊C4×C131Q814yes—
104C2×C42×C131—22no—
105C2×C42×C131—22no—
106C2×C42×C131—22no—
107C2×C42×C131—41no—
108C2×C42×C131—41no—
109C2×C42×C131—41no—
110#95×C131—22no—
111#95×C131—22no—
112#95×C131—22no—
113#95×C131—41no—
114#95×C131—41no—
115#95×C131—41no—
116#95×C131—41no—
117#95×C131—41no—
118#95×C131—41no—
119#95×C131—41no—
120#95×C131—41no—
121#95×C131—41no—
122#95×C131—41no—
123#95×C131—41no—
124#95×C131—41no—
125#95×C131—41no—
126#95×C131—41no—
127#95×C131—41no—
128#95×C131—41no—
129#95×C131—41no—
130#95×C131C2×C414yes—
131#95×C131C2×C414yes—
132C24×C131—21no—
133C24×C131—21no—
134C24×C131—21no—
135C24×C131—21no—
136C24×C131—21no—
137C24×C131—21no—
138C24×C131—21no—
139C24×C131—21no—
140C24×C131—21no—
141C24×C131—21no—
142C24×C131—21no—
143C24×C131—21no—
144C24×C131C22×C412yes—
145C24×C131C2×Q812yes—
146C24×C131#4112yes—
147C24×C131C2411yescharacteristic
148C22×C4×C131—21no—
149C22×C4×C131—21no—
150C22×C4×C131—21no—
151C22×C4×C131—21no—
152C22×C4×C131—21no—
153C22×C4×C131—21no—
154C22×C4×C131—21no—
155C22×C4×C131—21no—
156C22×C4×C131—21no—
157C22×C4×C131—21no—
158C22×C4×C131—21no—
159C22×C4×C131—21no—
160C22×C4×C131—21no—
161C22×C4×C131—21no—
162C22×C4×C131—21no—
163C22×C4×C131—21no—
164C22×C4×C131—21no—
165C22×C4×C131—21no—
166C22×C4×C131—21no—
167C22×C4×C131—21no—
168C22×C4×C131—21no—
169C22×C4×C131—21no—
170C22×C4×C131—21no—
171C22×C4×C131—21no—
172C22×C4×C131—21no—
173C22×C4×C131—21no—
174C22×C4×C131—21no—
175C22×C4×C131—21no—
176C22×C4×C131—21no—
177C22×C4×C131—21no—
178C22×C4×C131—21no—
179C22×C4×C131—21no—
180C22×C4×C131—21no—
181C22×C4×C131—21no—
182C22×C4×C131—21no—
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—21no—
195C22×C4×C131—21no—
196C22×C4×C131—21no—
197C22×C4×C131—21no—
198C22×C4×C131—21no—
199C22×C4×C131—21no—
200C22×C4×C131—21no—
201C22×C4×C131—21no—
202C22×C4×C131—21no—
203C22×C4×C131—21no—
204C22×C4×C131—21no—
205C22×C4×C131—21no—
206C22×C4×C131—21no—
207C22×C4×C131—21no—
208C22×C4×C131—21no—
209C22×C4×C131—21no—
210C22×C4×C131—21no—
211C22×C4×C131—21no—
212C22×C4×C131—21no—
213C22×C4×C131—21no—
214C22×C4×C131—21no—
215C22×C4×C131—21no—
216C22×C4×C131—21no—
217C22×C4×C131—21no—
218C22×C4×C131—21no—
219C22×C4×C131—21no—
220C22×C4×C131—21no—
221C22×C4×C131—21no—
222C22×C4×C131—21no—
223C22×C4×C131—21no—
224C22×C4×C131—21no—
225C22×C4×C131—21no—
226C22×C4×C131—21no—
227C22×C4×C131—21no—
228C22×C4×C131—21no—
229C22×C4×C131—21no—
230C22×C4×C131—21no—
231C22×C4×C131—21no—
232C22×C4×C131—21no—
233C22×C4×C131—21no—
234C22×C4×C131—44no—
235C22×C4×C131—44no—
236C22×C4×C131—44no—
237C22×C4×C131—44no—
238C22×C4×C131—44no—
239C22×C4×C131—44no—
240C22×C4×C131—44no—
241C22×C4×C131C22×C412yes—
242C22×C4×C131C22×C412yes—
243C22×C4×C131C22×C412yes—
244C22×C4×C131C22×C412yes—
245C22×C4×C131C22×C412yes—
246C22×C4×C131C22×C412yes—
247C22×C4×C131C2×Q812yes—
248C22×C4×C131C2×Q812yes—
249C22×C4×C131#4112yes—
250C22×C4×C131#4112yes—
251C22×C4×C131#4112yes—
252C22×C4×C131#4112yes—
253C4⋊C4×C131—44no—
254C4⋊C4×C131—44no—
255C4⋊C4×C131—44no—
256C4⋊C4×C131—44no—
257C22⋊C4×C131—28no—
258C22⋊C4×C131—44no—
259C22⋊C4×C131—44no—
260C22⋊C4×C131—44no—
261C22⋊C4×C131—44no—
262C22⋊C4×C131—44no—
263C42×C131—44no—
264C42×C131—44no—
265C23×C131—22no—
266C23×C131—22no—
267C23×C131—22no—
268C23×C131—22no—
269C23×C131—22no—
270C23×C131—22no—
271C23×C131—22no—
272C23×C131—22no—
273C23×C131—22no—
274C23×C131—22no—
275C23×C131—22no—
276C23×C131—22no—
277C23×C131—22no—
278C23×C131—22no—
279C23×C131—22no—
280C23×C131—22no—
281C23×C131—22no—
282C23×C131—22no—
283C23×C131—41no—
284C23×C131—41no—
285C23×C131—41no—
286C23×C131—41no—
287C23×C131—41no—
288C23×C131—41no—
289C23×C131—41no—
290C23×C131—41no—
291C23×C131—41no—
292C23×C131—41no—
293C23×C131—41no—
294C23×C131—41no—
295C23×C131—41no—
296C23×C131—41no—
297C23×C131—41no—
298C23×C131—41no—
299C23×C131C4×Q814yes—
300C23×C131C23×C411yescharacteristic
301C23×C131C22×Q811yescharacteristic
302C23×C131C2×#4111yescharacteristic
303C23×C131C2×#4111yescharacteristic
304C23×C131C2×#4111yescharacteristic
305C23×C131C2×#4111yescharacteristic
306C23×C131C2×#4111yescharacteristic
307C23×C131H(5,𝔽2)11yescharacteristic
308C23×C131H(5,𝔽2)11yescharacteristic
309C23×C131H(5,𝔽2)11yescharacteristic
310C23×C131H(5,𝔽2)11yescharacteristic
311C23×C131H(5,𝔽2)11yescharacteristic
312C23×C131H(5,𝔽2)11yescharacteristic
313C23×C131H(5,𝔽2)11yescharacteristic
314C23×C1312−1+411yescharacteristic
315C2×C4×C131—22no—
316C2×C4×C131—22no—
317C2×C4×C131—22no—
318C2×C4×C131—22no—
319C2×C4×C131—22no—
320C2×C4×C131—22no—
321C2×C4×C131—22no—
322C2×C4×C131—22no—
323C2×C4×C131—22no—
324C2×C4×C131—22no—
325C2×C4×C131—22no—
326C2×C4×C131—22no—
327C2×C4×C131—22no—
328C2×C4×C131—22no—
329C2×C4×C131—22no—
330C2×C4×C131—22no—
331C2×C4×C131—22no—
332C2×C4×C131—22no—
333C2×C4×C131—22no—
334C2×C4×C131—22no—
335C2×C4×C131—22no—
336C2×C4×C131—22no—
337C2×C4×C131—22no—
338C2×C4×C131—22no—
339C2×C4×C131—22no—
340C2×C4×C131—22no—
341C2×C4×C131—22no—
342C2×C4×C131—22no—
343C2×C4×C131—22no—
344C2×C4×C131—22no—
345C2×C4×C131—22no—
346C2×C4×C131—22no—
347C2×C4×C131—22no—
348C2×C4×C131—416no—
349C2×C4×C131—41no—
350C2×C4×C131—41no—
351C2×C4×C131—41no—
352C2×C4×C131—41no—
353C2×C4×C131—41no—
354C2×C4×C131—41no—
355C2×C4×C131—41no—
356C2×C4×C131—41no—
357C2×C4×C131—41no—
358C2×C4×C131—41no—
359C2×C4×C131—41no—
360C2×C4×C131—41no—
361C2×C4×C131—41no—
362C2×C4×C131—41no—
363C2×C4×C131—41no—
364C2×C4×C131—41no—
365C2×C4×C131—41no—
366C2×C4×C131—41no—
367C2×C4×C131—41no—
368C2×C4×C131—41no—
369C2×C4×C131—41no—
370C2×C4×C131—41no—
371C2×C4×C131—41no—
372C2×C4×C131—41no—
373C2×C4×C131—41no—
374C2×C4×C131—41no—
375C2×C4×C131—41no—
376C2×C4×C131—41no—
377C2×C4×C131—41no—
378C2×C4×C131—41no—
379C2×C4×C131—41no—
380C2×C4×C131—41no—
381C2×C4×C131—41no—
382C2×C4×C131—41no—
383C2×C4×C131—41no—
384C2×C4×C131—41no—
385C2×C4×C131—41no—
386C2×C4×C131—41no—
387C2×C4×C131—41no—
388C2×C4×C131—41no—
389C2×C4×C131—41no—
390C2×C4×C131—41no—
391C2×C4×C131—41no—
392C2×C4×C131—41no—
393C2×C4×C131—41no—
394C2×C4×C131—41no—
395C2×C4×C131—41no—
396C2×C4×C131—41no—
397C2×C4×C131—41no—
398C2×C4×C131—41no—
399C2×C4×C131—41no—
400C2×C4×C131—41no—
401C2×C4×C131—41no—
402C2×C4×C131—41no—
403C2×C4×C131—41no—
404C2×C4×C131—41no—
405C2×C4×C131—41no—
406C2×C4×C131—41no—
407C2×C4×C131—41no—
408C2×C4×C131—41no—
409C2×C4×C131—41no—
410C2×C4×C131—41no—
411C2×C4×C131—41no—
412C2×C4×C131—41no—
413C2×C4×C131#11714yes—
414C22×C131—24no—
415C22×C131—24no—
416C22×C131—24no—
417C22×C131—42no—
418C22×C131—42no—
419C22×C131—42no—
420C22×C131—42no—
421C22×C131—42no—
422C22×C131—42no—
423C22×C131—42no—
424C22×C131—42no—
425C22×C131—42no—
426C22×C131—42no—
427C22×C131—42no—
428C22×C131—42no—
429C22×C131C2×#11711yescharacteristic
430C22×C131C2×C4×Q811yescharacteristic
431C22×C131C4×#4111yescharacteristic
432C22×C131#51811yescharacteristic
433C22×C131#51811yescharacteristic
434C22×C131#51811yescharacteristic
435C22×C131#52011yescharacteristic
436C22×C131#53811yescharacteristic
437C22×C131#53811yescharacteristic
438C22×C131#53911yescharacteristic
439C22×C131#53911yescharacteristic
440C22×C131#54011yescharacteristic
441C22×C131#54011yescharacteristic
442C22×C131#54011yescharacteristic
443C22×C131#54211yescharacteristic
444C22×C131#54211yescharacteristic
445C22×C131#54211yescharacteristic
446C22×C131#54311yescharacteristic
447C22×C131#54411yescharacteristic
448C22×C131#55111yescharacteristic
449C22×C131#55111yescharacteristic
450C22×C131#55111yescharacteristic
451C22×C131#55111yescharacteristic
452C22×C131#55311yescharacteristic
453C22×C131#55311yescharacteristic
454C22×C131#55311yescharacteristic
455C22×C131#55311yescharacteristic
456C22×C131#55411yescharacteristic
457C22×C131#55411yescharacteristic
458C22×C131#55411yescharacteristic
459C22×C131#55411yescharacteristic
460C22×C131#56011yescharacteristic
461C22×C131#56011yescharacteristic
462C22×C131#56011yescharacteristic
463C22×C131H(3,𝔽4)11yescharacteristic
464C4×C131—24no—
465C4×C131—42no—
466C4×C131—42no—
467C4×C131—42no—
468C4×C131—42no—
469C4×C131—42no—
470C4×C131—42no—
471C4×C131—42no—
472C4×C131—42no—
473C4×C131—42no—
474C4×C131—81no—
475C4×C131—81no—
476C4×C131—81no—
477C4×C131—81no—
478C2×C131—44no—
479C2×C131#231911yescharacteristic
480C2×C131#232911yescharacteristic
481C2×C131#233511yescharacteristic
482C2×C131#234511yescharacteristic
483C2×C131#235311yescharacteristic
484C2×C131#236811yescharacteristic
485C2×C131#237511yescharacteristic
486C2×C131#274611yescharacteristic
487C2×C131#274811yescharacteristic
488C2×C131#274911yescharacteristic
489C2×C131#275311yescharacteristic
490C2×C131#275711yescharacteristic
491C2×C131#276311yescharacteristic
492C2×C131#278011yescharacteristic
493C2×C131#279011yescharacteristic
494#14456C13111yesmaximal, characteristic, direct product factor, Sylow
495C131#1445611yescharacteristic, direct product factor, Sylow
496C2×#385C2×C13111yescharacteristic
497#1445C2×C13111yescharacteristic, complemented
498#1443C2×C13111yescharacteristic, complemented
499#1441C2×C13111yescharacteristic, complemented
500#1441C2×C13111yescharacteristic, complemented
501#1439C2×C13111yescharacteristic
502#1439C2×C13111yescharacteristic
503#1437C2×C13111yescharacteristic
504#1437C2×C13111yescharacteristic
505#1436C2×C13111yescharacteristic, complemented
506C4⋊#95C2×C13111yescharacteristic, complemented
507#1434C2×C13111yescharacteristic, complemented
508#1434C2×C13111yescharacteristic, complemented
509C22⋊#95C2×C13111yescharacteristic
510C22⋊#95C2×C13111yescharacteristic
511C24×C4C22×C13111yescharacteristic
512C22×C4⋊C4C22×C13111yescharacteristic
513C22×C4⋊C4C22×C13111yescharacteristic
514C22×C4⋊C4C22×C13111yescharacteristic
515C22×C4⋊C4C22×C13111yescharacteristic
516C22×C22⋊C4C22×C13111yescharacteristic
517C22×C22⋊C4C22×C13111yescharacteristic
518C22×C22⋊C4C22×C13111yescharacteristic
519C22×C22⋊C4C22×C13111yescharacteristic
520C22×C22⋊C4C22×C13111yescharacteristic
521C22×C22⋊C4C22×C13111yescharacteristic
522C22×C42C22×C13111yescharacteristic
523C22×C42C22×C13111yescharacteristic
524#385C4×C13118yescomplemented
525C2×#95C22×C13111yescharacteristic
526C2×#95C22×C13111yescharacteristic
527C2×#95C22×C13111yescharacteristic
528C2×#95C22×C13111yescharacteristic
529C2×#95C22×C13111yescharacteristic
530C2×#95C22×C13111yescharacteristic
531C2×#95C22×C13111yescharacteristic
532C2×#95C22×C13111yescharacteristic
533C2×#95C22×C13111yescharacteristic
534C2×#95C22×C13111yescharacteristic
535C2×#95C22×C13111yescharacteristic
536C2×#95C22×C13111yescharacteristic
537C2×#95C22×C13111yescharacteristic
538C2×#95C22×C13111yescharacteristic
539C2×#95C22×C13111yescharacteristic
540C2×#95C22×C13111yescharacteristic
541C2×#95C22×C13111yescharacteristic
542C2×#95C22×C13111yescharacteristic
543C2×#95C22×C13111yescharacteristic
544C2×#95C22×C13111yescharacteristic
545C2×#95C22×C13111yescharacteristic
546C2×#95C22×C13111yescharacteristic
547C25C23×C13111yescharacteristic
548C23×C4—41no—
549C23×C4—41no—
550C23×C4—41no—
551C23×C4—41no—
552C23×C4—41no—
553C23×C4—41no—
554C23×C4C2×C4×C13114yes—
555C23×C4C23×C13111yescharacteristic
556C23×C4C23×C13111yescharacteristic
557C23×C4C23×C13111yescharacteristic
558C23×C4C23×C13111yescharacteristic
559C23×C4C23×C13111yescharacteristic
560C23×C4C23×C13111yescharacteristic
561C23×C4C23×C13111yescharacteristic
562C23×C4C23×C13111yescharacteristic
563C23×C4C23×C13111yescharacteristic
564C23×C4C23×C13111yescharacteristic
565C23×C4C23×C13111yescharacteristic
566C23×C4C23×C13111yescharacteristic
567C23×C4C23×C13111yescharacteristic
568C23×C4C23×C13111yescharacteristic
569C2×C4⋊C4—22no—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—41no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4—41no—
576C2×C4⋊C4—41no—
577C2×C4⋊C4—41no—
578C2×C4⋊C4—41no—
579C2×C4⋊C4C2×C4×C13114yes—
580C2×C4⋊C4C2×C4×C13114yes—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—41no—
589C2×C22⋊C4—41no—
590C2×C22⋊C4—41no—
591C2×C22⋊C4—41no—
592C2×C22⋊C4—41no—
593C2×C22⋊C4—41no—
594C2×C22⋊C4—41no—
595C2×C22⋊C4—41no—
596C2×C22⋊C4C2×C4×C13114yes—
597C2×C22⋊C4C2×C4×C13114yes—
598C2×C22⋊C4Q8×C13114yes—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42—22no—
602C2×C42—41no—
603C2×C42—41no—
604C2×C42—41no—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—41no—
609#95—41no—
610#95—41no—
611#95—41no—
612#95—41no—
613#95—41no—
614#95—41no—
615#95—41no—
616#95—41no—
617#95—41no—
618#95—41no—
619#95—41no—
620#95—41no—
621#95—41no—
622#95—41no—
623#95—41no—
624#95—41no—
625#95C2×C4×C13114yes—
626#95C2×C4×C13114yes—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24C22×C4×C13112yes—
640C24C2×Q8×C13112yes—
641C24#41×C13112yes—
642C24C24×C13111yescharacteristic
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4C22×C4×C13112yes—
737C22×C4C22×C4×C13112yes—
738C22×C4C22×C4×C13112yes—
739C22×C4C22×C4×C13112yes—
740C22×C4C22×C4×C13112yes—
741C22×C4C22×C4×C13112yes—
742C22×C4C2×Q8×C13112yes—
743C22×C4C2×Q8×C13112yes—
744C22×C4#41×C13112yes—
745C22×C4#41×C13112yes—
746C22×C4#41×C13112yes—
747C22×C4#41×C13112yes—
748C4⋊C4—44no—
749C4⋊C4—44no—
750C4⋊C4—44no—
751C4⋊C4—44no—
752C22⋊C4—28no—
753C22⋊C4—44no—
754C22⋊C4—44no—
755C22⋊C4—44no—
756C22⋊C4—44no—
757C22⋊C4—44no—
758C42—44no—
759C42—44no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23C4×Q8×C13114yes—
795C23C23×C4×C13111yescharacteristic
796C23C22×Q8×C13111yescharacteristic
797C23C2×#41×C13111yescharacteristic
798C23C2×#41×C13111yescharacteristic
799C23C2×#41×C13111yescharacteristic
800C23C2×#41×C13111yescharacteristic
801C23C2×#41×C13111yescharacteristic
802C23H(5,𝔽2)×C13111yescharacteristic
803C23H(5,𝔽2)×C13111yescharacteristic
804C23H(5,𝔽2)×C13111yescharacteristic
805C23H(5,𝔽2)×C13111yescharacteristic
806C23H(5,𝔽2)×C13111yescharacteristic
807C23H(5,𝔽2)×C13111yescharacteristic
808C23H(5,𝔽2)×C13111yescharacteristic
809C232−1+4×C13111yescharacteristic
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—416no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4#117×C13114yes—
909C22—24no—
910C22—24no—
911C22—24no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22C2×#117×C13111yescharacteristic
925C22C2×C4×Q8×C13111yescharacteristic
926C22C4×#41×C13111yescharacteristic
927C22#518×C13111yescharacteristic
928C22#518×C13111yescharacteristic
929C22#518×C13111yescharacteristic
930C22#520×C13111yescharacteristic
931C22#538×C13111yescharacteristic
932C22#538×C13111yescharacteristic
933C22#539×C13111yescharacteristic
934C22#539×C13111yescharacteristic
935C22#540×C13111yescharacteristic
936C22#540×C13111yescharacteristic
937C22#540×C13111yescharacteristic
938C22#542×C13111yescharacteristic
939C22#542×C13111yescharacteristic
940C22#542×C13111yescharacteristic
941C22#543×C13111yescharacteristic
942C22#544×C13111yescharacteristic
943C22#551×C13111yescharacteristic
944C22#551×C13111yescharacteristic
945C22#551×C13111yescharacteristic
946C22#551×C13111yescharacteristic
947C22#553×C13111yescharacteristic
948C22#553×C13111yescharacteristic
949C22#553×C13111yescharacteristic
950C22#553×C13111yescharacteristic
951C22#554×C13111yescharacteristic
952C22#554×C13111yescharacteristic
953C22#554×C13111yescharacteristic
954C22#554×C13111yescharacteristic
955C22#560×C13111yescharacteristic
956C22#560×C13111yescharacteristic
957C22#560×C13111yescharacteristic
958C22H(3,𝔽4)×C13111yescharacteristic
959C4—24no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—42no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—81no—
970C4—81no—
971C4—81no—
972C4—81no—
973C2—44no—
974C2#2319×C13111yescharacteristic
975C2#2329×C13111yescharacteristic
976C2#2335×C13111yescharacteristic
977C2#2345×C13111yescharacteristic
978C2#2353×C13111yescharacteristic
979C2#2368×C13111yescharacteristic
980C2#2375×C13111yescharacteristic
981C2#2746×C13111yescharacteristic
982C2#2748×C13111yescharacteristic
983C2#2749×C13111yescharacteristic
984C2#2753×C13111yescharacteristic
985C2#2757×C13111yescharacteristic
986C2#2763×C13111yescharacteristic
987C2#2780×C13111yescharacteristic
988C2#2790×C13111yescharacteristic
subgroupG/H
center, socleC24×C131C24
commutatorC23C23×C4×C131
Frattini, cosocleC24C24×C131
prime radicalC25×C131C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1445×C131C2semidirect
3. #1443×C131C2semidirect
4. #1441×C131C2semidirect
5. #1441×C131C2semidirect
10. #1436×C131C2semidirect
11. C4⋊#95×C131C2semidirect
12. #1434×C131C2semidirect
13. #1434×C131C2semidirect
29. #385×C131C4semidirect
494. #14456C131direct (N × H)
495. C131#14456direct (N × H)
497. #1445C2×C131semidirect
498. #1443C2×C131semidirect
499. #1441C2×C131semidirect
500. #1441C2×C131semidirect
505. #1436C2×C131semidirect
506. C4⋊#95C2×C131semidirect
507. #1434C2×C131semidirect
508. #1434C2×C131semidirect
524. #385C4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#385×C1312
#1445×C1312
#1443×C1312
#1441×C1312
#1439×C1312
#1437×C1312
#1436×C1312
C4⋊#95×C1312
#1434×C1312
C22⋊#95×C1312
#14456131