Finite Group Databasebeta

← C131×#34504 #45720388

Subgroups — C131×#34504 #45720388

Order 33536.

2156 conjugacy classes of subgroups.

The subgroup lattice has 1486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#551×C131C211yesmaximal, characteristic
2#2383×C131C211yesmaximal, characteristic, complemented
3#2378×C131C211yesmaximal, characteristic, complemented
4#2376×C131C211yesmaximal, characteristic, complemented
5#2375×C131C211yesmaximal, characteristic
6#2374×C131C211yesmaximal, characteristic, complemented
7#2373×C131C211yesmaximal, characteristic, complemented
8#2367×C131C211yesmaximal, characteristic, complemented
9#2362×C131C211yesmaximal, characteristic, complemented
10#2359×C131C211yesmaximal, characteristic, complemented
11#2354×C131C211yesmaximal, characteristic, complemented
12#2353×C131C211yesmaximal, characteristic, complemented
13#2347×C131C211yesmaximal, characteristic, complemented
14#2347×C131C211yesmaximal, characteristic, complemented
15#2342×C131C211yesmaximal, characteristic, complemented
16#2342×C131C211yesmaximal, characteristic, complemented
17#2337×C131C211yesmaximal, characteristic, complemented
18#2335×C131C211yesmaximal, characteristic, complemented
19#2335×C131C211yesmaximal, characteristic, complemented
20#2335×C131C211yesmaximal, characteristic, complemented
21#2334×C131C211yesmaximal, characteristic, complemented
22#2332×C131C211yesmaximal, characteristic, complemented
23#2323×C131C211yesmaximal, characteristic, complemented
24#2321×C131C211yesmaximal, characteristic
25#2318×C131C211yesmaximal, characteristic, complemented
26#2314×C131C211yesmaximal, characteristic, complemented
27#2312×C131C211yesmaximal, characteristic, complemented
28#2312×C131C211yesmaximal, characteristic, complemented
29C4×#126×C131C211yesmaximal, characteristic, complemented
30#2298×C131C211yesmaximal, characteristic, complemented
31#2293×C131C211yesmaximal, characteristic, complemented
32#551×C131C4116yescomplemented
33C2×#126×C131C2211yescharacteristic
34C2×#126×C131C2211yescharacteristic
35C2×#124×C131C2211yescharacteristic
36C2×#123×C131C2211yescharacteristic
37C2×#123×C131C2211yescharacteristic
38C2×#123×C131C2211yescharacteristic
39C2×C22⋊Q8×C131C2211yescharacteristic
40C2×C22⋊Q8×C131C2211yescharacteristic
41C2×#120×C131C2211yescharacteristic
42C2×C4×Q8×C131C2211yescharacteristic, complemented
43C2×C4×D4×C131C2211yescharacteristic
44C2×C4×D4×C131C2211yescharacteristic
45C2×C4×D4×C131C2211yescharacteristic
46C2×#117×C131C2211yescharacteristic
47C2×#117×C131C2211yescharacteristic
48C2×#117×C131C2211yescharacteristic
49C2×#117×C131C2211yescharacteristic
50C2×#117×C131C2211yescharacteristic, complemented
51C22×C22⋊C4×C131C2211yescharacteristic
52C22×C22⋊C4×C131C2211yescharacteristic
53C22×C22⋊C4×C131C2211yescharacteristic
54#391×C131C2211yescharacteristic, complemented
55#391×C131C2211yescharacteristic, complemented
56#391×C131C2211yescharacteristic, complemented
57#390×C131C2211yescharacteristic
58#390×C131C2211yescharacteristic
59#390×C131C2211yescharacteristic
60#390×C131C2211yescharacteristic
61#390×C131C2211yescharacteristic
62#389×C131C2211yescharacteristic, complemented
63#389×C131C2211yescharacteristic, complemented
64#389×C131C2211yescharacteristic, complemented
65#389×C131C2211yescharacteristic, complemented
66#389×C131C2211yescharacteristic, complemented
67#389×C131C2211yescharacteristic, complemented
68#389×C131C2211yescharacteristic, complemented
69#389×C131C2211yescharacteristic, complemented
70#388×C131C2211yescharacteristic
71#388×C131C2211yescharacteristic
72#388×C131C2211yescharacteristic
73#388×C131C2211yescharacteristic
74#388×C131C2211yescharacteristic
75#388×C131C2211yescharacteristic
76#388×C131C2211yescharacteristic
77#388×C131C2211yescharacteristic
78#388×C131C2211yescharacteristic
79#388×C131C2211yescharacteristic
80#388×C131C2211yescharacteristic
81#388×C131C2211yescharacteristic
82#388×C131C2211yescharacteristic
83#388×C131C2211yescharacteristic
84#388×C131C2211yescharacteristic
85#388×C131C2211yescharacteristic
86#388×C131C2211yescharacteristic
87#388×C131C2211yescharacteristic
88#388×C131C2211yescharacteristic
89#388×C131C2211yescharacteristic
90#388×C131C2211yescharacteristic
91#388×C131C2211yescharacteristic
92#388×C131C2211yescharacteristic
93#388×C131C2211yescharacteristic
94#388×C131C2211yescharacteristic
95#388×C131C2211yescharacteristic
96#388×C131C2211yescharacteristic
97#388×C131C2211yescharacteristic
98#388×C131C2211yescharacteristic
99#388×C131C2211yescharacteristic
100#388×C131C2211yescharacteristic
101#388×C131C2211yescharacteristic
102#388×C131C2211yescharacteristic
103#388×C131C2211yescharacteristic
104#388×C131C2211yescharacteristic, complemented
105#388×C131C2211yescharacteristic, complemented
106#388×C131C2211yescharacteristic, complemented
107#388×C131C2211yescharacteristic, complemented
108#388×C131C2211yescharacteristic, complemented
109#388×C131C2211yescharacteristic, complemented
110#387×C131C2211yescharacteristic, complemented
111#387×C131C2211yescharacteristic, complemented
112#387×C131C2211yescharacteristic, complemented
113#387×C131C2211yescharacteristic, complemented
114#387×C131C2211yescharacteristic, complemented
115#387×C131C2211yescharacteristic, complemented
116#387×C131C2211yescharacteristic, complemented
117#387×C131C2211yescharacteristic, complemented
118#387×C131C2211yescharacteristic, complemented
119#387×C131C2211yescharacteristic, complemented
120#387×C131C2211yescharacteristic, complemented
121#387×C131C2211yescharacteristic, complemented
122#387×C131C2211yescharacteristic, complemented
123#387×C131C2211yescharacteristic, complemented
124#387×C131C2211yescharacteristic, complemented
125#387×C131C2211yescharacteristic, complemented
126#386×C131C2211yescharacteristic
127#386×C131C2211yescharacteristic
128#386×C131C2211yescharacteristic
129#386×C131C2211yescharacteristic
130#386×C131C2211yescharacteristic
131#386×C131C2211yescharacteristic
132#385×C131C2211yescharacteristic
133#385×C131C2211yescharacteristic
134#385×C131C2211yescharacteristic
135#385×C131C2211yescharacteristic
136#385×C131C2211yescharacteristic
137#385×C131C2211yescharacteristic, complemented
138#385×C131C2211yescharacteristic, complemented
139#385×C131C2211yescharacteristic, complemented
140#384×C131C2211yescharacteristic, complemented
141#383×C131C2211yescharacteristic, complemented
142#383×C131C2211yescharacteristic, complemented
143#383×C131C2211yescharacteristic, complemented
144#382×C131C2211yescharacteristic, complemented
145#381×C131C2211yescharacteristic
146#381×C131C2211yescharacteristic
147#380×C131C2211yescharacteristic
148#380×C131C2211yescharacteristic
149#380×C131C2211yescharacteristic
150#380×C131C2211yescharacteristic
151#380×C131C2211yescharacteristic
152#380×C131C2211yescharacteristic
153#380×C131C2211yescharacteristic, complemented
154#379×C131C2211yescharacteristic
155#379×C131C2211yescharacteristic
156#379×C131C2211yescharacteristic
157C4×C4⋊C4×C131C2211yescharacteristic, complemented
158C4×C4⋊C4×C131C2211yescharacteristic, complemented
159C4×C4⋊C4×C131C2211yescharacteristic, complemented
160C4×C4⋊C4×C131C2211yescharacteristic, complemented
161C4×C4⋊C4×C131C2211yescharacteristic, complemented
162C4×C4⋊C4×C131C2211yescharacteristic, complemented
163C4×C4⋊C4×C131C2211yescharacteristic, complemented
164C4×C4⋊C4×C131C2211yescharacteristic, complemented
165C4×C4⋊C4×C131C2211yescharacteristic, complemented
166C4×C4⋊C4×C131C2211yescharacteristic, complemented
167C4×C4⋊C4×C131C2211yescharacteristic, complemented
168C4×C4⋊C4×C131C2211yescharacteristic, complemented
169C4×C4⋊C4×C131C2211yescharacteristic, complemented
170C4×C22⋊C4×C131C2211yescharacteristic
171C4×C22⋊C4×C131C2211yescharacteristic
172C4×C22⋊C4×C131C2211yescharacteristic
173C4×C22⋊C4×C131C2211yescharacteristic
174C4×C22⋊C4×C131C2211yescharacteristic
175C4×C22⋊C4×C131C2211yescharacteristic
176C4×C22⋊C4×C131C2211yescharacteristic
177C4×C22⋊C4×C131C2211yescharacteristic
178C4×C22⋊C4×C131C2211yescharacteristic
179C4×C22⋊C4×C131C2211yescharacteristic
180C4×C22⋊C4×C131C2211yescharacteristic
181C4×C22⋊C4×C131C2211yescharacteristic, complemented
182C4×C22⋊C4×C131C2211yescharacteristic, complemented
183C4×C22⋊C4×C131C2211yescharacteristic, complemented
184C4×C22⋊C4×C131C2211yescharacteristic, complemented
185#376×C131C2211yescharacteristic, complemented
186C2×#95×C131C2211yescharacteristic, complemented
187C43×C131C2211yescharacteristic, complemented
188C25×C131C2311yescharacteristic
189C22×Q8×C131C2311yescharacteristic
190C22×D4×C131C2311yescharacteristic
191C22×D4×C131C2311yescharacteristic
192C22×D4×C131C2311yescharacteristic
193C23×C4×C131C2311yescharacteristic
194C23×C4×C131C2311yescharacteristic
195C23×C4×C131C2311yescharacteristic
196C23×C4×C131C2311yescharacteristic
197C23×C4×C131C2311yescharacteristic
198C23×C4×C131C2311yescharacteristic
199C23×C4×C131C2311yescharacteristic
200C23×C4×C131C2311yescharacteristic
201C23×C4×C131C2311yescharacteristic
202#126×C131C2×C418yescomplemented
203#126×C131C2×C418yescomplemented
204#124×C131C2×C418yes—
205#123×C131C2×C418yes—
206#123×C131C2×C418yescomplemented
207#123×C131C2×C418yescomplemented
208C22⋊Q8×C131C2×C418yescomplemented
209C22⋊Q8×C131C2×C418yescomplemented
210#120×C131C2×C418yes—
211C4×Q8×C131—42no—
212C4×D4×C131—42no—
213C4×D4×C131C2×C418yescomplemented
214C4×D4×C131C2×C418yescomplemented
215#117×C131—42no—
216#117×C131—42no—
217#117×C131—42no—
218#117×C131C2×C418yescomplemented
219#117×C131C2×C418yescomplemented
220C2×C4⋊C4×C131C2311yescharacteristic
221C2×C4⋊C4×C131C2311yescharacteristic
222C2×C4⋊C4×C131C2311yescharacteristic
223C2×C4⋊C4×C131C2311yescharacteristic
224C2×C4⋊C4×C131C2311yescharacteristic
225C2×C4⋊C4×C131C2311yescharacteristic
226C2×C4⋊C4×C131C2311yescharacteristic
227C2×C4⋊C4×C131C2311yescharacteristic
228C2×C4⋊C4×C131C2311yescharacteristic
229C2×C4⋊C4×C131C2311yescharacteristic
230C2×C4⋊C4×C131C2311yescharacteristic
231C2×C4⋊C4×C131C2311yescharacteristic
232C2×C4⋊C4×C131C2311yescharacteristic
233C2×C4⋊C4×C131C2311yescharacteristic
234C2×C4⋊C4×C131C2311yescharacteristic
235C2×C4⋊C4×C131C2311yescharacteristic
236C2×C4⋊C4×C131C2311yescharacteristic
237C2×C4⋊C4×C131C2311yescharacteristic
238C2×C4⋊C4×C131C2311yescharacteristic
239C2×C4⋊C4×C131C2311yescharacteristic
240C2×C4⋊C4×C131C2311yescharacteristic
241C2×C4⋊C4×C131C2311yescharacteristic
242C2×C4⋊C4×C131C2311yescharacteristic
243C2×C4⋊C4×C131C2311yescharacteristic
244C2×C4⋊C4×C131C2311yescharacteristic
245C2×C4⋊C4×C131C2311yescharacteristic
246C2×C4⋊C4×C131C2311yescharacteristic
247C2×C4⋊C4×C131C2311yescharacteristic
248C2×C4⋊C4×C131C2311yescharacteristic
249C2×C4⋊C4×C131C2311yescharacteristic
250C2×C22⋊C4×C131—42no—
251C2×C22⋊C4×C131C2×C418yescomplemented
252C2×C22⋊C4×C131C2×C418yescomplemented
253C2×C22⋊C4×C131C2311yescharacteristic
254C2×C22⋊C4×C131C2311yescharacteristic
255C2×C22⋊C4×C131C2311yescharacteristic
256C2×C22⋊C4×C131C2311yescharacteristic
257C2×C22⋊C4×C131C2311yescharacteristic
258C2×C22⋊C4×C131C2311yescharacteristic
259C2×C22⋊C4×C131C2311yescharacteristic
260C2×C22⋊C4×C131C2311yescharacteristic
261C2×C22⋊C4×C131C2311yescharacteristic
262C2×C22⋊C4×C131C2311yescharacteristic
263C2×C22⋊C4×C131C2311yescharacteristic
264C2×C22⋊C4×C131C2311yescharacteristic
265C2×C22⋊C4×C131C2311yescharacteristic
266C2×C22⋊C4×C131C2311yescharacteristic
267C2×C22⋊C4×C131C2311yescharacteristic
268C2×C22⋊C4×C131C2311yescharacteristic
269C2×C22⋊C4×C131C2311yescharacteristic
270C2×C22⋊C4×C131C2311yescharacteristic
271C2×C22⋊C4×C131C2311yescharacteristic
272C2×C22⋊C4×C131C2311yescharacteristic
273C2×C22⋊C4×C131C2311yescharacteristic
274C2×C22⋊C4×C131C2311yescharacteristic
275C2×C22⋊C4×C131C2311yescharacteristic
276C2×C22⋊C4×C131C2311yescharacteristic
277C2×C22⋊C4×C131C2311yescharacteristic
278C2×C22⋊C4×C131C2311yescharacteristic
279C2×C22⋊C4×C131C2311yescharacteristic
280C2×C22⋊C4×C131C2311yescharacteristic
281C2×C22⋊C4×C131C2311yescharacteristic
282C2×C22⋊C4×C131C2311yescharacteristic
283C2×C22⋊C4×C131C2311yescharacteristic
284C2×C22⋊C4×C131C2311yescharacteristic
285C2×C22⋊C4×C131C2311yescharacteristic
286C2×C22⋊C4×C131C2311yescharacteristic
287C2×C22⋊C4×C131C2311yescharacteristic
288C2×C22⋊C4×C131C2311yescharacteristic
289C2×C22⋊C4×C131C2311yescharacteristic
290C2×C22⋊C4×C131C2311yescharacteristic
291C2×C22⋊C4×C131C2311yescharacteristic
292C2×C22⋊C4×C131C2311yescharacteristic
293C2×C22⋊C4×C131C2311yescharacteristic
294C2×C22⋊C4×C131C2311yescharacteristic
295C2×C42×C131C2311yescharacteristic
296C2×C42×C131C2311yescharacteristic
297C2×C42×C131C2311yescharacteristic
298C2×C42×C131C2311yescharacteristic
299C2×C42×C131C2311yescharacteristic
300C2×C42×C131C2311yescharacteristic
301C2×C42×C131C2311yescharacteristic
302C2×C42×C131C2311yescharacteristic
303C2×C42×C131C2311yescharacteristic
304C2×C42×C131C2311yescharacteristic
305C2×C42×C131C2311yescharacteristic
306C2×C42×C131C2311yescharacteristic
307C2×C42×C131C2311yescharacteristic
308C2×C42×C131C2311yescharacteristic
309C2×C42×C131C2311yescharacteristic
310C2×C42×C131C2311yescharacteristic
311C2×C42×C131C2311yescharacteristic
312C2×C42×C131C2311yescharacteristic
313C2×C42×C131C2311yescharacteristic
314C2×C42×C131C2311yescharacteristic
315C2×C42×C131C2311yescharacteristic
316C2×C42×C131C2311yescharacteristic
317C2×C42×C131C2311yescharacteristic
318C2×C42×C131C2311yescharacteristic
319C2×C42×C131C2311yescharacteristic
320#95×C131C2311yescharacteristic
321#95×C131C2311yescharacteristic
322#95×C131C2311yescharacteristic
323#95×C131C2311yescharacteristic
324#95×C131C2311yescharacteristic
325#95×C131C2311yescharacteristic
326#95×C131C2311yescharacteristic
327#95×C131C2311yescharacteristic
328#95×C131C2311yescharacteristic
329#95×C131C2311yescharacteristic
330#95×C131C2311yescharacteristic
331#95×C131C2311yescharacteristic
332#95×C131C2311yescharacteristic
333#95×C131C2311yescharacteristic
334#95×C131C2311yescharacteristic
335#95×C131C2311yescharacteristic
336#95×C131C2311yescharacteristic
337#95×C131C2311yescharacteristic
338#95×C131C2311yescharacteristic
339#95×C131C2311yescharacteristic
340#95×C131C2311yescharacteristic
341#95×C131C2311yescharacteristic
342#95×C131C2311yescharacteristic
343#95×C131C2311yescharacteristic
344#95×C131C2311yescharacteristic
345#95×C131C2311yescharacteristic
346#95×C131C2311yescharacteristic
347#95×C131C2311yescharacteristic
348#95×C131C2311yescharacteristic
349#95×C131C2311yescharacteristic
350#95×C131C2311yescharacteristic
351#95×C131C2311yescharacteristic
352#95×C131C2311yescharacteristic
353#95×C131C2311yescharacteristic
354#95×C131C2311yescharacteristic
355#95×C131C2311yescharacteristic
356#95×C131C2311yescharacteristic
357#95×C131C2311yescharacteristic
358#95×C131C2311yescharacteristic
359#95×C131C2311yescharacteristic
360#95×C131C2311yescharacteristic
361#95×C131C2311yescharacteristic
362#95×C131C2311yescharacteristic
363#95×C131C2311yescharacteristic
364C24×C131—41no—
365C24×C131—41no—
366C24×C131—41no—
367C24×C131—41no—
368C24×C131—41no—
369C24×C131—41no—
370C24×C131C22×C414yes—
371C24×C131C2411yescharacteristic
372C24×C131C2411yescharacteristic
373C24×C131C2411yescharacteristic
374C24×C131C2411yescharacteristic
375C2×Q8×C131—41no—
376C2×Q8×C131—41no—
377C2×Q8×C131C22×C414yes—
378C2×D4×C131—41no—
379C2×D4×C131—41no—
380C2×D4×C131—41no—
381C2×D4×C131—41no—
382C2×D4×C131—41no—
383C2×D4×C131—41no—
384C2×D4×C131C22×C414yes—
385C2×D4×C131C22×C414yes—
386C2×D4×C131C22×C414yes—
387C22×C4×C131—22no—
388C22×C4×C131—41no—
389C22×C4×C131—41no—
390C22×C4×C131—41no—
391C22×C4×C131—41no—
392C22×C4×C131—41no—
393C22×C4×C131—41no—
394C22×C4×C131—41no—
395C22×C4×C131—41no—
396C22×C4×C131—41no—
397C22×C4×C131—41no—
398C22×C4×C131—41no—
399C22×C4×C131—41no—
400C22×C4×C131—41no—
401C22×C4×C131—41no—
402C22×C4×C131—41no—
403C22×C4×C131—41no—
404C22×C4×C131—41no—
405C22×C4×C131—41no—
406C22×C4×C131—41no—
407C22×C4×C131—41no—
408C22×C4×C131—41no—
409C22×C4×C131C22×C414yes—
410C22×C4×C131C22×C414yes—
411C22×C4×C131C22×C414yes—
412C22×C4×C131C22×C414yes—
413C22×C4×C131C22×C414yes—
414C22×C4×C131C2411yescharacteristic
415C22×C4×C131C2411yescharacteristic
416C22×C4×C131C2411yescharacteristic
417C22×C4×C131C2411yescharacteristic
418C22×C4×C131C2411yescharacteristic
419C22×C4×C131C2411yescharacteristic
420C22×C4×C131C2411yescharacteristic
421C22×C4×C131C2411yescharacteristic
422C22×C4×C131C2411yescharacteristic
423C22×C4×C131C2411yescharacteristic
424C22×C4×C131C2411yescharacteristic
425C22×C4×C131C2411yescharacteristic
426C22×C4×C131C2411yescharacteristic
427C22×C4×C131C2411yescharacteristic
428C22×C4×C131C2411yescharacteristic
429C22×C4×C131C2411yescharacteristic
430C22×C4×C131C2411yescharacteristic
431C22×C4×C131C2411yescharacteristic
432C22×C4×C131C2411yescharacteristic
433C22×C4×C131C2411yescharacteristic
434C22×C4×C131C2411yescharacteristic
435C22×C4×C131C2411yescharacteristic
436C22×C4×C131C2411yescharacteristic
437C22×C4×C131C2411yescharacteristic
438C22×C4×C131C2411yescharacteristic
439C22×C4×C131C2411yescharacteristic
440C22×C4×C131C2411yescharacteristic
441C4⋊C4×C131—22no—
442C4⋊C4×C131—22no—
443C4⋊C4×C131—22no—
444C4⋊C4×C131—41no—
445C4⋊C4×C131—41no—
446C4⋊C4×C131—41no—
447C4⋊C4×C131—41no—
448C4⋊C4×C131—41no—
449C4⋊C4×C131—41no—
450C4⋊C4×C131—41no—
451C4⋊C4×C131—41no—
452C4⋊C4×C131—41no—
453C4⋊C4×C131—41no—
454C4⋊C4×C131—41no—
455C4⋊C4×C131—41no—
456C4⋊C4×C131—41no—
457C4⋊C4×C131—41no—
458C4⋊C4×C131—41no—
459C4⋊C4×C131—41no—
460C4⋊C4×C131—41no—
461C4⋊C4×C131—41no—
462C4⋊C4×C131—41no—
463C4⋊C4×C131C22×C414yes—
464C4⋊C4×C131C22×C414yes—
465C4⋊C4×C131C22×C414yes—
466C4⋊C4×C131C22×C414yes—
467C4⋊C4×C131C22×C414yes—
468C4⋊C4×C131C22×C414yes—
469C4⋊C4×C131C22×C414yes—
470C4⋊C4×C131C22×C414yes—
471C22⋊C4×C131—22no—
472C22⋊C4×C131—22no—
473C22⋊C4×C131—22no—
474C22⋊C4×C131—41no—
475C22⋊C4×C131—41no—
476C22⋊C4×C131—41no—
477C22⋊C4×C131—41no—
478C22⋊C4×C131—41no—
479C22⋊C4×C131—41no—
480C22⋊C4×C131—41no—
481C22⋊C4×C131—41no—
482C22⋊C4×C131—41no—
483C22⋊C4×C131—41no—
484C22⋊C4×C131—41no—
485C22⋊C4×C131—41no—
486C22⋊C4×C131—41no—
487C22⋊C4×C131—41no—
488C22⋊C4×C131—41no—
489C22⋊C4×C131—41no—
490C22⋊C4×C131—41no—
491C22⋊C4×C131—41no—
492C22⋊C4×C131—41no—
493C22⋊C4×C131—41no—
494C22⋊C4×C131—41no—
495C22⋊C4×C131—41no—
496C22⋊C4×C131—41no—
497C22⋊C4×C131—41no—
498C22⋊C4×C131—41no—
499C22⋊C4×C131C22×C414yes—
500C22⋊C4×C131C22×C414yes—
501C22⋊C4×C131C22×C414yes—
502C22⋊C4×C131C22×C414yes—
503C22⋊C4×C131C22×C414yes—
504C22⋊C4×C131C22×C414yes—
505C22⋊C4×C131C22×C414yes—
506C22⋊C4×C131C22×C414yes—
507C22⋊C4×C131C22×C414yes—
508C22⋊C4×C131C22×C414yes—
509C22⋊C4×C131C22×C414yes—
510C22⋊C4×C131C22×C414yes—
511C22⋊C4×C131C22×C414yes—
512C22⋊C4×C131C22×C414yes—
513C42×C131—22no—
514C42×C131—22no—
515C42×C131—41no—
516C42×C131—41no—
517C42×C131—41no—
518C42×C131—41no—
519C42×C131—41no—
520C42×C131—41no—
521C42×C131—41no—
522C42×C131—41no—
523C42×C131—41no—
524C42×C131—41no—
525C42×C131—41no—
526C42×C131—41no—
527C42×C131—41no—
528C42×C131—41no—
529C42×C131—41no—
530C42×C131—41no—
531C42×C131—41no—
532C42×C131—41no—
533C42×C131—41no—
534C42×C131—41no—
535C42×C131C22×C414yes—
536C42×C131C22×C414yes—
537C42×C131C22×C414yes—
538C23×C131—21no—
539C23×C131—21no—
540C23×C131—21no—
541C23×C131—21no—
542C23×C131—21no—
543C23×C131—21no—
544C23×C131—21no—
545C23×C131—21no—
546C23×C131—21no—
547C23×C131—21no—
548C23×C131—21no—
549C23×C131—21no—
550C23×C131—21no—
551C23×C131—21no—
552C23×C131—21no—
553C23×C131—21no—
554C23×C131—21no—
555C23×C131—21no—
556C23×C131—21no—
557C23×C131—21no—
558C23×C131—21no—
559C23×C131—21no—
560C23×C131—21no—
561C23×C131—21no—
562C23×C131—44no—
563C23×C131—44no—
564C23×C131—44no—
565C23×C131—82no—
566C23×C131—82no—
567C23×C131—82no—
568C23×C131—82no—
569C23×C131C23×C412yes—
570C23×C131C23×C412yes—
571C23×C131C23×C412yes—
572C23×C131C23×C412yes—
573C23×C131C2511yescharacteristic
574Q8×C131—44no—
575D4×C131—44no—
576D4×C131—44no—
577D4×C131—44no—
578C2×C4×C131—21no—
579C2×C4×C131—21no—
580C2×C4×C131—21no—
581C2×C4×C131—21no—
582C2×C4×C131—21no—
583C2×C4×C131—21no—
584C2×C4×C131—21no—
585C2×C4×C131—21no—
586C2×C4×C131—21no—
587C2×C4×C131—21no—
588C2×C4×C131—21no—
589C2×C4×C131—21no—
590C2×C4×C131—21no—
591C2×C4×C131—21no—
592C2×C4×C131—21no—
593C2×C4×C131—21no—
594C2×C4×C131—21no—
595C2×C4×C131—21no—
596C2×C4×C131—21no—
597C2×C4×C131—21no—
598C2×C4×C131—21no—
599C2×C4×C131—21no—
600C2×C4×C131—21no—
601C2×C4×C131—21no—
602C2×C4×C131—21no—
603C2×C4×C131—21no—
604C2×C4×C131—21no—
605C2×C4×C131—21no—
606C2×C4×C131—21no—
607C2×C4×C131—21no—
608C2×C4×C131—21no—
609C2×C4×C131—21no—
610C2×C4×C131—21no—
611C2×C4×C131—21no—
612C2×C4×C131—21no—
613C2×C4×C131—21no—
614C2×C4×C131—21no—
615C2×C4×C131—21no—
616C2×C4×C131—21no—
617C2×C4×C131—21no—
618C2×C4×C131—21no—
619C2×C4×C131—21no—
620C2×C4×C131—21no—
621C2×C4×C131—21no—
622C2×C4×C131—21no—
623C2×C4×C131—21no—
624C2×C4×C131—21no—
625C2×C4×C131—21no—
626C2×C4×C131—21no—
627C2×C4×C131—21no—
628C2×C4×C131—21no—
629C2×C4×C131—21no—
630C2×C4×C131—21no—
631C2×C4×C131—21no—
632C2×C4×C131—21no—
633C2×C4×C131—21no—
634C2×C4×C131—21no—
635C2×C4×C131—21no—
636C2×C4×C131—21no—
637C2×C4×C131—21no—
638C2×C4×C131—21no—
639C2×C4×C131—21no—
640C2×C4×C131—21no—
641C2×C4×C131—21no—
642C2×C4×C131—21no—
643C2×C4×C131—21no—
644C2×C4×C131—21no—
645C2×C4×C131—21no—
646C2×C4×C131—21no—
647C2×C4×C131—44no—
648C2×C4×C131—44no—
649C2×C4×C131—44no—
650C2×C4×C131—44no—
651C2×C4×C131—44no—
652C2×C4×C131—82no—
653C2×C4×C131—82no—
654C2×C4×C131—82no—
655C2×C4×C131—82no—
656C2×C4×C131C23×C412yes—
657C2×C4×C131C23×C412yes—
658C2×C4×C131C23×C412yes—
659C2×C4×C131C23×C412yes—
660C2×C4×C131C23×C412yes—
661C2×C4×C131C23×C412yes—
662C2×C4×C131C23×C412yes—
663C2×C4×C131C23×C412yes—
664C2×C4×C131C23×C412yes—
665C2×C4×C131C23×C412yes—
666C2×C4×C131C23×C412yes—
667C2×C4×C131H(5,𝔽2)12yes—
668C22×C131—22no—
669C22×C131—22no—
670C22×C131—22no—
671C22×C131—22no—
672C22×C131—22no—
673C22×C131—22no—
674C22×C131—22no—
675C22×C131—22no—
676C22×C131—22no—
677C22×C131—22no—
678C22×C131—22no—
679C22×C131—22no—
680C22×C131—41no—
681C22×C131—41no—
682C22×C131—41no—
683C22×C131—41no—
684C22×C131—41no—
685C22×C131—41no—
686C22×C131—41no—
687C22×C131—41no—
688C22×C131—41no—
689C22×C131—41no—
690C22×C131—41no—
691C22×C131—41no—
692C22×C131—41no—
693C22×C131—41no—
694C22×C131—41no—
695C22×C131—41no—
696C22×C131—88no—
697C22×C131C24×C411yescharacteristic
698C22×C131C2×H(5,𝔽2)11yescharacteristic
699C22×C131#58511yescharacteristic
700C22×C131#58511yescharacteristic
701C22×C131#58511yescharacteristic
702C22×C131#58511yescharacteristic
703C22×C131#58511yescharacteristic
704C4×C131—22no—
705C4×C131—22no—
706C4×C131—22no—
707C4×C131—22no—
708C4×C131—22no—
709C4×C131—22no—
710C4×C131—22no—
711C4×C131—22no—
712C4×C131—22no—
713C4×C131—22no—
714C4×C131—22no—
715C4×C131—22no—
716C4×C131—41no—
717C4×C131—41no—
718C4×C131—41no—
719C4×C131—41no—
720C4×C131—41no—
721C4×C131—41no—
722C4×C131—41no—
723C4×C131—41no—
724C4×C131—41no—
725C4×C131—41no—
726C4×C131—41no—
727C4×C131—41no—
728C4×C131—41no—
729C4×C131—41no—
730C4×C131—41no—
731C2×C131—42no—
732C2×C131—42no—
733C2×C131—42no—
734C2×C131—42no—
735C2×C131#342811yescharacteristic
736C2×C131#342811yescharacteristic
737C2×C131C4×H(5,𝔽2)11yescharacteristic
738C2×C131#356011yescharacteristic
739C2×C131#356211yescharacteristic
740C2×C131#356611yescharacteristic
741C2×C131#356811yescharacteristic
742#34504C13111yesmaximal, characteristic, direct product factor, Sylow
743C131#3450411yescharacteristic, direct product factor, Sylow
744C2×#551C2×C13111yescharacteristic
745#2383C2×C13111yescharacteristic, complemented
746#2378C2×C13111yescharacteristic, complemented
747#2376C2×C13111yescharacteristic, complemented
748#2375C2×C13111yescharacteristic
749#2374C2×C13111yescharacteristic, complemented
750#2373C2×C13111yescharacteristic, complemented
751#2367C2×C13111yescharacteristic, complemented
752#2362C2×C13111yescharacteristic, complemented
753#2359C2×C13111yescharacteristic, complemented
754#2354C2×C13111yescharacteristic, complemented
755#2353C2×C13111yescharacteristic, complemented
756#2347C2×C13111yescharacteristic, complemented
757#2347C2×C13111yescharacteristic, complemented
758#2342C2×C13111yescharacteristic, complemented
759#2342C2×C13111yescharacteristic, complemented
760#2337C2×C13111yescharacteristic, complemented
761#2335C2×C13111yescharacteristic, complemented
762#2335C2×C13111yescharacteristic, complemented
763#2335C2×C13111yescharacteristic, complemented
764#2334C2×C13111yescharacteristic, complemented
765#2332C2×C13111yescharacteristic, complemented
766#2323C2×C13111yescharacteristic, complemented
767#2321C2×C13111yescharacteristic
768#2318C2×C13111yescharacteristic, complemented
769#2314C2×C13111yescharacteristic, complemented
770#2312C2×C13111yescharacteristic, complemented
771#2312C2×C13111yescharacteristic, complemented
772C4×#126C2×C13111yescharacteristic, complemented
773#2298C2×C13111yescharacteristic, complemented
774#2293C2×C13111yescharacteristic, complemented
775#551C4×C131116yescomplemented
776C2×#126C22×C13111yescharacteristic
777C2×#126C22×C13111yescharacteristic
778C2×#124C22×C13111yescharacteristic
779C2×#123C22×C13111yescharacteristic
780C2×#123C22×C13111yescharacteristic
781C2×#123C22×C13111yescharacteristic
782C2×C22⋊Q8C22×C13111yescharacteristic
783C2×C22⋊Q8C22×C13111yescharacteristic
784C2×#120C22×C13111yescharacteristic
785C2×C4×Q8C22×C13111yescharacteristic, complemented
786C2×C4×D4C22×C13111yescharacteristic
787C2×C4×D4C22×C13111yescharacteristic
788C2×C4×D4C22×C13111yescharacteristic
789C2×#117C22×C13111yescharacteristic
790C2×#117C22×C13111yescharacteristic
791C2×#117C22×C13111yescharacteristic
792C2×#117C22×C13111yescharacteristic
793C2×#117C22×C13111yescharacteristic, complemented
794C22×C22⋊C4C22×C13111yescharacteristic
795C22×C22⋊C4C22×C13111yescharacteristic
796C22×C22⋊C4C22×C13111yescharacteristic
797#391C22×C13111yescharacteristic, complemented
798#391C22×C13111yescharacteristic, complemented
799#391C22×C13111yescharacteristic, complemented
800#390C22×C13111yescharacteristic
801#390C22×C13111yescharacteristic
802#390C22×C13111yescharacteristic
803#390C22×C13111yescharacteristic
804#390C22×C13111yescharacteristic
805#389C22×C13111yescharacteristic, complemented
806#389C22×C13111yescharacteristic, complemented
807#389C22×C13111yescharacteristic, complemented
808#389C22×C13111yescharacteristic, complemented
809#389C22×C13111yescharacteristic, complemented
810#389C22×C13111yescharacteristic, complemented
811#389C22×C13111yescharacteristic, complemented
812#389C22×C13111yescharacteristic, complemented
813#388C22×C13111yescharacteristic
814#388C22×C13111yescharacteristic
815#388C22×C13111yescharacteristic
816#388C22×C13111yescharacteristic
817#388C22×C13111yescharacteristic
818#388C22×C13111yescharacteristic
819#388C22×C13111yescharacteristic
820#388C22×C13111yescharacteristic
821#388C22×C13111yescharacteristic
822#388C22×C13111yescharacteristic
823#388C22×C13111yescharacteristic
824#388C22×C13111yescharacteristic
825#388C22×C13111yescharacteristic
826#388C22×C13111yescharacteristic
827#388C22×C13111yescharacteristic
828#388C22×C13111yescharacteristic
829#388C22×C13111yescharacteristic
830#388C22×C13111yescharacteristic
831#388C22×C13111yescharacteristic
832#388C22×C13111yescharacteristic
833#388C22×C13111yescharacteristic
834#388C22×C13111yescharacteristic
835#388C22×C13111yescharacteristic
836#388C22×C13111yescharacteristic
837#388C22×C13111yescharacteristic
838#388C22×C13111yescharacteristic
839#388C22×C13111yescharacteristic
840#388C22×C13111yescharacteristic
841#388C22×C13111yescharacteristic
842#388C22×C13111yescharacteristic
843#388C22×C13111yescharacteristic
844#388C22×C13111yescharacteristic
845#388C22×C13111yescharacteristic
846#388C22×C13111yescharacteristic
847#388C22×C13111yescharacteristic, complemented
848#388C22×C13111yescharacteristic, complemented
849#388C22×C13111yescharacteristic, complemented
850#388C22×C13111yescharacteristic, complemented
851#388C22×C13111yescharacteristic, complemented
852#388C22×C13111yescharacteristic, complemented
853#387C22×C13111yescharacteristic, complemented
854#387C22×C13111yescharacteristic, complemented
855#387C22×C13111yescharacteristic, complemented
856#387C22×C13111yescharacteristic, complemented
857#387C22×C13111yescharacteristic, complemented
858#387C22×C13111yescharacteristic, complemented
859#387C22×C13111yescharacteristic, complemented
860#387C22×C13111yescharacteristic, complemented
861#387C22×C13111yescharacteristic, complemented
862#387C22×C13111yescharacteristic, complemented
863#387C22×C13111yescharacteristic, complemented
864#387C22×C13111yescharacteristic, complemented
865#387C22×C13111yescharacteristic, complemented
866#387C22×C13111yescharacteristic, complemented
867#387C22×C13111yescharacteristic, complemented
868#387C22×C13111yescharacteristic, complemented
869#386C22×C13111yescharacteristic
870#386C22×C13111yescharacteristic
871#386C22×C13111yescharacteristic
872#386C22×C13111yescharacteristic
873#386C22×C13111yescharacteristic
874#386C22×C13111yescharacteristic
875#385C22×C13111yescharacteristic
876#385C22×C13111yescharacteristic
877#385C22×C13111yescharacteristic
878#385C22×C13111yescharacteristic
879#385C22×C13111yescharacteristic
880#385C22×C13111yescharacteristic, complemented
881#385C22×C13111yescharacteristic, complemented
882#385C22×C13111yescharacteristic, complemented
883#384C22×C13111yescharacteristic, complemented
884#383C22×C13111yescharacteristic, complemented
885#383C22×C13111yescharacteristic, complemented
886#383C22×C13111yescharacteristic, complemented
887#382C22×C13111yescharacteristic, complemented
888#381C22×C13111yescharacteristic
889#381C22×C13111yescharacteristic
890#380C22×C13111yescharacteristic
891#380C22×C13111yescharacteristic
892#380C22×C13111yescharacteristic
893#380C22×C13111yescharacteristic
894#380C22×C13111yescharacteristic
895#380C22×C13111yescharacteristic
896#380C22×C13111yescharacteristic, complemented
897#379C22×C13111yescharacteristic
898#379C22×C13111yescharacteristic
899#379C22×C13111yescharacteristic
900C4×C4⋊C4C22×C13111yescharacteristic, complemented
901C4×C4⋊C4C22×C13111yescharacteristic, complemented
902C4×C4⋊C4C22×C13111yescharacteristic, complemented
903C4×C4⋊C4C22×C13111yescharacteristic, complemented
904C4×C4⋊C4C22×C13111yescharacteristic, complemented
905C4×C4⋊C4C22×C13111yescharacteristic, complemented
906C4×C4⋊C4C22×C13111yescharacteristic, complemented
907C4×C4⋊C4C22×C13111yescharacteristic, complemented
908C4×C4⋊C4C22×C13111yescharacteristic, complemented
909C4×C4⋊C4C22×C13111yescharacteristic, complemented
910C4×C4⋊C4C22×C13111yescharacteristic, complemented
911C4×C4⋊C4C22×C13111yescharacteristic, complemented
912C4×C4⋊C4C22×C13111yescharacteristic, complemented
913C4×C22⋊C4C22×C13111yescharacteristic
914C4×C22⋊C4C22×C13111yescharacteristic
915C4×C22⋊C4C22×C13111yescharacteristic
916C4×C22⋊C4C22×C13111yescharacteristic
917C4×C22⋊C4C22×C13111yescharacteristic
918C4×C22⋊C4C22×C13111yescharacteristic
919C4×C22⋊C4C22×C13111yescharacteristic
920C4×C22⋊C4C22×C13111yescharacteristic
921C4×C22⋊C4C22×C13111yescharacteristic
922C4×C22⋊C4C22×C13111yescharacteristic
923C4×C22⋊C4C22×C13111yescharacteristic
924C4×C22⋊C4C22×C13111yescharacteristic, complemented
925C4×C22⋊C4C22×C13111yescharacteristic, complemented
926C4×C22⋊C4C22×C13111yescharacteristic, complemented
927C4×C22⋊C4C22×C13111yescharacteristic, complemented
928#376C22×C13111yescharacteristic, complemented
929C2×#95C22×C13111yescharacteristic, complemented
930C43C22×C13111yescharacteristic, complemented
931C25C23×C13111yescharacteristic
932C22×Q8C23×C13111yescharacteristic
933C22×D4C23×C13111yescharacteristic
934C22×D4C23×C13111yescharacteristic
935C22×D4C23×C13111yescharacteristic
936C23×C4C23×C13111yescharacteristic
937C23×C4C23×C13111yescharacteristic
938C23×C4C23×C13111yescharacteristic
939C23×C4C23×C13111yescharacteristic
940C23×C4C23×C13111yescharacteristic
941C23×C4C23×C13111yescharacteristic
942C23×C4C23×C13111yescharacteristic
943C23×C4C23×C13111yescharacteristic
944C23×C4C23×C13111yescharacteristic
945#126C2×C4×C13118yescomplemented
946#126C2×C4×C13118yescomplemented
947#124C2×C4×C13118yes—
948#123C2×C4×C13118yes—
949#123C2×C4×C13118yescomplemented
950#123C2×C4×C13118yescomplemented
951C22⋊Q8C2×C4×C13118yescomplemented
952C22⋊Q8C2×C4×C13118yescomplemented
953#120C2×C4×C13118yes—
954C4×Q8—42no—
955C4×D4—42no—
956C4×D4C2×C4×C13118yescomplemented
957C4×D4C2×C4×C13118yescomplemented
958#117—42no—
959#117—42no—
960#117—42no—
961#117C2×C4×C13118yescomplemented
962#117C2×C4×C13118yescomplemented
963C2×C4⋊C4C23×C13111yescharacteristic
964C2×C4⋊C4C23×C13111yescharacteristic
965C2×C4⋊C4C23×C13111yescharacteristic
966C2×C4⋊C4C23×C13111yescharacteristic
967C2×C4⋊C4C23×C13111yescharacteristic
968C2×C4⋊C4C23×C13111yescharacteristic
969C2×C4⋊C4C23×C13111yescharacteristic
970C2×C4⋊C4C23×C13111yescharacteristic
971C2×C4⋊C4C23×C13111yescharacteristic
972C2×C4⋊C4C23×C13111yescharacteristic
973C2×C4⋊C4C23×C13111yescharacteristic
974C2×C4⋊C4C23×C13111yescharacteristic
975C2×C4⋊C4C23×C13111yescharacteristic
976C2×C4⋊C4C23×C13111yescharacteristic
977C2×C4⋊C4C23×C13111yescharacteristic
978C2×C4⋊C4C23×C13111yescharacteristic
979C2×C4⋊C4C23×C13111yescharacteristic
980C2×C4⋊C4C23×C13111yescharacteristic
981C2×C4⋊C4C23×C13111yescharacteristic
982C2×C4⋊C4C23×C13111yescharacteristic
983C2×C4⋊C4C23×C13111yescharacteristic
984C2×C4⋊C4C23×C13111yescharacteristic
985C2×C4⋊C4C23×C13111yescharacteristic
986C2×C4⋊C4C23×C13111yescharacteristic
987C2×C4⋊C4C23×C13111yescharacteristic
988C2×C4⋊C4C23×C13111yescharacteristic
989C2×C4⋊C4C23×C13111yescharacteristic
990C2×C4⋊C4C23×C13111yescharacteristic
991C2×C4⋊C4C23×C13111yescharacteristic
992C2×C4⋊C4C23×C13111yescharacteristic
993C2×C22⋊C4—42no—
994C2×C22⋊C4C2×C4×C13118yescomplemented
995C2×C22⋊C4C2×C4×C13118yescomplemented
996C2×C22⋊C4C23×C13111yescharacteristic
997C2×C22⋊C4C23×C13111yescharacteristic
998C2×C22⋊C4C23×C13111yescharacteristic
999C2×C22⋊C4C23×C13111yescharacteristic
1000C2×C22⋊C4C23×C13111yescharacteristic
1001C2×C22⋊C4C23×C13111yescharacteristic
1002C2×C22⋊C4C23×C13111yescharacteristic
1003C2×C22⋊C4C23×C13111yescharacteristic
1004C2×C22⋊C4C23×C13111yescharacteristic
1005C2×C22⋊C4C23×C13111yescharacteristic
1006C2×C22⋊C4C23×C13111yescharacteristic
1007C2×C22⋊C4C23×C13111yescharacteristic
1008C2×C22⋊C4C23×C13111yescharacteristic
1009C2×C22⋊C4C23×C13111yescharacteristic
1010C2×C22⋊C4C23×C13111yescharacteristic
1011C2×C22⋊C4C23×C13111yescharacteristic
1012C2×C22⋊C4C23×C13111yescharacteristic
1013C2×C22⋊C4C23×C13111yescharacteristic
1014C2×C22⋊C4C23×C13111yescharacteristic
1015C2×C22⋊C4C23×C13111yescharacteristic
1016C2×C22⋊C4C23×C13111yescharacteristic
1017C2×C22⋊C4C23×C13111yescharacteristic
1018C2×C22⋊C4C23×C13111yescharacteristic
1019C2×C22⋊C4C23×C13111yescharacteristic
1020C2×C22⋊C4C23×C13111yescharacteristic
1021C2×C22⋊C4C23×C13111yescharacteristic
1022C2×C22⋊C4C23×C13111yescharacteristic
1023C2×C22⋊C4C23×C13111yescharacteristic
1024C2×C22⋊C4C23×C13111yescharacteristic
1025C2×C22⋊C4C23×C13111yescharacteristic
1026C2×C22⋊C4C23×C13111yescharacteristic
1027C2×C22⋊C4C23×C13111yescharacteristic
1028C2×C22⋊C4C23×C13111yescharacteristic
1029C2×C22⋊C4C23×C13111yescharacteristic
1030C2×C22⋊C4C23×C13111yescharacteristic
1031C2×C22⋊C4C23×C13111yescharacteristic
1032C2×C22⋊C4C23×C13111yescharacteristic
1033C2×C22⋊C4C23×C13111yescharacteristic
1034C2×C22⋊C4C23×C13111yescharacteristic
1035C2×C22⋊C4C23×C13111yescharacteristic
1036C2×C22⋊C4C23×C13111yescharacteristic
1037C2×C22⋊C4C23×C13111yescharacteristic
1038C2×C42C23×C13111yescharacteristic
1039C2×C42C23×C13111yescharacteristic
1040C2×C42C23×C13111yescharacteristic
1041C2×C42C23×C13111yescharacteristic
1042C2×C42C23×C13111yescharacteristic
1043C2×C42C23×C13111yescharacteristic
1044C2×C42C23×C13111yescharacteristic
1045C2×C42C23×C13111yescharacteristic
1046C2×C42C23×C13111yescharacteristic
1047C2×C42C23×C13111yescharacteristic
1048C2×C42C23×C13111yescharacteristic
1049C2×C42C23×C13111yescharacteristic
1050C2×C42C23×C13111yescharacteristic
1051C2×C42C23×C13111yescharacteristic
1052C2×C42C23×C13111yescharacteristic
1053C2×C42C23×C13111yescharacteristic
1054C2×C42C23×C13111yescharacteristic
1055C2×C42C23×C13111yescharacteristic
1056C2×C42C23×C13111yescharacteristic
1057C2×C42C23×C13111yescharacteristic
1058C2×C42C23×C13111yescharacteristic
1059C2×C42C23×C13111yescharacteristic
1060C2×C42C23×C13111yescharacteristic
1061C2×C42C23×C13111yescharacteristic
1062C2×C42C23×C13111yescharacteristic
1063#95C23×C13111yescharacteristic
1064#95C23×C13111yescharacteristic
1065#95C23×C13111yescharacteristic
1066#95C23×C13111yescharacteristic
1067#95C23×C13111yescharacteristic
1068#95C23×C13111yescharacteristic
1069#95C23×C13111yescharacteristic
1070#95C23×C13111yescharacteristic
1071#95C23×C13111yescharacteristic
1072#95C23×C13111yescharacteristic
1073#95C23×C13111yescharacteristic
1074#95C23×C13111yescharacteristic
1075#95C23×C13111yescharacteristic
1076#95C23×C13111yescharacteristic
1077#95C23×C13111yescharacteristic
1078#95C23×C13111yescharacteristic
1079#95C23×C13111yescharacteristic
1080#95C23×C13111yescharacteristic
1081#95C23×C13111yescharacteristic
1082#95C23×C13111yescharacteristic
1083#95C23×C13111yescharacteristic
1084#95C23×C13111yescharacteristic
1085#95C23×C13111yescharacteristic
1086#95C23×C13111yescharacteristic
1087#95C23×C13111yescharacteristic
1088#95C23×C13111yescharacteristic
1089#95C23×C13111yescharacteristic
1090#95C23×C13111yescharacteristic
1091#95C23×C13111yescharacteristic
1092#95C23×C13111yescharacteristic
1093#95C23×C13111yescharacteristic
1094#95C23×C13111yescharacteristic
1095#95C23×C13111yescharacteristic
1096#95C23×C13111yescharacteristic
1097#95C23×C13111yescharacteristic
1098#95C23×C13111yescharacteristic
1099#95C23×C13111yescharacteristic
1100#95C23×C13111yescharacteristic
1101#95C23×C13111yescharacteristic
1102#95C23×C13111yescharacteristic
1103#95C23×C13111yescharacteristic
1104#95C23×C13111yescharacteristic
1105#95C23×C13111yescharacteristic
1106#95C23×C13111yescharacteristic
1107C24—41no—
1108C24—41no—
1109C24—41no—
1110C24—41no—
1111C24—41no—
1112C24—41no—
1113C24C22×C4×C13114yes—
1114C24C24×C13111yescharacteristic
1115C24C24×C13111yescharacteristic
1116C24C24×C13111yescharacteristic
1117C24C24×C13111yescharacteristic
1118C2×Q8—41no—
1119C2×Q8—41no—
1120C2×Q8C22×C4×C13114yes—
1121C2×D4—41no—
1122C2×D4—41no—
1123C2×D4—41no—
1124C2×D4—41no—
1125C2×D4—41no—
1126C2×D4—41no—
1127C2×D4C22×C4×C13114yes—
1128C2×D4C22×C4×C13114yes—
1129C2×D4C22×C4×C13114yes—
1130C22×C4—22no—
1131C22×C4—41no—
1132C22×C4—41no—
1133C22×C4—41no—
1134C22×C4—41no—
1135C22×C4—41no—
1136C22×C4—41no—
1137C22×C4—41no—
1138C22×C4—41no—
1139C22×C4—41no—
1140C22×C4—41no—
1141C22×C4—41no—
1142C22×C4—41no—
1143C22×C4—41no—
1144C22×C4—41no—
1145C22×C4—41no—
1146C22×C4—41no—
1147C22×C4—41no—
1148C22×C4—41no—
1149C22×C4—41no—
1150C22×C4—41no—
1151C22×C4—41no—
1152C22×C4C22×C4×C13114yes—
1153C22×C4C22×C4×C13114yes—
1154C22×C4C22×C4×C13114yes—
1155C22×C4C22×C4×C13114yes—
1156C22×C4C22×C4×C13114yes—
1157C22×C4C24×C13111yescharacteristic
1158C22×C4C24×C13111yescharacteristic
1159C22×C4C24×C13111yescharacteristic
1160C22×C4C24×C13111yescharacteristic
1161C22×C4C24×C13111yescharacteristic
1162C22×C4C24×C13111yescharacteristic
1163C22×C4C24×C13111yescharacteristic
1164C22×C4C24×C13111yescharacteristic
1165C22×C4C24×C13111yescharacteristic
1166C22×C4C24×C13111yescharacteristic
1167C22×C4C24×C13111yescharacteristic
1168C22×C4C24×C13111yescharacteristic
1169C22×C4C24×C13111yescharacteristic
1170C22×C4C24×C13111yescharacteristic
1171C22×C4C24×C13111yescharacteristic
1172C22×C4C24×C13111yescharacteristic
1173C22×C4C24×C13111yescharacteristic
1174C22×C4C24×C13111yescharacteristic
1175C22×C4C24×C13111yescharacteristic
1176C22×C4C24×C13111yescharacteristic
1177C22×C4C24×C13111yescharacteristic
1178C22×C4C24×C13111yescharacteristic
1179C22×C4C24×C13111yescharacteristic
1180C22×C4C24×C13111yescharacteristic
1181C22×C4C24×C13111yescharacteristic
1182C22×C4C24×C13111yescharacteristic
1183C22×C4C24×C13111yescharacteristic
1184C4⋊C4—22no—
1185C4⋊C4—22no—
1186C4⋊C4—22no—
1187C4⋊C4—41no—
1188C4⋊C4—41no—
1189C4⋊C4—41no—
1190C4⋊C4—41no—
1191C4⋊C4—41no—
1192C4⋊C4—41no—
1193C4⋊C4—41no—
1194C4⋊C4—41no—
1195C4⋊C4—41no—
1196C4⋊C4—41no—
1197C4⋊C4—41no—
1198C4⋊C4—41no—
1199C4⋊C4—41no—
1200C4⋊C4—41no—
1201C4⋊C4—41no—
1202C4⋊C4—41no—
1203C4⋊C4—41no—
1204C4⋊C4—41no—
1205C4⋊C4—41no—
1206C4⋊C4C22×C4×C13114yes—
1207C4⋊C4C22×C4×C13114yes—
1208C4⋊C4C22×C4×C13114yes—
1209C4⋊C4C22×C4×C13114yes—
1210C4⋊C4C22×C4×C13114yes—
1211C4⋊C4C22×C4×C13114yes—
1212C4⋊C4C22×C4×C13114yes—
1213C4⋊C4C22×C4×C13114yes—
1214C22⋊C4—22no—
1215C22⋊C4—22no—
1216C22⋊C4—22no—
1217C22⋊C4—41no—
1218C22⋊C4—41no—
1219C22⋊C4—41no—
1220C22⋊C4—41no—
1221C22⋊C4—41no—
1222C22⋊C4—41no—
1223C22⋊C4—41no—
1224C22⋊C4—41no—
1225C22⋊C4—41no—
1226C22⋊C4—41no—
1227C22⋊C4—41no—
1228C22⋊C4—41no—
1229C22⋊C4—41no—
1230C22⋊C4—41no—
1231C22⋊C4—41no—
1232C22⋊C4—41no—
1233C22⋊C4—41no—
1234C22⋊C4—41no—
1235C22⋊C4—41no—
1236C22⋊C4—41no—
1237C22⋊C4—41no—
1238C22⋊C4—41no—
1239C22⋊C4—41no—
1240C22⋊C4—41no—
1241C22⋊C4—41no—
1242C22⋊C4C22×C4×C13114yes—
1243C22⋊C4C22×C4×C13114yes—
1244C22⋊C4C22×C4×C13114yes—
1245C22⋊C4C22×C4×C13114yes—
1246C22⋊C4C22×C4×C13114yes—
1247C22⋊C4C22×C4×C13114yes—
1248C22⋊C4C22×C4×C13114yes—
1249C22⋊C4C22×C4×C13114yes—
1250C22⋊C4C22×C4×C13114yes—
1251C22⋊C4C22×C4×C13114yes—
1252C22⋊C4C22×C4×C13114yes—
1253C22⋊C4C22×C4×C13114yes—
1254C22⋊C4C22×C4×C13114yes—
1255C22⋊C4C22×C4×C13114yes—
1256C42—22no—
1257C42—22no—
1258C42—41no—
1259C42—41no—
1260C42—41no—
1261C42—41no—
1262C42—41no—
1263C42—41no—
1264C42—41no—
1265C42—41no—
1266C42—41no—
1267C42—41no—
1268C42—41no—
1269C42—41no—
1270C42—41no—
1271C42—41no—
1272C42—41no—
1273C42—41no—
1274C42—41no—
1275C42—41no—
1276C42—41no—
1277C42—41no—
1278C42C22×C4×C13114yes—
1279C42C22×C4×C13114yes—
1280C42C22×C4×C13114yes—
1281C23—21no—
1282C23—21no—
1283C23—21no—
1284C23—21no—
1285C23—21no—
1286C23—21no—
1287C23—21no—
1288C23—21no—
1289C23—21no—
1290C23—21no—
1291C23—21no—
1292C23—21no—
1293C23—21no—
1294C23—21no—
1295C23—21no—
1296C23—21no—
1297C23—21no—
1298C23—21no—
1299C23—21no—
1300C23—21no—
1301C23—21no—
1302C23—21no—
1303C23—21no—
1304C23—21no—
1305C23—44no—
1306C23—44no—
1307C23—44no—
1308C23—82no—
1309C23—82no—
1310C23—82no—
1311C23—82no—
1312C23C23×C4×C13112yes—
1313C23C23×C4×C13112yes—
1314C23C23×C4×C13112yes—
1315C23C23×C4×C13112yes—
1316C23C25×C13111yescharacteristic
1317Q8—44no—
1318D4—44no—
1319D4—44no—
1320D4—44no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—44no—
1391C2×C4—44no—
1392C2×C4—44no—
1393C2×C4—44no—
1394C2×C4—44no—
1395C2×C4—82no—
1396C2×C4—82no—
1397C2×C4—82no—
1398C2×C4—82no—
1399C2×C4C23×C4×C13112yes—
1400C2×C4C23×C4×C13112yes—
1401C2×C4C23×C4×C13112yes—
1402C2×C4C23×C4×C13112yes—
1403C2×C4C23×C4×C13112yes—
1404C2×C4C23×C4×C13112yes—
1405C2×C4C23×C4×C13112yes—
1406C2×C4C23×C4×C13112yes—
1407C2×C4C23×C4×C13112yes—
1408C2×C4C23×C4×C13112yes—
1409C2×C4C23×C4×C13112yes—
1410C2×C4H(5,𝔽2)×C13112yes—
1411C22—22no—
1412C22—22no—
1413C22—22no—
1414C22—22no—
1415C22—22no—
1416C22—22no—
1417C22—22no—
1418C22—22no—
1419C22—22no—
1420C22—22no—
1421C22—22no—
1422C22—22no—
1423C22—41no—
1424C22—41no—
1425C22—41no—
1426C22—41no—
1427C22—41no—
1428C22—41no—
1429C22—41no—
1430C22—41no—
1431C22—41no—
1432C22—41no—
1433C22—41no—
1434C22—41no—
1435C22—41no—
1436C22—41no—
1437C22—41no—
1438C22—41no—
1439C22—88no—
1440C22C24×C4×C13111yescharacteristic
1441C22C2×H(5,𝔽2)×C13111yescharacteristic
1442C22#585×C13111yescharacteristic
1443C22#585×C13111yescharacteristic
1444C22#585×C13111yescharacteristic
1445C22#585×C13111yescharacteristic
1446C22#585×C13111yescharacteristic
1447C4—22no—
1448C4—22no—
1449C4—22no—
1450C4—22no—
1451C4—22no—
1452C4—22no—
1453C4—22no—
1454C4—22no—
1455C4—22no—
1456C4—22no—
1457C4—22no—
1458C4—22no—
1459C4—41no—
1460C4—41no—
1461C4—41no—
1462C4—41no—
1463C4—41no—
1464C4—41no—
1465C4—41no—
1466C4—41no—
1467C4—41no—
1468C4—41no—
1469C4—41no—
1470C4—41no—
1471C4—41no—
1472C4—41no—
1473C4—41no—
1474C2—42no—
1475C2—42no—
1476C2—42no—
1477C2—42no—
1478C2#3428×C13111yescharacteristic
1479C2#3428×C13111yescharacteristic
1480C2C4×H(5,𝔽2)×C13111yescharacteristic
1481C2#3560×C13111yescharacteristic
1482C2#3562×C13111yescharacteristic
1483C2#3566×C13111yescharacteristic
1484C2#3568×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C25
commutatorC22C24×C4×C131
Frattini, cosocleC23C25×C131
prime radicalC2×#120×C131C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2383×C131C2semidirect
3. #2378×C131C2semidirect
4. #2376×C131C2semidirect
6. #2374×C131C2semidirect
7. #2373×C131C2semidirect
8. #2367×C131C2semidirect
9. #2362×C131C2semidirect
10. #2359×C131C2semidirect
11. #2354×C131C2semidirect
12. #2353×C131C2semidirect
13. #2347×C131C2semidirect
14. #2347×C131C2semidirect
15. #2342×C131C2semidirect
16. #2342×C131C2semidirect
17. #2337×C131C2semidirect
18. #2335×C131C2semidirect
19. #2335×C131C2semidirect
20. #2335×C131C2semidirect
21. #2334×C131C2semidirect
22. #2332×C131C2semidirect
23. #2323×C131C2semidirect
25. #2318×C131C2semidirect
26. #2314×C131C2semidirect
27. #2312×C131C2semidirect
28. #2312×C131C2semidirect
29. C4×#126×C131C2semidirect
30. #2298×C131C2semidirect
31. #2293×C131C2semidirect
32. #551×C131C4semidirect
42. C2×C4×Q8×C131C22semidirect
50. C2×#117×C131C22semidirect
54. #391×C131C22semidirect
55. #391×C131C22semidirect
56. #391×C131C22semidirect
62. #389×C131C22semidirect
63. #389×C131C22semidirect
64. #389×C131C22semidirect
65. #389×C131C22semidirect
66. #389×C131C22semidirect
67. #389×C131C22semidirect
68. #389×C131C22semidirect
69. #389×C131C22semidirect
104. #388×C131C22semidirect
105. #388×C131C22semidirect
106. #388×C131C22semidirect
107. #388×C131C22semidirect
108. #388×C131C22semidirect
109. #388×C131C22semidirect
110. #387×C131C22semidirect
111. #387×C131C22semidirect
112. #387×C131C22semidirect
113. #387×C131C22semidirect
114. #387×C131C22semidirect
115. #387×C131C22semidirect
116. #387×C131C22semidirect
117. #387×C131C22semidirect
118. #387×C131C22semidirect
119. #387×C131C22semidirect
120. #387×C131C22semidirect
121. #387×C131C22semidirect
122. #387×C131C22semidirect
123. #387×C131C22semidirect
124. #387×C131C22semidirect
125. #387×C131C22semidirect
137. #385×C131C22semidirect
138. #385×C131C22semidirect
139. #385×C131C22semidirect
140. #384×C131C22semidirect
141. #383×C131C22semidirect
142. #383×C131C22semidirect
143. #383×C131C22semidirect
144. #382×C131C22semidirect
153. #380×C131C22semidirect
157. C4×C4⋊C4×C131C22semidirect
158. C4×C4⋊C4×C131C22semidirect
159. C4×C4⋊C4×C131C22semidirect
160. C4×C4⋊C4×C131C22semidirect
161. C4×C4⋊C4×C131C22semidirect
162. C4×C4⋊C4×C131C22semidirect
163. C4×C4⋊C4×C131C22semidirect
164. C4×C4⋊C4×C131C22semidirect
165. C4×C4⋊C4×C131C22semidirect
166. C4×C4⋊C4×C131C22semidirect
167. C4×C4⋊C4×C131C22semidirect
168. C4×C4⋊C4×C131C22semidirect
169. C4×C4⋊C4×C131C22semidirect
181. C4×C22⋊C4×C131C22semidirect
182. C4×C22⋊C4×C131C22semidirect
183. C4×C22⋊C4×C131C22semidirect
184. C4×C22⋊C4×C131C22semidirect
185. #376×C131C22semidirect
186. C2×#95×C131C22semidirect
187. C43×C131C22semidirect
202. #126×C131C2×C4semidirect
203. #126×C131C2×C4semidirect
206. #123×C131C2×C4semidirect
207. #123×C131C2×C4semidirect
208. C22⋊Q8×C131C2×C4semidirect
209. C22⋊Q8×C131C2×C4semidirect
213. C4×D4×C131C2×C4semidirect
214. C4×D4×C131C2×C4semidirect
218. #117×C131C2×C4semidirect
219. #117×C131C2×C4semidirect
251. C2×C22⋊C4×C131C2×C4semidirect
252. C2×C22⋊C4×C131C2×C4semidirect
742. #34504C131direct (N × H)
743. C131#34504direct (N × H)
745. #2383C2×C131semidirect
746. #2378C2×C131semidirect
747. #2376C2×C131semidirect
749. #2374C2×C131semidirect
750. #2373C2×C131semidirect
751. #2367C2×C131semidirect
752. #2362C2×C131semidirect
753. #2359C2×C131semidirect
754. #2354C2×C131semidirect
755. #2353C2×C131semidirect
756. #2347C2×C131semidirect
757. #2347C2×C131semidirect
758. #2342C2×C131semidirect
759. #2342C2×C131semidirect
760. #2337C2×C131semidirect
761. #2335C2×C131semidirect
762. #2335C2×C131semidirect
763. #2335C2×C131semidirect
764. #2334C2×C131semidirect
765. #2332C2×C131semidirect
766. #2323C2×C131semidirect
768. #2318C2×C131semidirect
769. #2314C2×C131semidirect
770. #2312C2×C131semidirect
771. #2312C2×C131semidirect
772. C4×#126C2×C131semidirect
773. #2298C2×C131semidirect
774. #2293C2×C131semidirect
775. #551C4×C131semidirect
785. C2×C4×Q8C22×C131semidirect
793. C2×#117C22×C131semidirect
797. #391C22×C131semidirect
798. #391C22×C131semidirect
799. #391C22×C131semidirect
805. #389C22×C131semidirect
806. #389C22×C131semidirect
807. #389C22×C131semidirect
808. #389C22×C131semidirect
809. #389C22×C131semidirect
810. #389C22×C131semidirect
811. #389C22×C131semidirect
812. #389C22×C131semidirect
847. #388C22×C131semidirect
848. #388C22×C131semidirect
849. #388C22×C131semidirect
850. #388C22×C131semidirect
851. #388C22×C131semidirect
852. #388C22×C131semidirect
853. #387C22×C131semidirect
854. #387C22×C131semidirect
855. #387C22×C131semidirect
856. #387C22×C131semidirect
857. #387C22×C131semidirect
858. #387C22×C131semidirect
859. #387C22×C131semidirect
860. #387C22×C131semidirect
861. #387C22×C131semidirect
862. #387C22×C131semidirect
863. #387C22×C131semidirect
864. #387C22×C131semidirect
865. #387C22×C131semidirect
866. #387C22×C131semidirect
867. #387C22×C131semidirect
868. #387C22×C131semidirect
880. #385C22×C131semidirect
881. #385C22×C131semidirect
882. #385C22×C131semidirect
883. #384C22×C131semidirect
884. #383C22×C131semidirect
885. #383C22×C131semidirect
886. #383C22×C131semidirect
887. #382C22×C131semidirect
896. #380C22×C131semidirect
900. C4×C4⋊C4C22×C131semidirect
901. C4×C4⋊C4C22×C131semidirect
902. C4×C4⋊C4C22×C131semidirect
903. C4×C4⋊C4C22×C131semidirect
904. C4×C4⋊C4C22×C131semidirect
905. C4×C4⋊C4C22×C131semidirect
906. C4×C4⋊C4C22×C131semidirect
907. C4×C4⋊C4C22×C131semidirect
908. C4×C4⋊C4C22×C131semidirect
909. C4×C4⋊C4C22×C131semidirect
910. C4×C4⋊C4C22×C131semidirect
911. C4×C4⋊C4C22×C131semidirect
912. C4×C4⋊C4C22×C131semidirect
924. C4×C22⋊C4C22×C131semidirect
925. C4×C22⋊C4C22×C131semidirect
926. C4×C22⋊C4C22×C131semidirect
927. C4×C22⋊C4C22×C131semidirect
928. #376C22×C131semidirect
929. C2×#95C22×C131semidirect
930. C43C22×C131semidirect
945. #126C2×C4×C131semidirect
946. #126C2×C4×C131semidirect
949. #123C2×C4×C131semidirect
950. #123C2×C4×C131semidirect
951. C22⋊Q8C2×C4×C131semidirect
952. C22⋊Q8C2×C4×C131semidirect
956. C4×D4C2×C4×C131semidirect
957. C4×D4C2×C4×C131semidirect
961. #117C2×C4×C131semidirect
962. #117C2×C4×C131semidirect
994. C2×C22⋊C4C2×C4×C131semidirect
995. C2×C22⋊C4C2×C4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#551×C1312
#2383×C1312
#2378×C1312
#2376×C1312
#2375×C1312
#2374×C1312
#2373×C1312
#2367×C1312
#2362×C1312
#2359×C1312
#2354×C1312
#2353×C1312
#2347×C1312
#2342×C1312
#2337×C1312
#2335×C1312
#2334×C1312
#2332×C1312
#2323×C1312
#2321×C1312
#2318×C1312
#2314×C1312
#2312×C1312
C4×#126×C1312
#2298×C1312
#2293×C1312
#34504131