Finite Group Databasebeta

← C131×#10401 #45696285

Subgroups — C131×#10401 #45696285

Order 33536.

570 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2627×C131C211yesmaximal, characteristic
2#1872×C131C211yesmaximal, characteristic
3#1853×C131C211yesmaximal, characteristic
4C2×#328×C131C211yesmaximal, characteristic
5C2×#324×C131C211yesmaximal, characteristic
6#1441×C131C211yesmaximal, characteristic
7#1294×C131C211yesmaximal, characteristic
8C2×C22⋊Q8×C131C2211yescharacteristic
9C22×C4⋊C4×C131C2211yescharacteristic
10C22×C4⋊C4×C131C2211yescharacteristic
11C2×#106×C131—21no—
12C2×#103×C131—21no—
13C2×C22⋊C8×C131C2211yescharacteristic
14C2×C22⋊C8×C131C2211yescharacteristic
15#400×C131—21no—
16#398×C131—21no—
17#398×C131—21no—
18#395×C131—21no—
19#385×C131—21no—
20#381×C131—21no—
21#380×C131C2211yescharacteristic
22C2×#95×C131—21no—
23C2×#95×C131—21no—
24C2×#95×C131C2211yescharacteristic
25#340×C131—21no—
26#340×C131—21no—
27#328×C131—22no—
28#324×C131—22no—
29C22×Q8×C131D411yescharacteristic
30C23×C4×C131—21no—
31C23×C4×C131—21no—
32C23×C4×C131D411yescharacteristic
33C23×C4×C131D411yescharacteristic
34C23×C4×C131C2311yescharacteristic
35C22×C8×C131—21no—
36C22×C8×C131—21no—
37C22⋊Q8×C131—21no—
38C22⋊Q8×C131—21no—
39C22⋊Q8×C131—21no—
40C22⋊Q8×C131—21no—
41C2×C4⋊C4×C131—21no—
42C2×C4⋊C4×C131—21no—
43C2×C4⋊C4×C131—21no—
44C2×C4⋊C4×C131—21no—
45C2×C4⋊C4×C131—21no—
46C2×C4⋊C4×C131—21no—
47C2×C4⋊C4×C131—21no—
48C2×C4⋊C4×C131—21no—
49C2×C4⋊C4×C131—21no—
50C2×C4⋊C4×C131—21no—
51C2×C4⋊C4×C131—21no—
52C2×C4⋊C4×C131—42no—
53C2×C4⋊C4×C131D411yescharacteristic
54C2×C4⋊C4×C131D411yescharacteristic
55C2×C4⋊C4×C131D411yescharacteristic
56C2×C22⋊C4×C131—21no—
57C2×C22⋊C4×C131—21no—
58#106×C131—42no—
59#103×C131—42no—
60C22⋊C8×C131—21no—
61C22⋊C8×C131—21no—
62C22⋊C8×C131—21no—
63C22⋊C8×C131D412yes—
64#95×C131—21no—
65#95×C131—21no—
66#95×C131—21no—
67#95×C131—21no—
68#95×C131—21no—
69#95×C131—21no—
70#95×C131—21no—
71#95×C131—21no—
72#95×C131—21no—
73#95×C131—42no—
74#95×C131—42no—
75C24×C131C2×D411yescharacteristic
76C2×Q8×C131—21no—
77C2×Q8×C131—21no—
78C2×Q8×C131—41no—
79C2×Q8×C131—41no—
80C22×C4×C131—21no—
81C22×C4×C131—21no—
82C22×C4×C131—21no—
83C22×C4×C131—21no—
84C22×C4×C131—21no—
85C22×C4×C131—21no—
86C22×C4×C131—22no—
87C22×C4×C131—22no—
88C22×C4×C131—21no—
89C22×C4×C131—21no—
90C22×C4×C131—21no—
91C22×C4×C131—21no—
92C22×C4×C131—21no—
93C22×C4×C131—21no—
94C22×C4×C131—21no—
95C22×C4×C131—41no—
96C22×C4×C131—41no—
97C22×C4×C131—41no—
98C22×C4×C131—41no—
99C22×C4×C131—41no—
100C22×C4×C131—41no—
101C22×C4×C131—41no—
102C22×C4×C131—41no—
103C22×C4×C131—41no—
104C22×C4×C131—41no—
105C22×C4×C131—41no—
106C22×C4×C131—41no—
107C22×C4×C131—41no—
108C22×C4×C131—41no—
109C22×C4×C131—41no—
110C22×C4×C131—41no—
111C22×C4×C131SD1612yes—
112C22×C4×C131C2×D411yescharacteristic
113C22×C4×C131C2×D411yescharacteristic
114C22×C4×C131C2×D411yescharacteristic
115C22×C4×C131#4111yescharacteristic
116C22×C4×C131#4111yescharacteristic
117C22×C4×C131#4111yescharacteristic
118C2×C8×C131—22no—
119C2×C8×C131—41no—
120C2×C8×C131—41no—
121C2×C8×C131—41no—
122C2×C8×C131—41no—
123C2×C8×C131—41no—
124C4⋊C4×C131—22no—
125C4⋊C4×C131—22no—
126C4⋊C4×C131—21no—
127C4⋊C4×C131—21no—
128C4⋊C4×C131—41no—
129C4⋊C4×C131—41no—
130C4⋊C4×C131—41no—
131C4⋊C4×C131—41no—
132C4⋊C4×C131—41no—
133C4⋊C4×C131—41no—
134C4⋊C4×C131—41no—
135C4⋊C4×C131—41no—
136C4⋊C4×C131—41no—
137C4⋊C4×C131—41no—
138C4⋊C4×C131—81no—
139C4⋊C4×C131—81no—
140C22⋊C4×C131—41no—
141C22⋊C4×C131—41no—
142C22⋊C4×C131—41no—
143C22⋊C4×C131—41no—
144C23×C131—21no—
145C23×C131—21no—
146C23×C131—21no—
147C23×C131—21no—
148C23×C131#12011yescharacteristic
149C23×C131#12111yescharacteristic
150C23×C131#12311yescharacteristic
151C23×C131C2×SD1611yescharacteristic
152C23×C131#13511yescharacteristic
153C23×C131#13711yescharacteristic
154C23×C131#13711yescharacteristic
155Q8×C131—42no—
156Q8×C131—81no—
157C2×C4×C131—21no—
158C2×C4×C131—21no—
159C2×C4×C131—21no—
160C2×C4×C131—21no—
161C2×C4×C131—22no—
162C2×C4×C131—22no—
163C2×C4×C131—22no—
164C2×C4×C131—41no—
165C2×C4×C131—41no—
166C2×C4×C131—41no—
167C2×C4×C131—41no—
168C2×C4×C131—41no—
169C2×C4×C131—41no—
170C2×C4×C131—41no—
171C2×C4×C131—41no—
172C2×C4×C131—42no—
173C2×C4×C131—42no—
174C2×C4×C131—42no—
175C2×C4×C131—42no—
176C2×C4×C131—42no—
177C2×C4×C131—42no—
178C2×C4×C131—41no—
179C2×C4×C131—41no—
180C2×C4×C131—41no—
181C2×C4×C131—41no—
182C2×C4×C131—41no—
183C2×C4×C131—41no—
184C2×C4×C131—41no—
185C2×C4×C131—41no—
186C2×C4×C131—41no—
187C2×C4×C131—42no—
188C2×C4×C131—41no—
189C2×C4×C131—41no—
190C2×C4×C131—41no—
191C2×C4×C131—41no—
192C2×C4×C131—41no—
193C2×C4×C131—41no—
194C2×C4×C131—81no—
195C2×C4×C131—81no—
196C2×C4×C131—81no—
197C2×C4×C131—81no—
198C2×C4×C131—81no—
199C2×C4×C131—81no—
200C2×C4×C131—81no—
201C2×C4×C131—81no—
202C2×C4×C131—81no—
203C2×C4×C131#12111yescharacteristic
204C2×C4×C131#12111yescharacteristic
205C2×C4×C131#12311yescharacteristic
206C2×C4×C131#12411yescharacteristic
207C8×C131—42no—
208C8×C131—81no—
209C22×C131—21no—
210C22×C131—21no—
211C22×C131—21no—
212C22×C131—21no—
213C22×C131—21no—
214C22×C131—21no—
215C22×C131—21no—
216C22×C131—21no—
217C22×C131—21no—
218C22×C131—21no—
219C22×C131—21no—
220C22×C131—21no—
221C22×C131#39411yescharacteristic
222C22×C131#44811yescharacteristic
223C22×C131#45211yescharacteristic
224C22×C131#45411yescharacteristic
225C22×C131#45611yescharacteristic
226C22×C131B(4,𝔽2)11yescharacteristic
227C22×C131#45811yescharacteristic
228C22×C131#46511yescharacteristic
229C22×C131#47011yescharacteristic
230C22×C131#48311yescharacteristic
231C22×C131#48511yescharacteristic
232C4×C131—21no—
233C4×C131—21no—
234C4×C131—21no—
235C4×C131—21no—
236C4×C131—42no—
237C4×C131—82no—
238C4×C131—82no—
239C4×C131—81no—
240C4×C131—81no—
241C4×C131—81no—
242C4×C131—81no—
243C4×C131—81no—
244C2×C131—21no—
245C2×C131—21no—
246C2×C131—21no—
247C2×C131—21no—
248C2×C131#159911yescharacteristic
249C2×C131#160311yescharacteristic
250C2×C131#161111yescharacteristic
251C2×C131#161511yescharacteristic
252C2×C131#203511yescharacteristic
253C2×C131#203811yescharacteristic
254C2×C131#204411yescharacteristic
255#10401C13111yesmaximal, characteristic, direct product factor, Sylow
256C131#1040111yescharacteristic, direct product factor, Sylow
257#2627C2×C13111yescharacteristic
258#1872C2×C13111yescharacteristic
259#1853C2×C13111yescharacteristic
260C2×#328C2×C13111yescharacteristic
261C2×#324C2×C13111yescharacteristic
262#1441C2×C13111yescharacteristic
263#1294C2×C13111yescharacteristic
264C2×C22⋊Q8C22×C13111yescharacteristic
265C22×C4⋊C4C22×C13111yescharacteristic
266C22×C4⋊C4C22×C13111yescharacteristic
267C2×#106—21no—
268C2×#103—21no—
269C2×C22⋊C8C22×C13111yescharacteristic
270C2×C22⋊C8C22×C13111yescharacteristic
271#400—21no—
272#398—21no—
273#398—21no—
274#395—21no—
275#385—21no—
276#381—21no—
277#380C22×C13111yescharacteristic
278C2×#95—21no—
279C2×#95—21no—
280C2×#95C22×C13111yescharacteristic
281#340—21no—
282#340—21no—
283#328—22no—
284#324—22no—
285C22×Q8D4×C13111yescharacteristic
286C23×C4—21no—
287C23×C4—21no—
288C23×C4D4×C13111yescharacteristic
289C23×C4D4×C13111yescharacteristic
290C23×C4C23×C13111yescharacteristic
291C22×C8—21no—
292C22×C8—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4D4×C13111yescharacteristic
310C2×C4⋊C4D4×C13111yescharacteristic
311C2×C4⋊C4D4×C13111yescharacteristic
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314#106—42no—
315#103—42no—
316C22⋊C8—21no—
317C22⋊C8—21no—
318C22⋊C8—21no—
319C22⋊C8D4×C13112yes—
320#95—21no—
321#95—21no—
322#95—21no—
323#95—21no—
324#95—21no—
325#95—21no—
326#95—21no—
327#95—21no—
328#95—21no—
329#95—42no—
330#95—42no—
331C24C2×D4×C13111yescharacteristic
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—41no—
335C2×Q8—41no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4SD16×C13112yes—
368C22×C4C2×D4×C13111yescharacteristic
369C22×C4C2×D4×C13111yescharacteristic
370C22×C4C2×D4×C13111yescharacteristic
371C22×C4#41×C13111yescharacteristic
372C22×C4#41×C13111yescharacteristic
373C22×C4#41×C13111yescharacteristic
374C2×C8—22no—
375C2×C8—41no—
376C2×C8—41no—
377C2×C8—41no—
378C2×C8—41no—
379C2×C8—41no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4—81no—
395C4⋊C4—81no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23#120×C13111yescharacteristic
405C23#121×C13111yescharacteristic
406C23#123×C13111yescharacteristic
407C23C2×SD16×C13111yescharacteristic
408C23#135×C13111yescharacteristic
409C23#137×C13111yescharacteristic
410C23#137×C13111yescharacteristic
411Q8—42no—
412Q8—81no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—81no—
451C2×C4—81no—
452C2×C4—81no—
453C2×C4—81no—
454C2×C4—81no—
455C2×C4—81no—
456C2×C4—81no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4#121×C13111yescharacteristic
460C2×C4#121×C13111yescharacteristic
461C2×C4#123×C13111yescharacteristic
462C2×C4#124×C13111yescharacteristic
463C8—42no—
464C8—81no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22#394×C13111yescharacteristic
478C22#448×C13111yescharacteristic
479C22#452×C13111yescharacteristic
480C22#454×C13111yescharacteristic
481C22#456×C13111yescharacteristic
482C22B(4,𝔽2)×C13111yescharacteristic
483C22#458×C13111yescharacteristic
484C22#465×C13111yescharacteristic
485C22#470×C13111yescharacteristic
486C22#483×C13111yescharacteristic
487C22#485×C13111yescharacteristic
488C4—21no—
489C4—21no—
490C4—21no—
491C4—21no—
492C4—42no—
493C4—82no—
494C4—81no—
495C4—81no—
496C4—81no—
497C4—82no—
498C4—81no—
499C4—81no—
500C2—21no—
501C2—21no—
502C2—21no—
503C2—21no—
504C2#1599×C13111yescharacteristic
505C2#1603×C13111yescharacteristic
506C2#1611×C13111yescharacteristic
507C2#1615×C13111yescharacteristic
508C2#2035×C13111yescharacteristic
509C2#2038×C13111yescharacteristic
510C2#2044×C13111yescharacteristic
subgroupG/H
center, socleC23×C131#120
commutator, Frattini, cosocleC23×C4C23×C131
prime radicalC24×C131C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
255. #10401C131direct (N × H)
256. C131#10401direct (N × H)

Maximal subgroups

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

subgroupindex
#2627×C1312
#1872×C1312
#1853×C1312
C2×#328×C1312
C2×#324×C1312
#1441×C1312
#1294×C1312
#10401131