Finite Group Databasebeta

← C131×#36888 #45722772

Subgroups — C131×#36888 #45722772

Order 33536.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2849×C131C211yesmaximal, characteristic, complemented
2#2848×C131C211yesmaximal, characteristic, complemented
3#2796×C131C211yesmaximal, characteristic, complemented
4#2790×C131C211yesmaximal, characteristic, complemented
5#2779×C131C211yesmaximal, characteristic, complemented
6#2753×C131C211yesmaximal, characteristic, complemented
7#2748×C131C211yesmaximal, characteristic, complemented
8#2740×C131C211yesmaximal, characteristic, complemented
9#2735×C131C211yesmaximal, characteristic, complemented
10#2730×C131C211yesmaximal, characteristic, complemented
11#2720×C131C211yesmaximal, characteristic, complemented
12#2707×C131C211yesmaximal, characteristic, complemented
13#2698×C131C211yesmaximal, characteristic, complemented
14#2695×C131C211yesmaximal, characteristic, complemented
15#2685×C131C211yesmaximal, characteristic, complemented
16#2685×C131C211yesmaximal, characteristic, complemented
17#2678×C131C211yesmaximal, characteristic
18#2672×C131C211yesmaximal, characteristic, complemented
19#2633×C131C211yesmaximal, characteristic, complemented
20#2630×C131C211yesmaximal, characteristic, complemented
21#2578×C131C211yesmaximal, characteristic, complemented
22#2573×C131C211yesmaximal, characteristic, complemented
23#2558×C131C211yesmaximal, characteristic, complemented
24#2556×C131C211yesmaximal, characteristic, complemented
25#2468×C131C211yesmaximal, characteristic, complemented
26#2461×C131C211yesmaximal, characteristic, complemented
27#2454×C131C211yesmaximal, characteristic, complemented
28#2422×C131C211yesmaximal, characteristic, complemented
29#2335×C131C211yesmaximal, characteristic, complemented
30#2334×C131C211yesmaximal, characteristic, complemented
31C4×#120×C131C211yesmaximal, characteristic, complemented
32C24×C4×C131C2211yescharacteristic
33C2×#126×C131C2211yescharacteristic
34C2×#126×C131C2211yescharacteristic
35C2×#125×C131C2211yescharacteristic, complemented
36C2×#125×C131C2211yescharacteristic, complemented
37C2×#124×C131C2211yescharacteristic, complemented
38C2×#123×C131C2211yescharacteristic
39C2×#123×C131C2211yescharacteristic
40C2×#123×C131C2211yescharacteristic
41C2×#123×C131C2211yescharacteristic, complemented
42C2×C22⋊Q8×C131C2211yescharacteristic
43C2×C22⋊Q8×C131C2211yescharacteristic
44C2×C22⋊Q8×C131C2211yescharacteristic
45C2×#121×C131C2211yescharacteristic
46C2×#120×C131C2211yescharacteristic
47C2×#120×C131C2211yescharacteristic
48C2×C4×D4×C131C2211yescharacteristic
49C2×C4×D4×C131C2211yescharacteristic
50C2×C4×D4×C131C2211yescharacteristic
51#400×C131C2211yescharacteristic, complemented
52#400×C131C2211yescharacteristic, complemented
53#400×C131C2211yescharacteristic, complemented
54#400×C131C2211yescharacteristic, complemented
55#399×C131C2211yescharacteristic
56#399×C131C2211yescharacteristic
57#399×C131C2211yescharacteristic
58#399×C131C2211yescharacteristic, complemented
59#399×C131C2211yescharacteristic, complemented
60#398×C131C2211yescharacteristic, complemented
61#398×C131C2211yescharacteristic, complemented
62#398×C131C2211yescharacteristic, complemented
63#398×C131C2211yescharacteristic, complemented
64#398×C131C2211yescharacteristic, complemented
65#398×C131C2211yescharacteristic, complemented
66#397×C131C2211yescharacteristic
67#397×C131C2211yescharacteristic
68#397×C131C2211yescharacteristic
69#397×C131C2211yescharacteristic
70#397×C131C2211yescharacteristic, complemented
71#397×C131C2211yescharacteristic, complemented
72#397×C131C2211yescharacteristic, complemented
73#397×C131C2211yescharacteristic, complemented
74#396×C131C2211yescharacteristic
75#396×C131C2211yescharacteristic
76#396×C131C2211yescharacteristic
77#396×C131C2211yescharacteristic
78#396×C131C2211yescharacteristic
79#396×C131C2211yescharacteristic, complemented
80#396×C131C2211yescharacteristic, complemented
81#396×C131C2211yescharacteristic, complemented
82#396×C131C2211yescharacteristic, complemented
83#395×C131C2211yescharacteristic, complemented
84#395×C131C2211yescharacteristic, complemented
85#394×C131C2211yescharacteristic
86#394×C131C2211yescharacteristic
87#394×C131C2211yescharacteristic
88#394×C131C2211yescharacteristic
89#394×C131C2211yescharacteristic
90#394×C131C2211yescharacteristic
91#394×C131C2211yescharacteristic
92#394×C131C2211yescharacteristic
93#394×C131C2211yescharacteristic
94#394×C131C2211yescharacteristic
95#394×C131C2211yescharacteristic, complemented
96#394×C131C2211yescharacteristic, complemented
97#392×C131C2211yescharacteristic
98#392×C131C2211yescharacteristic
99#391×C131C2211yescharacteristic, complemented
100#390×C131C2211yescharacteristic
101#390×C131C2211yescharacteristic
102#390×C131C2211yescharacteristic
103#390×C131C2211yescharacteristic
104#390×C131C2211yescharacteristic
105#390×C131C2211yescharacteristic
106#389×C131C2211yescharacteristic, complemented
107#389×C131C2211yescharacteristic, complemented
108#389×C131C2211yescharacteristic, complemented
109#389×C131C2211yescharacteristic, complemented
110#389×C131C2211yescharacteristic, complemented
111#389×C131C2211yescharacteristic, complemented
112#388×C131C2211yescharacteristic
113#388×C131C2211yescharacteristic
114#388×C131C2211yescharacteristic
115#388×C131C2211yescharacteristic
116#388×C131C2211yescharacteristic
117#388×C131C2211yescharacteristic
118#388×C131C2211yescharacteristic
119#388×C131C2211yescharacteristic
120#388×C131C2211yescharacteristic
121#388×C131C2211yescharacteristic
122#388×C131C2211yescharacteristic
123#388×C131C2211yescharacteristic
124#388×C131C2211yescharacteristic
125#388×C131C2211yescharacteristic, complemented
126#388×C131C2211yescharacteristic, complemented
127#388×C131C2211yescharacteristic, complemented
128#388×C131C2211yescharacteristic, complemented
129#388×C131C2211yescharacteristic, complemented
130#388×C131C2211yescharacteristic, complemented
131#388×C131C2211yescharacteristic, complemented
132#387×C131C2211yescharacteristic, complemented
133#387×C131C2211yescharacteristic, complemented
134#387×C131C2211yescharacteristic, complemented
135#387×C131C2211yescharacteristic, complemented
136#387×C131C2211yescharacteristic, complemented
137#387×C131C2211yescharacteristic, complemented
138#387×C131C2211yescharacteristic, complemented
139#387×C131C2211yescharacteristic, complemented
140#387×C131C2211yescharacteristic, complemented
141#386×C131C2211yescharacteristic
142#386×C131C2211yescharacteristic
143#386×C131C2211yescharacteristic
144#386×C131C2211yescharacteristic
145#386×C131C2211yescharacteristic
146#386×C131C2211yescharacteristic
147#386×C131C2211yescharacteristic
148#386×C131C2211yescharacteristic
149#385×C131C2211yescharacteristic
150#385×C131C2211yescharacteristic
151#385×C131C2211yescharacteristic
152#385×C131C2211yescharacteristic
153#385×C131C2211yescharacteristic
154#385×C131C2211yescharacteristic
155#385×C131C2211yescharacteristic
156#385×C131C2211yescharacteristic
157#385×C131C2211yescharacteristic
158#385×C131C2211yescharacteristic
159#385×C131C2211yescharacteristic
160#385×C131C2211yescharacteristic
161#385×C131C2211yescharacteristic
162#385×C131C2211yescharacteristic, complemented
163#385×C131C2211yescharacteristic, complemented
164#385×C131C2211yescharacteristic, complemented
165#384×C131C2211yescharacteristic, complemented
166#383×C131C2211yescharacteristic, complemented
167#382×C131C2211yescharacteristic, complemented
168#381×C131C2211yescharacteristic
169#381×C131C2211yescharacteristic
170#380×C131C2211yescharacteristic
171#380×C131C2211yescharacteristic
172#380×C131C2211yescharacteristic
173#380×C131C2211yescharacteristic, complemented
174#380×C131C2211yescharacteristic, complemented
175#380×C131C2211yescharacteristic, complemented
176#379×C131C2211yescharacteristic
177#379×C131C2211yescharacteristic
178#379×C131C2211yescharacteristic
179#379×C131C2211yescharacteristic
180C4×C4⋊C4×C131C2211yescharacteristic, complemented
181C4×C4⋊C4×C131C2211yescharacteristic, complemented
182C4×C4⋊C4×C131C2211yescharacteristic, complemented
183C4×C22⋊C4×C131C2211yescharacteristic
184C4×C22⋊C4×C131C2211yescharacteristic
185C4×C22⋊C4×C131C2211yescharacteristic
186C4×C22⋊C4×C131C2211yescharacteristic, complemented
187C25×C131C2311yescharacteristic
188C22×Q8×C131C2311yescharacteristic
189C22×D4×C131C2311yescharacteristic
190C22×D4×C131C2311yescharacteristic
191C22×D4×C131C2311yescharacteristic
192C22×D4×C131C2311yescharacteristic
193C22×D4×C131C2311yescharacteristic
194C22×D4×C131C2311yescharacteristic
195C22×D4×C131C2311yescharacteristic
196C23×C4×C131—42no—
197C23×C4×C131—42no—
198C23×C4×C131—42no—
199C23×C4×C131C2311yescharacteristic
200C23×C4×C131C2311yescharacteristic
201C23×C4×C131C2311yescharacteristic
202C23×C4×C131C2311yescharacteristic
203C23×C4×C131C2311yescharacteristic
204C23×C4×C131C2311yescharacteristic
205C23×C4×C131C2311yescharacteristic
206C23×C4×C131C2311yescharacteristic
207#126×C131—24no—
208#126×C131—42no—
209#125×C131—42no—
210#125×C131—42no—
211#124×C131—42no—
212#123×C131—24no—
213#123×C131—42no—
214#123×C131—42no—
215#123×C131—42no—
216C22⋊Q8×C131—42no—
217C22⋊Q8×C131—42no—
218C22⋊Q8×C131—42no—
219#121×C131—42no—
220#120×C131—24no—
221#120×C131—42no—
222C4×D4×C131—42no—
223C4×D4×C131—42no—
224C4×D4×C131—42no—
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×C4⋊C4×C131C2311yescharacteristic
251C2×C4⋊C4×C131C2311yescharacteristic
252C2×C4⋊C4×C131C2311yescharacteristic
253C2×C4⋊C4×C131C2311yescharacteristic
254C2×C4⋊C4×C131C2311yescharacteristic
255C2×C4⋊C4×C131C2311yescharacteristic
256C2×C4⋊C4×C131C2311yescharacteristic
257C2×C4⋊C4×C131C2311yescharacteristic
258C2×C4⋊C4×C131C2311yescharacteristic
259C2×C4⋊C4×C131C2311yescharacteristic
260C2×C4⋊C4×C131C2311yescharacteristic
261C2×C4⋊C4×C131C2311yescharacteristic
262C2×C4⋊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×C22⋊C4×C131C2311yescharacteristic
296C2×C22⋊C4×C131C2311yescharacteristic
297C2×C22⋊C4×C131C2311yescharacteristic
298C2×C22⋊C4×C131C2311yescharacteristic
299C2×C22⋊C4×C131C2311yescharacteristic
300C2×C22⋊C4×C131C2311yescharacteristic
301C2×C22⋊C4×C131C2311yescharacteristic
302C2×C22⋊C4×C131C2311yescharacteristic
303C2×C22⋊C4×C131C2311yescharacteristic
304C2×C22⋊C4×C131C2311yescharacteristic
305C2×C22⋊C4×C131C2311yescharacteristic
306C2×C22⋊C4×C131C2311yescharacteristic
307C2×C22⋊C4×C131C2311yescharacteristic
308C2×C22⋊C4×C131C2311yescharacteristic
309C2×C22⋊C4×C131C2311yescharacteristic
310C2×C22⋊C4×C131C2311yescharacteristic
311C2×C22⋊C4×C131C2311yescharacteristic
312C2×C22⋊C4×C131C2311yescharacteristic
313C2×C42×C131C2311yescharacteristic
314C2×C42×C131C2311yescharacteristic
315C2×C42×C131C2311yescharacteristic
316C2×C42×C131C2311yescharacteristic
317C2×C42×C131C2311yescharacteristic
318C2×C42×C131C2311yescharacteristic
319C2×C42×C131C2311yescharacteristic
320C2×C42×C131C2311yescharacteristic
321C2×C42×C131C2311yescharacteristic
322C2×C42×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
363C24×C131—22no—
364C24×C131—22no—
365C24×C131—22no—
366C24×C131—41no—
367C24×C131—41no—
368C24×C131—41no—
369C24×C131—41no—
370C24×C131C2411yescharacteristic
371C24×C131C2411yescharacteristic
372C24×C131C2411yescharacteristic
373C24×C131C2411yescharacteristic
374C24×C131C2411yescharacteristic
375C2×Q8×C131—22no—
376C2×Q8×C131—41no—
377C2×Q8×C131—41no—
378C2×D4×C131—22no—
379C2×D4×C131—22no—
380C2×D4×C131—22no—
381C2×D4×C131—22no—
382C2×D4×C131—22no—
383C2×D4×C131—22no—
384C2×D4×C131—22no—
385C2×D4×C131—22no—
386C2×D4×C131—41no—
387C2×D4×C131—41no—
388C2×D4×C131—41no—
389C2×D4×C131—41no—
390C2×D4×C131—41no—
391C2×D4×C131—41no—
392C2×D4×C131—41no—
393C2×D4×C131—41no—
394C2×D4×C131—41no—
395C2×D4×C131—41no—
396C2×D4×C131—41no—
397C2×D4×C131—41no—
398C2×D4×C131—41no—
399C22×C4×C131—22no—
400C22×C4×C131—22no—
401C22×C4×C131—22no—
402C22×C4×C131—22no—
403C22×C4×C131—22no—
404C22×C4×C131—22no—
405C22×C4×C131—22no—
406C22×C4×C131—22no—
407C22×C4×C131—22no—
408C22×C4×C131—22no—
409C22×C4×C131—41no—
410C22×C4×C131—41no—
411C22×C4×C131—41no—
412C22×C4×C131—41no—
413C22×C4×C131—41no—
414C22×C4×C131—41no—
415C22×C4×C131—41no—
416C22×C4×C131—41no—
417C22×C4×C131—41no—
418C22×C4×C131—41no—
419C22×C4×C131—41no—
420C22×C4×C131—41no—
421C22×C4×C131—41no—
422C22×C4×C131—41no—
423C22×C4×C131—416no—
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
441C22×C4×C131C2411yescharacteristic
442C22×C4×C131C2411yescharacteristic
443C22×C4×C131C2411yescharacteristic
444C22×C4×C131C2411yescharacteristic
445C22×C4×C131C2411yescharacteristic
446C22×C4×C131C2411yescharacteristic
447C22×C4×C131C2411yescharacteristic
448C22×C4×C131C2411yescharacteristic
449C22×C4×C131C2411yescharacteristic
450C4⋊C4×C131—22no—
451C4⋊C4×C131—22no—
452C4⋊C4×C131—22no—
453C4⋊C4×C131—22no—
454C4⋊C4×C131—22no—
455C4⋊C4×C131—22no—
456C4⋊C4×C131—22no—
457C4⋊C4×C131—22no—
458C4⋊C4×C131—22no—
459C4⋊C4×C131—22no—
460C4⋊C4×C131—22no—
461C4⋊C4×C131—41no—
462C4⋊C4×C131—41no—
463C4⋊C4×C131—41no—
464C4⋊C4×C131—41no—
465C4⋊C4×C131—41no—
466C4⋊C4×C131—41no—
467C4⋊C4×C131—41no—
468C4⋊C4×C131—41no—
469C4⋊C4×C131—41no—
470C4⋊C4×C131—41no—
471C4⋊C4×C131—41no—
472C4⋊C4×C131—41no—
473C4⋊C4×C131—41no—
474C4⋊C4×C131—41no—
475C4⋊C4×C131—41no—
476C4⋊C4×C131—41no—
477C4⋊C4×C131—41no—
478C4⋊C4×C131—41no—
479C4⋊C4×C131—41no—
480C4⋊C4×C131—41no—
481C4⋊C4×C131—41no—
482C4⋊C4×C131—41no—
483C4⋊C4×C131—41no—
484C4⋊C4×C131—41no—
485C4⋊C4×C131—41no—
486C4⋊C4×C131—41no—
487C4⋊C4×C131—41no—
488C22⋊C4×C131—22no—
489C22⋊C4×C131—22no—
490C22⋊C4×C131—22no—
491C22⋊C4×C131—22no—
492C22⋊C4×C131—22no—
493C22⋊C4×C131—22no—
494C22⋊C4×C131—22no—
495C22⋊C4×C131—22no—
496C22⋊C4×C131—22no—
497C22⋊C4×C131—22no—
498C22⋊C4×C131—22no—
499C22⋊C4×C131—22no—
500C22⋊C4×C131—22no—
501C22⋊C4×C131—22no—
502C22⋊C4×C131—22no—
503C22⋊C4×C131—41no—
504C22⋊C4×C131—41no—
505C22⋊C4×C131—41no—
506C22⋊C4×C131—41no—
507C22⋊C4×C131—41no—
508C22⋊C4×C131—41no—
509C22⋊C4×C131—41no—
510C22⋊C4×C131—41no—
511C22⋊C4×C131—41no—
512C22⋊C4×C131—41no—
513C22⋊C4×C131—41no—
514C22⋊C4×C131—41no—
515C22⋊C4×C131—41no—
516C22⋊C4×C131—41no—
517C22⋊C4×C131—41no—
518C22⋊C4×C131—41no—
519C22⋊C4×C131—41no—
520C22⋊C4×C131—41no—
521C22⋊C4×C131—41no—
522C22⋊C4×C131—41no—
523C22⋊C4×C131—41no—
524C22⋊C4×C131—41no—
525C22⋊C4×C131—41no—
526C22⋊C4×C131—41no—
527C22⋊C4×C131—41no—
528C22⋊C4×C131—41no—
529C22⋊C4×C131—41no—
530C22⋊C4×C131—41no—
531C22⋊C4×C131—41no—
532C22⋊C4×C131—41no—
533C22⋊C4×C131—41no—
534C22⋊C4×C131—41no—
535C22⋊C4×C131—41no—
536C22⋊C4×C131—41no—
537C22⋊C4×C131#4114yes—
538C42×C131—22no—
539C42×C131—22no—
540C42×C131—41no—
541C42×C131—41no—
542C42×C131—41no—
543C42×C131—41no—
544C42×C131—41no—
545C42×C131—41no—
546C42×C131—41no—
547C42×C131—41no—
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—21no—
563C23×C131—21no—
564C23×C131—21no—
565C23×C131—21no—
566C23×C131—21no—
567C23×C131—21no—
568C23×C131—21no—
569C23×C131—21no—
570C23×C131—21no—
571C23×C131—21no—
572C23×C131—21no—
573C23×C131—21no—
574C23×C131—21no—
575C23×C131—21no—
576C23×C131—21no—
577C23×C131—21no—
578C23×C131—21no—
579C23×C131—21no—
580C23×C131—44no—
581C23×C131—44no—
582C23×C131—44no—
583C23×C131—44no—
584C23×C131—44no—
585C23×C131—44no—
586C23×C131—44no—
587C23×C131C2×#4112yes—
588C23×C131H(5,𝔽2)12yes—
589C23×C1312−1+412yes—
590C23×C131C2511yescharacteristic
591Q8×C131—82no—
592D4×C131—44no—
593D4×C131—44no—
594D4×C131—44no—
595D4×C131—82no—
596D4×C131—82no—
597D4×C131—82no—
598D4×C131—82no—
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—21no—
648C2×C4×C131—21no—
649C2×C4×C131—21no—
650C2×C4×C131—21no—
651C2×C4×C131—21no—
652C2×C4×C131—21no—
653C2×C4×C131—21no—
654C2×C4×C131—21no—
655C2×C4×C131—21no—
656C2×C4×C131—21no—
657C2×C4×C131—21no—
658C2×C4×C131—21no—
659C2×C4×C131—21no—
660C2×C4×C131—21no—
661C2×C4×C131—21no—
662C2×C4×C131—21no—
663C2×C4×C131—21no—
664C2×C4×C131—21no—
665C2×C4×C131—21no—
666C2×C4×C131—21no—
667C2×C4×C131—21no—
668C2×C4×C131—21no—
669C2×C4×C131—21no—
670C2×C4×C131—21no—
671C2×C4×C131—21no—
672C2×C4×C131—21no—
673C2×C4×C131—44no—
674C2×C4×C131—44no—
675C2×C4×C131—44no—
676C2×C4×C131—44no—
677C2×C4×C131—44no—
678C2×C4×C131—44no—
679C2×C4×C131—82no—
680C2×C4×C131—82no—
681C2×C4×C131C2×#4112yes—
682C2×C4×C131C2×#4112yes—
683C2×C4×C131H(5,𝔽2)12yes—
684C2×C4×C131H(5,𝔽2)12yes—
685C22×C131—22no—
686C22×C131—22no—
687C22×C131—22no—
688C22×C131—22no—
689C22×C131—22no—
690C22×C131—22no—
691C22×C131—22no—
692C22×C131—22no—
693C22×C131—22no—
694C22×C131—416no—
695C22×C131—41no—
696C22×C131—41no—
697C22×C131—41no—
698C22×C131—41no—
699C22×C131—41no—
700C22×C131—41no—
701C22×C131—41no—
702C22×C131—41no—
703C22×C131—41no—
704C22×C131—41no—
705C22×C131—41no—
706C22×C131—41no—
707C22×C131—41no—
708C22×C131—41no—
709C22×C131—41no—
710C22×C131—41no—
711C22×C131—41no—
712C22×C131—41no—
713C22×C131—41no—
714C22×C131—41no—
715C22×C131—41no—
716C22×C131—41no—
717C22×C131—41no—
718C22×C131—41no—
719C22×C131—41no—
720C22×C131—41no—
721C22×C131C22×#4111yescharacteristic
722C22×C131C2×H(5,𝔽2)11yescharacteristic
723C22×C131C2×H(5,𝔽2)11yescharacteristic
724C22×C131C2×H(5,𝔽2)11yescharacteristic
725C22×C131C2×2−1+411yescharacteristic
726C22×C131#58511yescharacteristic
727C22×C131#58511yescharacteristic
728C4×C131—22no—
729C4×C131—22no—
730C4×C131—22no—
731C4×C131—22no—
732C4×C131—41no—
733C4×C131—41no—
734C4×C131—41no—
735C4×C131—41no—
736C4×C131—41no—
737C4×C131—41no—
738C4×C131—41no—
739C4×C131—41no—
740C4×C131—41no—
741C4×C131—41no—
742C4×C131—41no—
743C4×C131—41no—
744C4×C131—41no—
745C4×C131—41no—
746C4×C131—41no—
747C4×C131—41no—
748C4×C131—41no—
749C4×C131—41no—
750C4×C131—41no—
751C4×C131—41no—
752C4×C131—41no—
753C4×C131—41no—
754C2×C131—42no—
755C2×C131—42no—
756C2×C131—42no—
757C2×C131—81no—
758C2×C131—81no—
759C2×C131#346011yescharacteristic
760C2×C131#351311yescharacteristic
761C2×C131#352011yescharacteristic
762C2×C131#353211yescharacteristic
763C2×C131#353511yescharacteristic
764C2×C131#353911yescharacteristic
765C2×C131#354111yescharacteristic
766#36888C13111yesmaximal, characteristic, direct product factor, Sylow
767C131#3688811yescharacteristic, direct product factor, Sylow
768#2849C2×C13111yescharacteristic, complemented
769#2848C2×C13111yescharacteristic, complemented
770#2796C2×C13111yescharacteristic, complemented
771#2790C2×C13111yescharacteristic, complemented
772#2779C2×C13111yescharacteristic, complemented
773#2753C2×C13111yescharacteristic, complemented
774#2748C2×C13111yescharacteristic, complemented
775#2740C2×C13111yescharacteristic, complemented
776#2735C2×C13111yescharacteristic, complemented
777#2730C2×C13111yescharacteristic, complemented
778#2720C2×C13111yescharacteristic, complemented
779#2707C2×C13111yescharacteristic, complemented
780#2698C2×C13111yescharacteristic, complemented
781#2695C2×C13111yescharacteristic, complemented
782#2685C2×C13111yescharacteristic, complemented
783#2685C2×C13111yescharacteristic, complemented
784#2678C2×C13111yescharacteristic
785#2672C2×C13111yescharacteristic, complemented
786#2633C2×C13111yescharacteristic, complemented
787#2630C2×C13111yescharacteristic, complemented
788#2578C2×C13111yescharacteristic, complemented
789#2573C2×C13111yescharacteristic, complemented
790#2558C2×C13111yescharacteristic, complemented
791#2556C2×C13111yescharacteristic, complemented
792#2468C2×C13111yescharacteristic, complemented
793#2461C2×C13111yescharacteristic, complemented
794#2454C2×C13111yescharacteristic, complemented
795#2422C2×C13111yescharacteristic, complemented
796#2335C2×C13111yescharacteristic, complemented
797#2334C2×C13111yescharacteristic, complemented
798C4×#120C2×C13111yescharacteristic, complemented
799C24×C4C22×C13111yescharacteristic
800C2×#126C22×C13111yescharacteristic
801C2×#126C22×C13111yescharacteristic
802C2×#125C22×C13111yescharacteristic, complemented
803C2×#125C22×C13111yescharacteristic, complemented
804C2×#124C22×C13111yescharacteristic, complemented
805C2×#123C22×C13111yescharacteristic
806C2×#123C22×C13111yescharacteristic
807C2×#123C22×C13111yescharacteristic
808C2×#123C22×C13111yescharacteristic, complemented
809C2×C22⋊Q8C22×C13111yescharacteristic
810C2×C22⋊Q8C22×C13111yescharacteristic
811C2×C22⋊Q8C22×C13111yescharacteristic
812C2×#121C22×C13111yescharacteristic
813C2×#120C22×C13111yescharacteristic
814C2×#120C22×C13111yescharacteristic
815C2×C4×D4C22×C13111yescharacteristic
816C2×C4×D4C22×C13111yescharacteristic
817C2×C4×D4C22×C13111yescharacteristic
818#400C22×C13111yescharacteristic, complemented
819#400C22×C13111yescharacteristic, complemented
820#400C22×C13111yescharacteristic, complemented
821#400C22×C13111yescharacteristic, complemented
822#399C22×C13111yescharacteristic
823#399C22×C13111yescharacteristic
824#399C22×C13111yescharacteristic
825#399C22×C13111yescharacteristic, complemented
826#399C22×C13111yescharacteristic, complemented
827#398C22×C13111yescharacteristic, complemented
828#398C22×C13111yescharacteristic, complemented
829#398C22×C13111yescharacteristic, complemented
830#398C22×C13111yescharacteristic, complemented
831#398C22×C13111yescharacteristic, complemented
832#398C22×C13111yescharacteristic, complemented
833#397C22×C13111yescharacteristic
834#397C22×C13111yescharacteristic
835#397C22×C13111yescharacteristic
836#397C22×C13111yescharacteristic
837#397C22×C13111yescharacteristic, complemented
838#397C22×C13111yescharacteristic, complemented
839#397C22×C13111yescharacteristic, complemented
840#397C22×C13111yescharacteristic, complemented
841#396C22×C13111yescharacteristic
842#396C22×C13111yescharacteristic
843#396C22×C13111yescharacteristic
844#396C22×C13111yescharacteristic
845#396C22×C13111yescharacteristic
846#396C22×C13111yescharacteristic, complemented
847#396C22×C13111yescharacteristic, complemented
848#396C22×C13111yescharacteristic, complemented
849#396C22×C13111yescharacteristic, complemented
850#395C22×C13111yescharacteristic, complemented
851#395C22×C13111yescharacteristic, complemented
852#394C22×C13111yescharacteristic
853#394C22×C13111yescharacteristic
854#394C22×C13111yescharacteristic
855#394C22×C13111yescharacteristic
856#394C22×C13111yescharacteristic
857#394C22×C13111yescharacteristic
858#394C22×C13111yescharacteristic
859#394C22×C13111yescharacteristic
860#394C22×C13111yescharacteristic
861#394C22×C13111yescharacteristic
862#394C22×C13111yescharacteristic, complemented
863#394C22×C13111yescharacteristic, complemented
864#392C22×C13111yescharacteristic
865#392C22×C13111yescharacteristic
866#391C22×C13111yescharacteristic, complemented
867#390C22×C13111yescharacteristic
868#390C22×C13111yescharacteristic
869#390C22×C13111yescharacteristic
870#390C22×C13111yescharacteristic
871#390C22×C13111yescharacteristic
872#390C22×C13111yescharacteristic
873#389C22×C13111yescharacteristic, complemented
874#389C22×C13111yescharacteristic, complemented
875#389C22×C13111yescharacteristic, complemented
876#389C22×C13111yescharacteristic, complemented
877#389C22×C13111yescharacteristic, complemented
878#389C22×C13111yescharacteristic, complemented
879#388C22×C13111yescharacteristic
880#388C22×C13111yescharacteristic
881#388C22×C13111yescharacteristic
882#388C22×C13111yescharacteristic
883#388C22×C13111yescharacteristic
884#388C22×C13111yescharacteristic
885#388C22×C13111yescharacteristic
886#388C22×C13111yescharacteristic
887#388C22×C13111yescharacteristic
888#388C22×C13111yescharacteristic
889#388C22×C13111yescharacteristic
890#388C22×C13111yescharacteristic
891#388C22×C13111yescharacteristic
892#388C22×C13111yescharacteristic, complemented
893#388C22×C13111yescharacteristic, complemented
894#388C22×C13111yescharacteristic, complemented
895#388C22×C13111yescharacteristic, complemented
896#388C22×C13111yescharacteristic, complemented
897#388C22×C13111yescharacteristic, complemented
898#388C22×C13111yescharacteristic, complemented
899#387C22×C13111yescharacteristic, complemented
900#387C22×C13111yescharacteristic, complemented
901#387C22×C13111yescharacteristic, complemented
902#387C22×C13111yescharacteristic, complemented
903#387C22×C13111yescharacteristic, complemented
904#387C22×C13111yescharacteristic, complemented
905#387C22×C13111yescharacteristic, complemented
906#387C22×C13111yescharacteristic, complemented
907#387C22×C13111yescharacteristic, complemented
908#386C22×C13111yescharacteristic
909#386C22×C13111yescharacteristic
910#386C22×C13111yescharacteristic
911#386C22×C13111yescharacteristic
912#386C22×C13111yescharacteristic
913#386C22×C13111yescharacteristic
914#386C22×C13111yescharacteristic
915#386C22×C13111yescharacteristic
916#385C22×C13111yescharacteristic
917#385C22×C13111yescharacteristic
918#385C22×C13111yescharacteristic
919#385C22×C13111yescharacteristic
920#385C22×C13111yescharacteristic
921#385C22×C13111yescharacteristic
922#385C22×C13111yescharacteristic
923#385C22×C13111yescharacteristic
924#385C22×C13111yescharacteristic
925#385C22×C13111yescharacteristic
926#385C22×C13111yescharacteristic
927#385C22×C13111yescharacteristic
928#385C22×C13111yescharacteristic
929#385C22×C13111yescharacteristic, complemented
930#385C22×C13111yescharacteristic, complemented
931#385C22×C13111yescharacteristic, complemented
932#384C22×C13111yescharacteristic, complemented
933#383C22×C13111yescharacteristic, complemented
934#382C22×C13111yescharacteristic, complemented
935#381C22×C13111yescharacteristic
936#381C22×C13111yescharacteristic
937#380C22×C13111yescharacteristic
938#380C22×C13111yescharacteristic
939#380C22×C13111yescharacteristic
940#380C22×C13111yescharacteristic, complemented
941#380C22×C13111yescharacteristic, complemented
942#380C22×C13111yescharacteristic, complemented
943#379C22×C13111yescharacteristic
944#379C22×C13111yescharacteristic
945#379C22×C13111yescharacteristic
946#379C22×C13111yescharacteristic
947C4×C4⋊C4C22×C13111yescharacteristic, complemented
948C4×C4⋊C4C22×C13111yescharacteristic, complemented
949C4×C4⋊C4C22×C13111yescharacteristic, complemented
950C4×C22⋊C4C22×C13111yescharacteristic
951C4×C22⋊C4C22×C13111yescharacteristic
952C4×C22⋊C4C22×C13111yescharacteristic
953C4×C22⋊C4C22×C13111yescharacteristic, complemented
954C25C23×C13111yescharacteristic
955C22×Q8C23×C13111yescharacteristic
956C22×D4C23×C13111yescharacteristic
957C22×D4C23×C13111yescharacteristic
958C22×D4C23×C13111yescharacteristic
959C22×D4C23×C13111yescharacteristic
960C22×D4C23×C13111yescharacteristic
961C22×D4C23×C13111yescharacteristic
962C22×D4C23×C13111yescharacteristic
963C23×C4—42no—
964C23×C4—42no—
965C23×C4—42no—
966C23×C4C23×C13111yescharacteristic
967C23×C4C23×C13111yescharacteristic
968C23×C4C23×C13111yescharacteristic
969C23×C4C23×C13111yescharacteristic
970C23×C4C23×C13111yescharacteristic
971C23×C4C23×C13111yescharacteristic
972C23×C4C23×C13111yescharacteristic
973C23×C4C23×C13111yescharacteristic
974#126—24no—
975#126—42no—
976#125—42no—
977#125—42no—
978#124—42no—
979#123—24no—
980#123—42no—
981#123—42no—
982#123—42no—
983C22⋊Q8—42no—
984C22⋊Q8—42no—
985C22⋊Q8—42no—
986#121—42no—
987#120—24no—
988#120—42no—
989C4×D4—42no—
990C4×D4—42no—
991C4×D4—42no—
992C2×C4⋊C4C23×C13111yescharacteristic
993C2×C4⋊C4C23×C13111yescharacteristic
994C2×C4⋊C4C23×C13111yescharacteristic
995C2×C4⋊C4C23×C13111yescharacteristic
996C2×C4⋊C4C23×C13111yescharacteristic
997C2×C4⋊C4C23×C13111yescharacteristic
998C2×C4⋊C4C23×C13111yescharacteristic
999C2×C4⋊C4C23×C13111yescharacteristic
1000C2×C4⋊C4C23×C13111yescharacteristic
1001C2×C4⋊C4C23×C13111yescharacteristic
1002C2×C4⋊C4C23×C13111yescharacteristic
1003C2×C4⋊C4C23×C13111yescharacteristic
1004C2×C4⋊C4C23×C13111yescharacteristic
1005C2×C4⋊C4C23×C13111yescharacteristic
1006C2×C4⋊C4C23×C13111yescharacteristic
1007C2×C4⋊C4C23×C13111yescharacteristic
1008C2×C4⋊C4C23×C13111yescharacteristic
1009C2×C4⋊C4C23×C13111yescharacteristic
1010C2×C4⋊C4C23×C13111yescharacteristic
1011C2×C4⋊C4C23×C13111yescharacteristic
1012C2×C4⋊C4C23×C13111yescharacteristic
1013C2×C4⋊C4C23×C13111yescharacteristic
1014C2×C4⋊C4C23×C13111yescharacteristic
1015C2×C4⋊C4C23×C13111yescharacteristic
1016C2×C4⋊C4C23×C13111yescharacteristic
1017C2×C4⋊C4C23×C13111yescharacteristic
1018C2×C4⋊C4C23×C13111yescharacteristic
1019C2×C4⋊C4C23×C13111yescharacteristic
1020C2×C4⋊C4C23×C13111yescharacteristic
1021C2×C4⋊C4C23×C13111yescharacteristic
1022C2×C4⋊C4C23×C13111yescharacteristic
1023C2×C4⋊C4C23×C13111yescharacteristic
1024C2×C4⋊C4C23×C13111yescharacteristic
1025C2×C4⋊C4C23×C13111yescharacteristic
1026C2×C4⋊C4C23×C13111yescharacteristic
1027C2×C4⋊C4C23×C13111yescharacteristic
1028C2×C4⋊C4C23×C13111yescharacteristic
1029C2×C4⋊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×C22⋊C4C23×C13111yescharacteristic
1039C2×C22⋊C4C23×C13111yescharacteristic
1040C2×C22⋊C4C23×C13111yescharacteristic
1041C2×C22⋊C4C23×C13111yescharacteristic
1042C2×C22⋊C4C23×C13111yescharacteristic
1043C2×C22⋊C4C23×C13111yescharacteristic
1044C2×C22⋊C4C23×C13111yescharacteristic
1045C2×C22⋊C4C23×C13111yescharacteristic
1046C2×C22⋊C4C23×C13111yescharacteristic
1047C2×C22⋊C4C23×C13111yescharacteristic
1048C2×C22⋊C4C23×C13111yescharacteristic
1049C2×C22⋊C4C23×C13111yescharacteristic
1050C2×C22⋊C4C23×C13111yescharacteristic
1051C2×C22⋊C4C23×C13111yescharacteristic
1052C2×C22⋊C4C23×C13111yescharacteristic
1053C2×C22⋊C4C23×C13111yescharacteristic
1054C2×C22⋊C4C23×C13111yescharacteristic
1055C2×C22⋊C4C23×C13111yescharacteristic
1056C2×C22⋊C4C23×C13111yescharacteristic
1057C2×C22⋊C4C23×C13111yescharacteristic
1058C2×C22⋊C4C23×C13111yescharacteristic
1059C2×C22⋊C4C23×C13111yescharacteristic
1060C2×C22⋊C4C23×C13111yescharacteristic
1061C2×C22⋊C4C23×C13111yescharacteristic
1062C2×C22⋊C4C23×C13111yescharacteristic
1063C2×C22⋊C4C23×C13111yescharacteristic
1064C2×C22⋊C4C23×C13111yescharacteristic
1065C2×C22⋊C4C23×C13111yescharacteristic
1066C2×C22⋊C4C23×C13111yescharacteristic
1067C2×C22⋊C4C23×C13111yescharacteristic
1068C2×C22⋊C4C23×C13111yescharacteristic
1069C2×C22⋊C4C23×C13111yescharacteristic
1070C2×C22⋊C4C23×C13111yescharacteristic
1071C2×C22⋊C4C23×C13111yescharacteristic
1072C2×C22⋊C4C23×C13111yescharacteristic
1073C2×C22⋊C4C23×C13111yescharacteristic
1074C2×C22⋊C4C23×C13111yescharacteristic
1075C2×C22⋊C4C23×C13111yescharacteristic
1076C2×C22⋊C4C23×C13111yescharacteristic
1077C2×C22⋊C4C23×C13111yescharacteristic
1078C2×C22⋊C4C23×C13111yescharacteristic
1079C2×C22⋊C4C23×C13111yescharacteristic
1080C2×C42C23×C13111yescharacteristic
1081C2×C42C23×C13111yescharacteristic
1082C2×C42C23×C13111yescharacteristic
1083C2×C42C23×C13111yescharacteristic
1084C2×C42C23×C13111yescharacteristic
1085C2×C42C23×C13111yescharacteristic
1086C2×C42C23×C13111yescharacteristic
1087C2×C42C23×C13111yescharacteristic
1088C2×C42C23×C13111yescharacteristic
1089C2×C42C23×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
1107#95C23×C13111yescharacteristic
1108#95C23×C13111yescharacteristic
1109#95C23×C13111yescharacteristic
1110#95C23×C13111yescharacteristic
1111#95C23×C13111yescharacteristic
1112#95C23×C13111yescharacteristic
1113#95C23×C13111yescharacteristic
1114#95C23×C13111yescharacteristic
1115#95C23×C13111yescharacteristic
1116#95C23×C13111yescharacteristic
1117#95C23×C13111yescharacteristic
1118#95C23×C13111yescharacteristic
1119#95C23×C13111yescharacteristic
1120#95C23×C13111yescharacteristic
1121#95C23×C13111yescharacteristic
1122#95C23×C13111yescharacteristic
1123#95C23×C13111yescharacteristic
1124#95C23×C13111yescharacteristic
1125#95C23×C13111yescharacteristic
1126#95C23×C13111yescharacteristic
1127#95C23×C13111yescharacteristic
1128#95C23×C13111yescharacteristic
1129#95C23×C13111yescharacteristic
1130C24—22no—
1131C24—22no—
1132C24—22no—
1133C24—41no—
1134C24—41no—
1135C24—41no—
1136C24—41no—
1137C24C24×C13111yescharacteristic
1138C24C24×C13111yescharacteristic
1139C24C24×C13111yescharacteristic
1140C24C24×C13111yescharacteristic
1141C24C24×C13111yescharacteristic
1142C2×Q8—22no—
1143C2×Q8—41no—
1144C2×Q8—41no—
1145C2×D4—22no—
1146C2×D4—22no—
1147C2×D4—22no—
1148C2×D4—22no—
1149C2×D4—22no—
1150C2×D4—22no—
1151C2×D4—22no—
1152C2×D4—22no—
1153C2×D4—41no—
1154C2×D4—41no—
1155C2×D4—41no—
1156C2×D4—41no—
1157C2×D4—41no—
1158C2×D4—41no—
1159C2×D4—41no—
1160C2×D4—41no—
1161C2×D4—41no—
1162C2×D4—41no—
1163C2×D4—41no—
1164C2×D4—41no—
1165C2×D4—41no—
1166C22×C4—22no—
1167C22×C4—22no—
1168C22×C4—22no—
1169C22×C4—22no—
1170C22×C4—22no—
1171C22×C4—22no—
1172C22×C4—22no—
1173C22×C4—22no—
1174C22×C4—22no—
1175C22×C4—22no—
1176C22×C4—41no—
1177C22×C4—41no—
1178C22×C4—41no—
1179C22×C4—41no—
1180C22×C4—41no—
1181C22×C4—41no—
1182C22×C4—41no—
1183C22×C4—41no—
1184C22×C4—41no—
1185C22×C4—41no—
1186C22×C4—41no—
1187C22×C4—41no—
1188C22×C4—41no—
1189C22×C4—41no—
1190C22×C4—416no—
1191C22×C4C24×C13111yescharacteristic
1192C22×C4C24×C13111yescharacteristic
1193C22×C4C24×C13111yescharacteristic
1194C22×C4C24×C13111yescharacteristic
1195C22×C4C24×C13111yescharacteristic
1196C22×C4C24×C13111yescharacteristic
1197C22×C4C24×C13111yescharacteristic
1198C22×C4C24×C13111yescharacteristic
1199C22×C4C24×C13111yescharacteristic
1200C22×C4C24×C13111yescharacteristic
1201C22×C4C24×C13111yescharacteristic
1202C22×C4C24×C13111yescharacteristic
1203C22×C4C24×C13111yescharacteristic
1204C22×C4C24×C13111yescharacteristic
1205C22×C4C24×C13111yescharacteristic
1206C22×C4C24×C13111yescharacteristic
1207C22×C4C24×C13111yescharacteristic
1208C22×C4C24×C13111yescharacteristic
1209C22×C4C24×C13111yescharacteristic
1210C22×C4C24×C13111yescharacteristic
1211C22×C4C24×C13111yescharacteristic
1212C22×C4C24×C13111yescharacteristic
1213C22×C4C24×C13111yescharacteristic
1214C22×C4C24×C13111yescharacteristic
1215C22×C4C24×C13111yescharacteristic
1216C22×C4C24×C13111yescharacteristic
1217C4⋊C4—22no—
1218C4⋊C4—22no—
1219C4⋊C4—22no—
1220C4⋊C4—22no—
1221C4⋊C4—22no—
1222C4⋊C4—22no—
1223C4⋊C4—22no—
1224C4⋊C4—22no—
1225C4⋊C4—22no—
1226C4⋊C4—22no—
1227C4⋊C4—22no—
1228C4⋊C4—41no—
1229C4⋊C4—41no—
1230C4⋊C4—41no—
1231C4⋊C4—41no—
1232C4⋊C4—41no—
1233C4⋊C4—41no—
1234C4⋊C4—41no—
1235C4⋊C4—41no—
1236C4⋊C4—41no—
1237C4⋊C4—41no—
1238C4⋊C4—41no—
1239C4⋊C4—41no—
1240C4⋊C4—41no—
1241C4⋊C4—41no—
1242C4⋊C4—41no—
1243C4⋊C4—41no—
1244C4⋊C4—41no—
1245C4⋊C4—41no—
1246C4⋊C4—41no—
1247C4⋊C4—41no—
1248C4⋊C4—41no—
1249C4⋊C4—41no—
1250C4⋊C4—41no—
1251C4⋊C4—41no—
1252C4⋊C4—41no—
1253C4⋊C4—41no—
1254C4⋊C4—41no—
1255C22⋊C4—22no—
1256C22⋊C4—22no—
1257C22⋊C4—22no—
1258C22⋊C4—22no—
1259C22⋊C4—22no—
1260C22⋊C4—22no—
1261C22⋊C4—22no—
1262C22⋊C4—22no—
1263C22⋊C4—22no—
1264C22⋊C4—22no—
1265C22⋊C4—22no—
1266C22⋊C4—22no—
1267C22⋊C4—22no—
1268C22⋊C4—22no—
1269C22⋊C4—22no—
1270C22⋊C4—41no—
1271C22⋊C4—41no—
1272C22⋊C4—41no—
1273C22⋊C4—41no—
1274C22⋊C4—41no—
1275C22⋊C4—41no—
1276C22⋊C4—41no—
1277C22⋊C4—41no—
1278C22⋊C4—41no—
1279C22⋊C4—41no—
1280C22⋊C4—41no—
1281C22⋊C4—41no—
1282C22⋊C4—41no—
1283C22⋊C4—41no—
1284C22⋊C4—41no—
1285C22⋊C4—41no—
1286C22⋊C4—41no—
1287C22⋊C4—41no—
1288C22⋊C4—41no—
1289C22⋊C4—41no—
1290C22⋊C4—41no—
1291C22⋊C4—41no—
1292C22⋊C4—41no—
1293C22⋊C4—41no—
1294C22⋊C4—41no—
1295C22⋊C4—41no—
1296C22⋊C4—41no—
1297C22⋊C4—41no—
1298C22⋊C4—41no—
1299C22⋊C4—41no—
1300C22⋊C4—41no—
1301C22⋊C4—41no—
1302C22⋊C4—41no—
1303C22⋊C4—41no—
1304C22⋊C4#41×C13114yes—
1305C42—22no—
1306C42—22no—
1307C42—41no—
1308C42—41no—
1309C42—41no—
1310C42—41no—
1311C42—41no—
1312C42—41no—
1313C42—41no—
1314C42—41no—
1315C23—21no—
1316C23—21no—
1317C23—21no—
1318C23—21no—
1319C23—21no—
1320C23—21no—
1321C23—21no—
1322C23—21no—
1323C23—21no—
1324C23—21no—
1325C23—21no—
1326C23—21no—
1327C23—21no—
1328C23—21no—
1329C23—21no—
1330C23—21no—
1331C23—21no—
1332C23—21no—
1333C23—21no—
1334C23—21no—
1335C23—21no—
1336C23—21no—
1337C23—21no—
1338C23—21no—
1339C23—21no—
1340C23—21no—
1341C23—21no—
1342C23—21no—
1343C23—21no—
1344C23—21no—
1345C23—21no—
1346C23—21no—
1347C23—44no—
1348C23—44no—
1349C23—44no—
1350C23—44no—
1351C23—44no—
1352C23—44no—
1353C23—44no—
1354C23C2×#41×C13112yes—
1355C23H(5,𝔽2)×C13112yes—
1356C232−1+4×C13112yes—
1357C23C25×C13111yescharacteristic
1358Q8—82no—
1359D4—44no—
1360D4—44no—
1361D4—44no—
1362D4—82no—
1363D4—82no—
1364D4—82no—
1365D4—82no—
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—21no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—44no—
1441C2×C4—44no—
1442C2×C4—44no—
1443C2×C4—44no—
1444C2×C4—44no—
1445C2×C4—44no—
1446C2×C4—82no—
1447C2×C4—82no—
1448C2×C4C2×#41×C13112yes—
1449C2×C4C2×#41×C13112yes—
1450C2×C4H(5,𝔽2)×C13112yes—
1451C2×C4H(5,𝔽2)×C13112yes—
1452C22—22no—
1453C22—22no—
1454C22—22no—
1455C22—22no—
1456C22—22no—
1457C22—22no—
1458C22—22no—
1459C22—22no—
1460C22—22no—
1461C22—416no—
1462C22—41no—
1463C22—41no—
1464C22—41no—
1465C22—41no—
1466C22—41no—
1467C22—41no—
1468C22—41no—
1469C22—41no—
1470C22—41no—
1471C22—41no—
1472C22—41no—
1473C22—41no—
1474C22—41no—
1475C22—41no—
1476C22—41no—
1477C22—41no—
1478C22—41no—
1479C22—41no—
1480C22—41no—
1481C22—41no—
1482C22—41no—
1483C22—41no—
1484C22—41no—
1485C22—41no—
1486C22—41no—
1487C22—41no—
1488C22C22×#41×C13111yescharacteristic
1489C22C2×H(5,𝔽2)×C13111yescharacteristic
1490C22C2×H(5,𝔽2)×C13111yescharacteristic
1491C22C2×H(5,𝔽2)×C13111yescharacteristic
1492C22C2×2−1+4×C13111yescharacteristic
1493C22#585×C13111yescharacteristic
1494C22#585×C13111yescharacteristic
1495C4—22no—
1496C4—22no—
1497C4—22no—
1498C4—22no—
1499C4—41no—
1500C4—41no—
1501C4—41no—
1502C4—41no—
1503C4—41no—
1504C4—41no—
1505C4—41no—
1506C4—41no—
1507C4—41no—
1508C4—41no—
1509C4—41no—
1510C4—41no—
1511C4—41no—
1512C4—41no—
1513C4—41no—
1514C4—41no—
1515C4—41no—
1516C4—41no—
1517C4—41no—
1518C4—41no—
1519C4—41no—
1520C4—41no—
1521C2—42no—
1522C2—42no—
1523C2—42no—
1524C2—81no—
1525C2—81no—
1526C2#3460×C13111yescharacteristic
1527C2#3513×C13111yescharacteristic
1528C2#3520×C13111yescharacteristic
1529C2#3532×C13111yescharacteristic
1530C2#3535×C13111yescharacteristic
1531C2#3539×C13111yescharacteristic
1532C2#3541×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C25
commutator, Frattini, cosocleC23C25×C131
prime radical#2678×C131C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2849×C131C2semidirect
2. #2848×C131C2semidirect
3. #2796×C131C2semidirect
4. #2790×C131C2semidirect
5. #2779×C131C2semidirect
6. #2753×C131C2semidirect
7. #2748×C131C2semidirect
8. #2740×C131C2semidirect
9. #2735×C131C2semidirect
10. #2730×C131C2semidirect
11. #2720×C131C2semidirect
12. #2707×C131C2semidirect
13. #2698×C131C2semidirect
14. #2695×C131C2semidirect
15. #2685×C131C2semidirect
16. #2685×C131C2semidirect
18. #2672×C131C2semidirect
19. #2633×C131C2semidirect
20. #2630×C131C2semidirect
21. #2578×C131C2semidirect
22. #2573×C131C2semidirect
23. #2558×C131C2semidirect
24. #2556×C131C2semidirect
25. #2468×C131C2semidirect
26. #2461×C131C2semidirect
27. #2454×C131C2semidirect
28. #2422×C131C2semidirect
29. #2335×C131C2semidirect
30. #2334×C131C2semidirect
31. C4×#120×C131C2semidirect
35. C2×#125×C131C22semidirect
36. C2×#125×C131C22semidirect
37. C2×#124×C131C22semidirect
41. C2×#123×C131C22semidirect
51. #400×C131C22semidirect
52. #400×C131C22semidirect
53. #400×C131C22semidirect
54. #400×C131C22semidirect
58. #399×C131C22semidirect
59. #399×C131C22semidirect
60. #398×C131C22semidirect
61. #398×C131C22semidirect
62. #398×C131C22semidirect
63. #398×C131C22semidirect
64. #398×C131C22semidirect
65. #398×C131C22semidirect
70. #397×C131C22semidirect
71. #397×C131C22semidirect
72. #397×C131C22semidirect
73. #397×C131C22semidirect
79. #396×C131C22semidirect
80. #396×C131C22semidirect
81. #396×C131C22semidirect
82. #396×C131C22semidirect
83. #395×C131C22semidirect
84. #395×C131C22semidirect
95. #394×C131C22semidirect
96. #394×C131C22semidirect
99. #391×C131C22semidirect
106. #389×C131C22semidirect
107. #389×C131C22semidirect
108. #389×C131C22semidirect
109. #389×C131C22semidirect
110. #389×C131C22semidirect
111. #389×C131C22semidirect
125. #388×C131C22semidirect
126. #388×C131C22semidirect
127. #388×C131C22semidirect
128. #388×C131C22semidirect
129. #388×C131C22semidirect
130. #388×C131C22semidirect
131. #388×C131C22semidirect
132. #387×C131C22semidirect
133. #387×C131C22semidirect
134. #387×C131C22semidirect
135. #387×C131C22semidirect
136. #387×C131C22semidirect
137. #387×C131C22semidirect
138. #387×C131C22semidirect
139. #387×C131C22semidirect
140. #387×C131C22semidirect
162. #385×C131C22semidirect
163. #385×C131C22semidirect
164. #385×C131C22semidirect
165. #384×C131C22semidirect
166. #383×C131C22semidirect
167. #382×C131C22semidirect
173. #380×C131C22semidirect
174. #380×C131C22semidirect
175. #380×C131C22semidirect
180. C4×C4⋊C4×C131C22semidirect
181. C4×C4⋊C4×C131C22semidirect
182. C4×C4⋊C4×C131C22semidirect
186. C4×C22⋊C4×C131C22semidirect
766. #36888C131direct (N × H)
767. C131#36888direct (N × H)
768. #2849C2×C131semidirect
769. #2848C2×C131semidirect
770. #2796C2×C131semidirect
771. #2790C2×C131semidirect
772. #2779C2×C131semidirect
773. #2753C2×C131semidirect
774. #2748C2×C131semidirect
775. #2740C2×C131semidirect
776. #2735C2×C131semidirect
777. #2730C2×C131semidirect
778. #2720C2×C131semidirect
779. #2707C2×C131semidirect
780. #2698C2×C131semidirect
781. #2695C2×C131semidirect
782. #2685C2×C131semidirect
783. #2685C2×C131semidirect
785. #2672C2×C131semidirect
786. #2633C2×C131semidirect
787. #2630C2×C131semidirect
788. #2578C2×C131semidirect
789. #2573C2×C131semidirect
790. #2558C2×C131semidirect
791. #2556C2×C131semidirect
792. #2468C2×C131semidirect
793. #2461C2×C131semidirect
794. #2454C2×C131semidirect
795. #2422C2×C131semidirect
796. #2335C2×C131semidirect
797. #2334C2×C131semidirect
798. C4×#120C2×C131semidirect
802. C2×#125C22×C131semidirect
803. C2×#125C22×C131semidirect
804. C2×#124C22×C131semidirect
808. C2×#123C22×C131semidirect
818. #400C22×C131semidirect
819. #400C22×C131semidirect
820. #400C22×C131semidirect
821. #400C22×C131semidirect
825. #399C22×C131semidirect
826. #399C22×C131semidirect
827. #398C22×C131semidirect
828. #398C22×C131semidirect
829. #398C22×C131semidirect
830. #398C22×C131semidirect
831. #398C22×C131semidirect
832. #398C22×C131semidirect
837. #397C22×C131semidirect
838. #397C22×C131semidirect
839. #397C22×C131semidirect
840. #397C22×C131semidirect
846. #396C22×C131semidirect
847. #396C22×C131semidirect
848. #396C22×C131semidirect
849. #396C22×C131semidirect
850. #395C22×C131semidirect
851. #395C22×C131semidirect
862. #394C22×C131semidirect
863. #394C22×C131semidirect
866. #391C22×C131semidirect
873. #389C22×C131semidirect
874. #389C22×C131semidirect
875. #389C22×C131semidirect
876. #389C22×C131semidirect
877. #389C22×C131semidirect
878. #389C22×C131semidirect
892. #388C22×C131semidirect
893. #388C22×C131semidirect
894. #388C22×C131semidirect
895. #388C22×C131semidirect
896. #388C22×C131semidirect
897. #388C22×C131semidirect
898. #388C22×C131semidirect
899. #387C22×C131semidirect
900. #387C22×C131semidirect
901. #387C22×C131semidirect
902. #387C22×C131semidirect
903. #387C22×C131semidirect
904. #387C22×C131semidirect
905. #387C22×C131semidirect
906. #387C22×C131semidirect
907. #387C22×C131semidirect
929. #385C22×C131semidirect
930. #385C22×C131semidirect
931. #385C22×C131semidirect
932. #384C22×C131semidirect
933. #383C22×C131semidirect
934. #382C22×C131semidirect
940. #380C22×C131semidirect
941. #380C22×C131semidirect
942. #380C22×C131semidirect
947. C4×C4⋊C4C22×C131semidirect
948. C4×C4⋊C4C22×C131semidirect
949. C4×C4⋊C4C22×C131semidirect
953. C4×C22⋊C4C22×C131semidirect

Maximal subgroups

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

subgroupindex
#2849×C1312
#2848×C1312
#2796×C1312
#2790×C1312
#2779×C1312
#2753×C1312
#2748×C1312
#2740×C1312
#2735×C1312
#2730×C1312
#2720×C1312
#2707×C1312
#2698×C1312
#2695×C1312
#2685×C1312
#2678×C1312
#2672×C1312
#2633×C1312
#2630×C1312
#2578×C1312
#2573×C1312
#2558×C1312
#2556×C1312
#2468×C1312
#2461×C1312
#2454×C1312
#2422×C1312
#2335×C1312
#2334×C1312
C4×#120×C1312
#36888131