Finite Group Databasebeta

← D13×#2655 #16029558

Subgroups — D13×#2655 #16029558

Order 3328.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13120936C211yesmaximal, characteristic, complemented
2#13120935C211yesmaximal, characteristic, complemented
3#13120934C211yesmaximal, characteristic, complemented
4#13120933C211yesmaximal, characteristic, complemented
5#13120932C211yesmaximal, characteristic, complemented
6#13120931C211yesmaximal, characteristic, complemented
7#13120930C211yesmaximal, characteristic, complemented
8#13120929C211yesmaximal, characteristic, complemented
9#13120928C211yesmaximal, characteristic, complemented
10#13120927C211yesmaximal, characteristic, complemented
11#13120926C211yesmaximal, characteristic, complemented
12#13120925C211yesmaximal, characteristic, complemented
13#13120924C211yesmaximal, characteristic, complemented
14#13120923C211yesmaximal, characteristic, complemented
15#13120922C211yesmaximal, characteristic, complemented
16D13×#401C211yesmaximal, characteristic
17D13×#400C211yesmaximal, characteristic
18D13×#400C211yesmaximal, characteristic
19D13×#400C211yesmaximal, characteristic
20D13×#400C211yesmaximal, characteristic
21D13×#398C211yesmaximal, characteristic
22D13×#398C211yesmaximal, characteristic
23D13×#398C211yesmaximal, characteristic
24D13×#389C211yesmaximal, characteristic
25D13×#387C211yesmaximal, characteristic
26D13×#387C211yesmaximal, characteristic
27D13×#387C211yesmaximal, characteristic
28D13×#387C211yesmaximal, characteristic
29D13×#387C211yesmaximal, characteristic
30C4×C4⋊C4×D13C211yesmaximal, characteristic
31C13×#2655C211yesmaximal, characteristic, complemented
32C2×C4⋊C4×D13C2211yescharacteristic
33C2×C4⋊C4×D13C2211yescharacteristic
34C2×C4⋊C4×D13C2211yescharacteristic
35C2×C4⋊C4×D13C2211yescharacteristic
36C2×C4⋊C4×D13C2211yescharacteristic
37C2×C4⋊C4×D13C2211yescharacteristic
38C2×C4⋊C4×D13C2211yescharacteristic
39C2×C4⋊C4×D13C2211yescharacteristic
40C2×C4⋊C4×D13C2211yescharacteristic
41C2×C4⋊C4×D13C2211yescharacteristic
42C2×C4⋊C4×D13C2211yescharacteristic
43C2×C4⋊C4×D13C2211yescharacteristic
44C2×C42×D13C2211yescharacteristic
45C2×C42×D13C2211yescharacteristic
46C2×C42×D13C2211yescharacteristic
47C13×#401C2211yescharacteristic
48C13×#400C2211yescharacteristic
49C13×#400C2211yescharacteristic
50C13×#400C2211yescharacteristic
51C13×#400C2211yescharacteristic
52C13×#398C2211yescharacteristic
53C13×#398C2211yescharacteristic
54C13×#398C2211yescharacteristic
55C13×#389C2211yescharacteristic
56C13×#387C2211yescharacteristic
57C13×#387C2211yescharacteristic
58C13×#387C2211yescharacteristic
59C13×#387C2211yescharacteristic
60C13×#387C2211yescharacteristic
61C4×C13×C4⋊C4C2211yescharacteristic
62#11718647C2211yescharacteristic
63#11718647C2211yescharacteristic
64#11718647C2211yescharacteristic
65#11718647C2211yescharacteristic
66#11718646C2211yescharacteristic
67#11718645C2211yescharacteristic
68#11718645C2211yescharacteristic
69#11718645C2211yescharacteristic
70#11718645C2211yescharacteristic
71#11718645C2211yescharacteristic
72#11718645C2211yescharacteristic
73#11718644C2211yescharacteristic
74#11718644C2211yescharacteristic
75#11718644C2211yescharacteristic
76#11718643C2211yescharacteristic
77#11718643C2211yescharacteristic
78#11718643C2211yescharacteristic
79#11718643C2211yescharacteristic
80#11718642C2211yescharacteristic
81#11718642C2211yescharacteristic
82#11718642C2211yescharacteristic
83#11718642C2211yescharacteristic
84#11718642C2211yescharacteristic
85#11718641C2211yescharacteristic
86#11718641C2211yescharacteristic
87#11718641C2211yescharacteristic
88#11718639C2211yescharacteristic
89#11718639C2211yescharacteristic
90#11718639C2211yescharacteristic
91#11718639C2211yescharacteristic
92#11718639C2211yescharacteristic
93C4⋊C4×Dic13C2211yescharacteristic
94C4⋊C4×Dic13C2211yescharacteristic
95#11718634C2211yescharacteristic
96#11718633C2211yescharacteristic
97#11718633C2211yescharacteristic
98C4×C4⋊Dic13C2211yescharacteristic
99#11718594C2211yescharacteristic
100#11718594C2211yescharacteristic
101#11718594C2211yescharacteristic
102#11718594C2211yescharacteristic
103#11718594C2211yescharacteristic
104C4×#6101C2211yescharacteristic
105C4×#6101C2211yescharacteristic
106#11718589C2211yescharacteristic
107D13×#95C2211yescharacteristic
108D13×#95C2211yescharacteristic
109D13×#95C2211yescharacteristic
110D13×#95C2211yescharacteristic
111D13×#95C2211yescharacteristic
112D13×#95C2211yescharacteristic
113D13×#95C2211yescharacteristic
114D13×#95C2211yescharacteristic
115D13×#95C2211yescharacteristic
116D13×#95C2211yescharacteristic
117D13×#95C2211yescharacteristic
118D13×#95C2211yescharacteristic
119D13×#95C2211yescharacteristic
120D13×#95C2211yescharacteristic
121D13×#95C2211yescharacteristic
122D13×#95C2211yescharacteristic
123D13×#95C2211yescharacteristic
124D13×#95C2211yescharacteristic
125D13×#95C2211yescharacteristic
126D13×#95C2211yescharacteristic
127C13⋊#401C2211yescharacteristic
128C13⋊#401C2211yescharacteristic
129C13⋊#401C2211yescharacteristic
130C13⋊#401C2211yescharacteristic
131C13⋊#401C2211yescharacteristic
132C13⋊#401C2211yescharacteristic
133C13⋊#401C2211yescharacteristic
134#11718322C2211yescharacteristic
135#11718322C2211yescharacteristic
136#11718322C2211yescharacteristic
137#11718321C2211yescharacteristic
138#11718321C2211yescharacteristic
139#11718321C2211yescharacteristic
140#11718321C2211yescharacteristic
141#11718321C2211yescharacteristic
142#11718321C2211yescharacteristic
143#11718321C2211yescharacteristic
144#11718321C2211yescharacteristic
145#11718320C2211yescharacteristic
146#11718320C2211yescharacteristic
147#11718320C2211yescharacteristic
148#11718320C2211yescharacteristic
149#11718319C2211yescharacteristic
150#11718319C2211yescharacteristic
151#11718319C2211yescharacteristic
152#11718319C2211yescharacteristic
153#11718319C2211yescharacteristic
154#11718319C2211yescharacteristic
155#11718319C2211yescharacteristic
156#11718319C2211yescharacteristic
157#11718318C2211yescharacteristic
158#11718318C2211yescharacteristic
159#11718318C2211yescharacteristic
160#11718318C2211yescharacteristic
161#11718318C2211yescharacteristic
162#11718318C2211yescharacteristic
163#11718316C2211yescharacteristic
164#11718316C2211yescharacteristic
165#11718316C2211yescharacteristic
166#11718316C2211yescharacteristic
167#11718316C2211yescharacteristic
168#11718315C2211yescharacteristic
169#11718315C2211yescharacteristic
170#11718315C2211yescharacteristic
171#11718315C2211yescharacteristic
172#11718315C2211yescharacteristic
173#11718314C2211yescharacteristic
174#11718314C2211yescharacteristic
175#11718314C2211yescharacteristic
176#11718314C2211yescharacteristic
177#11718314C2211yescharacteristic
178#11718313C2211yescharacteristic
179#11718313C2211yescharacteristic
180#11718313C2211yescharacteristic
181#11718313C2211yescharacteristic
182#11718313C2211yescharacteristic
183#11718310C2211yescharacteristic
184#11718310C2211yescharacteristic
185#11718308C2211yescharacteristic
186#11718308C2211yescharacteristic
187C22×C4×D13C2311yescharacteristic
188C22×C4×D13C2311yescharacteristic
189C22×C4×D13C2311yescharacteristic
190C22×C4×D13C2311yescharacteristic
191C22×C4×D13C2311yescharacteristic
192C22×C4×D13C2311yescharacteristic
193C22×C4×D13C2311yescharacteristic
194C22×C4×D13C2311yescharacteristic
195C22×C4×D13C2311yescharacteristic
196C22×C4×D13C2311yescharacteristic
197C22×C4×D13C2311yescharacteristic
198C22×C4×D13C2311yescharacteristic
199C22×C4×D13C2311yescharacteristic
200C22×C4×D13C2311yescharacteristic
201C22×C4×D13C2311yescharacteristic
202C2×C13×C4⋊C4C2311yescharacteristic
203C2×C13×C4⋊C4C2311yescharacteristic
204C2×C13×C4⋊C4C2311yescharacteristic
205C2×C13×C4⋊C4C2311yescharacteristic
206C2×C13×C4⋊C4C2311yescharacteristic
207C2×C13×C4⋊C4C2311yescharacteristic
208C2×C13×C4⋊C4C2311yescharacteristic
209C2×C13×C4⋊C4C2311yescharacteristic
210C2×C13×C4⋊C4C2311yescharacteristic
211C2×C13×C4⋊C4C2311yescharacteristic
212C2×C13×C4⋊C4C2311yescharacteristic
213C2×C13×C4⋊C4C2311yescharacteristic
214C2×C42×C13C2311yescharacteristic
215C2×C42×C13C2311yescharacteristic
216C2×C42×C13C2311yescharacteristic
217C2×C4⋊Dic13C2311yescharacteristic
218C2×C4⋊Dic13C2311yescharacteristic
219C2×C4⋊Dic13C2311yescharacteristic
220C2×C4⋊Dic13C2311yescharacteristic
221C2×C4⋊Dic13C2311yescharacteristic
222C2×C4⋊Dic13C2311yescharacteristic
223C2×C4⋊Dic13C2311yescharacteristic
224C2×C4⋊Dic13C2311yescharacteristic
225C2×C4⋊Dic13C2311yescharacteristic
226C2×C4⋊Dic13C2311yescharacteristic
227C2×C4⋊Dic13C2311yescharacteristic
228C2×C4⋊Dic13C2311yescharacteristic
229C2×#6101C2311yescharacteristic
230C2×#6101C2311yescharacteristic
231C2×#6101C2311yescharacteristic
232C2×#6101C2311yescharacteristic
233C2×#6101C2311yescharacteristic
234C2×#6101C2311yescharacteristic
235C2×#6101C2311yescharacteristic
236C2×#6101C2311yescharacteristic
237C2×#6101C2311yescharacteristic
238C2×#6101C2311yescharacteristic
239C2×#6101C2311yescharacteristic
240C2×#6101C2311yescharacteristic
241C2×#6101C2311yescharacteristic
242C2×#6101C2311yescharacteristic
243C2×#6101C2311yescharacteristic
244C2×#6101C2311yescharacteristic
245C2×#6101C2311yescharacteristic
246C2×#6101C2311yescharacteristic
247C2×#6101C2311yescharacteristic
248C2×#6101C2311yescharacteristic
249C2×#6101C2311yescharacteristic
250C2×#6101C2311yescharacteristic
251C2×#6101C2311yescharacteristic
252C2×#6101C2311yescharacteristic
253C2×C4×Dic13C2311yescharacteristic
254C2×C4×Dic13C2311yescharacteristic
255C2×C4×Dic13C2311yescharacteristic
256C2×C4×Dic13C2311yescharacteristic
257C2×C4×Dic13C2311yescharacteristic
258C2×C4×Dic13C2311yescharacteristic
259C2×C4×Dic13C2311yescharacteristic
260C2×C4×Dic13C2311yescharacteristic
261C2×C4×Dic13C2311yescharacteristic
262C4⋊C4×D13—24no—
263C4⋊C4×D13—24no—
264C4⋊C4×D13—24no—
265C4⋊C4×D13—24no—
266C4⋊C4×D13—24no—
267C4⋊C4×D13—24no—
268C4⋊C4×D13—24no—
269C4⋊C4×D13—24no—
270C4⋊C4×D13—42no—
271C4⋊C4×D13—42no—
272C4⋊C4×D13—42no—
273C4⋊C4×D13—42no—
274C42×D13—24no—
275C42×D13—42no—
276C42×D13—42no—
277C13×#95C2311yescharacteristic
278C13×#95C2311yescharacteristic
279C13×#95C2311yescharacteristic
280C13×#95C2311yescharacteristic
281C13×#95C2311yescharacteristic
282C13×#95C2311yescharacteristic
283C13×#95C2311yescharacteristic
284C13×#95C2311yescharacteristic
285C13×#95C2311yescharacteristic
286C13×#95C2311yescharacteristic
287C13×#95C2311yescharacteristic
288C13×#95C2311yescharacteristic
289C13×#95C2311yescharacteristic
290C13×#95C2311yescharacteristic
291C13×#95C2311yescharacteristic
292C13×#95C2311yescharacteristic
293C13×#95C2311yescharacteristic
294C13×#95C2311yescharacteristic
295C13×#95C2311yescharacteristic
296C13×#95C2311yescharacteristic
297#88071C2311yescharacteristic
298#88071C2311yescharacteristic
299#88071C2311yescharacteristic
300#88071C2311yescharacteristic
301#88071C2311yescharacteristic
302#88071C2311yescharacteristic
303#88071C2311yescharacteristic
304#88071C2311yescharacteristic
305#88071C2311yescharacteristic
306#88071C2311yescharacteristic
307#88071C2311yescharacteristic
308#88071C2311yescharacteristic
309#88071C2311yescharacteristic
310#88071C2311yescharacteristic
311#88071C2311yescharacteristic
312#88071C2311yescharacteristic
313#88071C2311yescharacteristic
314#88071C2311yescharacteristic
315#88071C2311yescharacteristic
316#88071C2311yescharacteristic
317#88071C2311yescharacteristic
318#88071C2311yescharacteristic
319#88071C2311yescharacteristic
320#88071C2311yescharacteristic
321#88071C2311yescharacteristic
322#88071C2311yescharacteristic
323#88071C2311yescharacteristic
324#88071C2311yescharacteristic
325#88071C2311yescharacteristic
326#88071C2311yescharacteristic
327#88071C2311yescharacteristic
328#88071C2311yescharacteristic
329#88071C2311yescharacteristic
330#88071C2311yescharacteristic
331#88071C2311yescharacteristic
332#88071C2311yescharacteristic
333#88071C2311yescharacteristic
334#88071C2311yescharacteristic
335#88071C2311yescharacteristic
336#88071C2311yescharacteristic
337#88071C2311yescharacteristic
338#88071C2311yescharacteristic
339#88071C2311yescharacteristic
340#88071C2311yescharacteristic
341#88071C2311yescharacteristic
342#88071C2311yescharacteristic
343#88071C2311yescharacteristic
344#88071C2311yescharacteristic
345#88071C2311yescharacteristic
346#88071C2311yescharacteristic
347#88071C2311yescharacteristic
348#88071C2311yescharacteristic
349#88071C2311yescharacteristic
350#88071C2311yescharacteristic
351#88071C2311yescharacteristic
352#88071C2311yescharacteristic
353#88071C2311yescharacteristic
354#88071C2311yescharacteristic
355#88071C2311yescharacteristic
356#88071C2311yescharacteristic
357C2×#2655—131nomaximal, Sylow
358C23×D13C2411yescharacteristic
359C22×C4×C13C2411yescharacteristic
360C22×C4×C13C2411yescharacteristic
361C22×C4×C13C2411yescharacteristic
362C22×C4×C13C2411yescharacteristic
363C22×C4×C13C2411yescharacteristic
364C22×C4×C13C2411yescharacteristic
365C22×C4×C13C2411yescharacteristic
366C22×C4×C13C2411yescharacteristic
367C22×C4×C13C2411yescharacteristic
368C22×C4×C13C2411yescharacteristic
369C22×C4×C13C2411yescharacteristic
370C22×C4×C13C2411yescharacteristic
371C22×C4×C13C2411yescharacteristic
372C22×C4×C13C2411yescharacteristic
373C22×C4×C13C2411yescharacteristic
374C22×Dic13C2411yescharacteristic
375C22×Dic13C2411yescharacteristic
376C22×Dic13C2411yescharacteristic
377C22×Dic13C2411yescharacteristic
378C22×Dic13C2411yescharacteristic
379C22×Dic13C2411yescharacteristic
380C22×Dic13C2411yescharacteristic
381C22×Dic13C2411yescharacteristic
382C22×Dic13C2411yescharacteristic
383C22×Dic13C2411yescharacteristic
384C22×Dic13C2411yescharacteristic
385C22×Dic13C2411yescharacteristic
386C22×Dic13C2411yescharacteristic
387C22×Dic13C2411yescharacteristic
388C22×Dic13C2411yescharacteristic
389C2×C4×D13—22no—
390C2×C4×D13—22no—
391C2×C4×D13—22no—
392C2×C4×D13—22no—
393C2×C4×D13—22no—
394C2×C4×D13—22no—
395C2×C4×D13—22no—
396C2×C4×D13—22no—
397C2×C4×D13—22no—
398C2×C4×D13—22no—
399C2×C4×D13—22no—
400C2×C4×D13—22no—
401C2×C4×D13—22no—
402C2×C4×D13—22no—
403C2×C4×D13—22no—
404C2×C4×D13—22no—
405C2×C4×D13—22no—
406C2×C4×D13—22no—
407C2×C4×D13—22no—
408C2×C4×D13—22no—
409C2×C4×D13—22no—
410C2×C4×D13—22no—
411C2×C4×D13—22no—
412C2×C4×D13—22no—
413C2×C4×D13—22no—
414C2×C4×D13—22no—
415C2×C4×D13—22no—
416C2×C4×D13—22no—
417C2×C4×D13—22no—
418C2×C4×D13—22no—
419C2×C4×D13—22no—
420C2×C4×D13—22no—
421C2×C4×D13—22no—
422C2×C4×D13—22no—
423C2×C4×D13—22no—
424C2×C4×D13—22no—
425C2×C4×D13—22no—
426C2×C4×D13—22no—
427C2×C4×D13—22no—
428C2×C4×D13—22no—
429C2×C4×D13—22no—
430C2×C4×D13—22no—
431C2×C4×D13#4114yes—
432C2×C4×D13#4114yes—
433C2×C4×D13#4114yes—
434C13×C4⋊C4—22no—
435C13×C4⋊C4—22no—
436C13×C4⋊C4—22no—
437C13×C4⋊C4—22no—
438C13×C4⋊C4—22no—
439C13×C4⋊C4—22no—
440C13×C4⋊C4—22no—
441C13×C4⋊C4—22no—
442C13×C4⋊C4—41no—
443C13×C4⋊C4—41no—
444C13×C4⋊C4—41no—
445C13×C4⋊C4—41no—
446C42×C13—22no—
447C42×C13—41no—
448C42×C13—41no—
449C4⋊Dic13—22no—
450C4⋊Dic13—22no—
451C4⋊Dic13—22no—
452C4⋊Dic13—22no—
453C4⋊Dic13—22no—
454C4⋊Dic13—22no—
455C4⋊Dic13—22no—
456C4⋊Dic13—22no—
457C4⋊Dic13—41no—
458C4⋊Dic13—41no—
459C4⋊Dic13—41no—
460C4⋊Dic13—41no—
461#6101—22no—
462#6101—22no—
463#6101—22no—
464#6101—22no—
465#6101—22no—
466#6101—22no—
467#6101—22no—
468#6101—22no—
469#6101—22no—
470#6101—22no—
471#6101—22no—
472#6101—22no—
473#6101—22no—
474#6101—22no—
475#6101—22no—
476#6101—22no—
477#6101—41no—
478#6101—41no—
479#6101—41no—
480#6101—41no—
481#6101—41no—
482#6101—41no—
483#6101—41no—
484#6101—41no—
485C4×Dic13—22no—
486C4×Dic13—22no—
487C4×Dic13—22no—
488C4×Dic13—41no—
489C4×Dic13—41no—
490C4×Dic13—41no—
491C4×Dic13—41no—
492C4×Dic13—41no—
493C4×Dic13—41no—
494#2655—131no—
495#2655—131no—
496#2655—131no—
497#2655—131no—
498#2655—131no—
499#2655—131no—
500#2655—131no—
501#2655—131no—
502#2655—131no—
503#2655—131no—
504#2655—131no—
505#2655—131no—
506#2655—131no—
507#2655—131no—
508#2655—131no—
509#2655D1311yescharacteristic, direct product factor
510C2×#401—131no—
511C2×#400—131no—
512C2×#400—131no—
513C2×#400—131no—
514C2×#400—131no—
515C2×#398—131no—
516C2×#398—131no—
517C2×#398—131no—
518C2×#389—131no—
519C2×#387—131no—
520C2×#387—131no—
521C2×#387—131no—
522C2×#387—131no—
523C2×#387—131no—
524C2×C4×C4⋊C4—131no—
525C23×C13C2511yescharacteristic
526C22×D13C2×#4112yes—
527C22×D13C2×#4112yes—
528C22×D13C2×#4112yes—
529C22×D13H(5,𝔽2)12yes—
530C22×D132−1+412yes—
531C22×D132−1+412yes—
532C22×D132−1+412yes—
533C2×C4×C13—21no—
534C2×C4×C13—21no—
535C2×C4×C13—21no—
536C2×C4×C13—21no—
537C2×C4×C13—21no—
538C2×C4×C13—21no—
539C2×C4×C13—21no—
540C2×C4×C13—21no—
541C2×C4×C13—21no—
542C2×C4×C13—21no—
543C2×C4×C13—21no—
544C2×C4×C13—21no—
545C2×C4×C13—21no—
546C2×C4×C13—21no—
547C2×C4×C13—21no—
548C2×C4×C13—21no—
549C2×C4×C13—21no—
550C2×C4×C13—21no—
551C2×C4×C13—21no—
552C2×C4×C13—21no—
553C2×C4×C13—21no—
554C2×C4×C13—21no—
555C2×C4×C13—21no—
556C2×C4×C13—21no—
557C2×C4×C13—21no—
558C2×C4×C13—21no—
559C2×C4×C13—21no—
560C2×C4×C13—21no—
561C2×C4×C13—21no—
562C2×C4×C13—21no—
563C2×C4×C13—21no—
564C2×C4×C13—21no—
565C2×C4×C13—21no—
566C2×C4×C13—21no—
567C2×C4×C13—21no—
568C2×C4×C13—21no—
569C2×C4×C13—21no—
570C2×C4×C13—21no—
571C2×C4×C13—21no—
572C2×C4×C13—21no—
573C2×C4×C13—21no—
574C2×C4×C13—21no—
575C2×C4×C13C2×#4112yes—
576C2×C4×C13C2×#4112yes—
577C2×C4×C13C2×#4112yes—
578C2×Dic13—21no—
579C2×Dic13—21no—
580C2×Dic13—21no—
581C2×Dic13—21no—
582C2×Dic13—21no—
583C2×Dic13—21no—
584C2×Dic13—21no—
585C2×Dic13—21no—
586C2×Dic13—21no—
587C2×Dic13—21no—
588C2×Dic13—21no—
589C2×Dic13—21no—
590C2×Dic13—21no—
591C2×Dic13—21no—
592C2×Dic13—21no—
593C2×Dic13—21no—
594C2×Dic13—21no—
595C2×Dic13—21no—
596C2×Dic13—21no—
597C2×Dic13—21no—
598C2×Dic13—21no—
599C2×Dic13—21no—
600C2×Dic13—21no—
601C2×Dic13—21no—
602C2×Dic13—21no—
603C2×Dic13—21no—
604C2×Dic13—21no—
605C2×Dic13—21no—
606C2×Dic13—21no—
607C2×Dic13—21no—
608C2×Dic13—21no—
609C2×Dic13—21no—
610C2×Dic13—21no—
611C2×Dic13—21no—
612C2×Dic13—21no—
613C2×Dic13—21no—
614C2×Dic13—21no—
615C2×Dic13—21no—
616C2×Dic13—21no—
617C2×Dic13—21no—
618C2×Dic13—21no—
619C2×Dic13—21no—
620C2×Dic13C2×#4112yes—
621C2×Dic13C2×#4112yes—
622C2×Dic13C2×#4112yes—
623C4×D13—28no—
624C4×D13—28no—
625C4×D13—28no—
626C4×D13—44no—
627C4×D13—44no—
628C4×D13—44no—
629C4×D13—44no—
630C4×D13—44no—
631C4×D13—44no—
632C4×D13—44no—
633C4×D13—44no—
634C4×D13—44no—
635C4×D13—44no—
636C4×D13—44no—
637C4×D13—44no—
638C22×C4⋊C4—131no—
639C22×C4⋊C4—131no—
640C22×C4⋊C4—131no—
641C22×C4⋊C4—131no—
642C22×C4⋊C4—131no—
643C22×C4⋊C4—131no—
644C22×C4⋊C4—131no—
645C22×C4⋊C4—131no—
646C22×C4⋊C4—131no—
647C22×C4⋊C4—131no—
648C22×C4⋊C4—131no—
649C22×C4⋊C4—131no—
650C22×C42—131no—
651C22×C42—131no—
652C22×C42—131no—
653#401—131no—
654#401—131no—
655#401—131no—
656#401—131no—
657#401—131no—
658#401—131no—
659#401—131no—
660#401C2×D1311yescharacteristic
661#400—131no—
662#400—131no—
663#400—131no—
664#400—131no—
665#400—131no—
666#400—131no—
667#400—131no—
668#400—131no—
669#400—131no—
670#400—131no—
671#400—131no—
672#400—131no—
673#400—131no—
674#400—131no—
675#400—131no—
676#400—131no—
677#400—131no—
678#400—131no—
679#400—131no—
680#400—131no—
681#400—131no—
682#400—131no—
683#400—131no—
684#400—131no—
685#400—131no—
686#400—131no—
687#400—131no—
688#400—131no—
689#400C2×D1311yescharacteristic
690#400C2×D1311yescharacteristic
691#400C2×D1311yescharacteristic
692#400C2×D1311yescharacteristic
693#398—131no—
694#398—131no—
695#398—131no—
696#398—131no—
697#398—131no—
698#398—131no—
699#398—131no—
700#398—131no—
701#398—131no—
702#398—131no—
703#398—131no—
704#398—131no—
705#398—131no—
706#398—131no—
707#398—131no—
708#398—131no—
709#398—131no—
710#398—131no—
711#398—131no—
712#398—131no—
713#398—131no—
714#398C2×D1311yescharacteristic
715#398C2×D1311yescharacteristic
716#398C2×D1311yescharacteristic
717#389—131no—
718#389—131no—
719#389—131no—
720#389—131no—
721#389—131no—
722#389—131no—
723#389—131no—
724#389C2×D1311yescharacteristic
725#387—131no—
726#387—131no—
727#387—131no—
728#387—131no—
729#387—131no—
730#387—131no—
731#387—131no—
732#387—131no—
733#387—131no—
734#387—131no—
735#387—131no—
736#387—131no—
737#387—131no—
738#387—131no—
739#387—131no—
740#387—131no—
741#387—131no—
742#387—131no—
743#387—131no—
744#387—131no—
745#387—131no—
746#387—131no—
747#387—131no—
748#387—131no—
749#387—131no—
750#387—131no—
751#387—131no—
752#387—131no—
753#387—131no—
754#387—131no—
755#387—131no—
756#387—131no—
757#387—131no—
758#387—131no—
759#387—131no—
760#387C2×D1311yescharacteristic
761#387C2×D1311yescharacteristic
762#387C2×D1311yescharacteristic
763#387C2×D1311yescharacteristic
764#387C2×D1311yescharacteristic
765C4×C4⋊C4—131no—
766C4×C4⋊C4—131no—
767C4×C4⋊C4—131no—
768C4×C4⋊C4—131no—
769C4×C4⋊C4—131no—
770C4×C4⋊C4—131no—
771C4×C4⋊C4—131no—
772C4×C4⋊C4C2×D1311yescharacteristic
773C2×#95—131no—
774C2×#95—131no—
775C2×#95—131no—
776C2×#95—131no—
777C2×#95—131no—
778C2×#95—131no—
779C2×#95—131no—
780C2×#95—131no—
781C2×#95—131no—
782C2×#95—131no—
783C2×#95—131no—
784C2×#95—131no—
785C2×#95—131no—
786C2×#95—131no—
787C2×#95—131no—
788C2×#95—131no—
789C2×#95—131no—
790C2×#95—131no—
791C2×#95—131no—
792C2×#95—131no—
793C22×C13C22×#4111yescharacteristic
794C22×C13C22×#4111yescharacteristic
795C22×C13C22×#4111yescharacteristic
796C22×C13C2×H(5,𝔽2)11yescharacteristic
797C22×C13C2×2−1+411yescharacteristic
798C22×C13C2×2−1+411yescharacteristic
799C22×C13C2×2−1+411yescharacteristic
800C2×D13#52914yes—
801C2×D13#53914yes—
802C2×D13#53914yes—
803C2×D13#54114yes—
804C2×D13#54114yes—
805C2×D13#54114yes—
806C2×D13#54214yes—
807C4×C13—22no—
808C4×C13—22no—
809C4×C13—22no—
810C4×C13—41no—
811C4×C13—41no—
812C4×C13—41no—
813C4×C13—41no—
814C4×C13—41no—
815C4×C13—41no—
816C4×C13—41no—
817C4×C13—41no—
818C4×C13—41no—
819C4×C13—41no—
820C4×C13—41no—
821C4×C13—41no—
822Dic13—22no—
823Dic13—22no—
824Dic13—22no—
825Dic13—41no—
826Dic13—41no—
827Dic13—41no—
828Dic13—41no—
829Dic13—41no—
830Dic13—41no—
831Dic13—41no—
832Dic13—41no—
833Dic13—41no—
834Dic13—41no—
835Dic13—41no—
836Dic13—41no—
837C23×C4—131no—
838C23×C4—131no—
839C23×C4—131no—
840C23×C4—131no—
841C23×C4—131no—
842C23×C4—131no—
843C23×C4—131no—
844C23×C4—131no—
845C23×C4—131no—
846C23×C4—131no—
847C23×C4—131no—
848C23×C4—131no—
849C23×C4—131no—
850C23×C4—131no—
851C23×C4—131no—
852C2×C4⋊C4—131no—
853C2×C4⋊C4—131no—
854C2×C4⋊C4—131no—
855C2×C4⋊C4—131no—
856C2×C4⋊C4—131no—
857C2×C4⋊C4—131no—
858C2×C4⋊C4—131no—
859C2×C4⋊C4—131no—
860C2×C4⋊C4—131no—
861C2×C4⋊C4—131no—
862C2×C4⋊C4—131no—
863C2×C4⋊C4—131no—
864C2×C4⋊C4—131no—
865C2×C4⋊C4—131no—
866C2×C4⋊C4—131no—
867C2×C4⋊C4—131no—
868C2×C4⋊C4—131no—
869C2×C4⋊C4—131no—
870C2×C4⋊C4—131no—
871C2×C4⋊C4—131no—
872C2×C4⋊C4—131no—
873C2×C4⋊C4—131no—
874C2×C4⋊C4—131no—
875C2×C4⋊C4—131no—
876C2×C4⋊C4—131no—
877C2×C4⋊C4—131no—
878C2×C4⋊C4—131no—
879C2×C4⋊C4—131no—
880C2×C4⋊C4—131no—
881C2×C4⋊C4—131no—
882C2×C4⋊C4—131no—
883C2×C4⋊C4—131no—
884C2×C4⋊C4—131no—
885C2×C4⋊C4—131no—
886C2×C4⋊C4—131no—
887C2×C4⋊C4—131no—
888C2×C4⋊C4—264no—
889C2×C4⋊C4—264no—
890C2×C4⋊C4—264no—
891C2×C4⋊C4—264no—
892C2×C4⋊C4—264no—
893C2×C4⋊C4—264no—
894C2×C4⋊C4—264no—
895C2×C4⋊C4—264no—
896C2×C4⋊C4—522no—
897C2×C4⋊C4—522no—
898C2×C4⋊C4—522no—
899C2×C4⋊C4—522no—
900C2×C4⋊C4C22×D1311yescharacteristic
901C2×C4⋊C4C22×D1311yescharacteristic
902C2×C4⋊C4C22×D1311yescharacteristic
903C2×C4⋊C4C22×D1311yescharacteristic
904C2×C4⋊C4C22×D1311yescharacteristic
905C2×C4⋊C4C22×D1311yescharacteristic
906C2×C4⋊C4C22×D1311yescharacteristic
907C2×C4⋊C4C22×D1311yescharacteristic
908C2×C4⋊C4C22×D1311yescharacteristic
909C2×C4⋊C4C22×D1311yescharacteristic
910C2×C4⋊C4C22×D1311yescharacteristic
911C2×C4⋊C4C22×D1311yescharacteristic
912C2×C42—131no—
913C2×C42—131no—
914C2×C42—131no—
915C2×C42—131no—
916C2×C42—131no—
917C2×C42—131no—
918C2×C42—131no—
919C2×C42—131no—
920C2×C42—131no—
921C2×C42—264no—
922C2×C42—522no—
923C2×C42—522no—
924C2×C42C22×D1311yescharacteristic
925C2×C42C22×D1311yescharacteristic
926C2×C42C22×D1311yescharacteristic
927#95—131no—
928#95—131no—
929#95—131no—
930#95—131no—
931#95—131no—
932#95—131no—
933#95—131no—
934#95—131no—
935#95—131no—
936#95—131no—
937#95—131no—
938#95—131no—
939#95—131no—
940#95—131no—
941#95—131no—
942#95—131no—
943#95—131no—
944#95—131no—
945#95—131no—
946#95—131no—
947#95—131no—
948#95—131no—
949#95—131no—
950#95—131no—
951#95—131no—
952#95—131no—
953#95—131no—
954#95—131no—
955#95—131no—
956#95—131no—
957#95—131no—
958#95—131no—
959#95—131no—
960#95—131no—
961#95—131no—
962#95—131no—
963#95—131no—
964#95—131no—
965#95—131no—
966#95—131no—
967#95—131no—
968#95—131no—
969#95—131no—
970#95—131no—
971#95—131no—
972#95—131no—
973#95—131no—
974#95—131no—
975#95—131no—
976#95—131no—
977#95—131no—
978#95—131no—
979#95—131no—
980#95—131no—
981#95—131no—
982#95—131no—
983#95—131no—
984#95—131no—
985#95—131no—
986#95—131no—
987#95C22×D1311yescharacteristic
988#95C22×D1311yescharacteristic
989#95C22×D1311yescharacteristic
990#95C22×D1311yescharacteristic
991#95C22×D1311yescharacteristic
992#95C22×D1311yescharacteristic
993#95C22×D1311yescharacteristic
994#95C22×D1311yescharacteristic
995#95C22×D1311yescharacteristic
996#95C22×D1311yescharacteristic
997#95C22×D1311yescharacteristic
998#95C22×D1311yescharacteristic
999#95C22×D1311yescharacteristic
1000#95C22×D1311yescharacteristic
1001#95C22×D1311yescharacteristic
1002#95C22×D1311yescharacteristic
1003#95C22×D1311yescharacteristic
1004#95C22×D1311yescharacteristic
1005#95C22×D1311yescharacteristic
1006#95C22×D1311yescharacteristic
1007C2×C13C2×#52911yescharacteristic
1008C2×C13C2×#53911yescharacteristic
1009C2×C13C2×#53911yescharacteristic
1010C2×C13C2×#54111yescharacteristic
1011C2×C13C2×#54111yescharacteristic
1012C2×C13C2×#54111yescharacteristic
1013C2×C13C2×#54211yescharacteristic
1014D13#265518yesdirect product factor
1015C24—131no—
1016C22×C4—131no—
1017C22×C4—131no—
1018C22×C4—131no—
1019C22×C4—134no—
1020C22×C4—134no—
1021C22×C4—134no—
1022C22×C4—131no—
1023C22×C4—131no—
1024C22×C4—131no—
1025C22×C4—131no—
1026C22×C4—131no—
1027C22×C4—131no—
1028C22×C4—131no—
1029C22×C4—131no—
1030C22×C4—131no—
1031C22×C4—131no—
1032C22×C4—131no—
1033C22×C4—131no—
1034C22×C4—262no—
1035C22×C4—262no—
1036C22×C4—262no—
1037C22×C4—262no—
1038C22×C4—262no—
1039C22×C4—262no—
1040C22×C4—262no—
1041C22×C4—262no—
1042C22×C4—262no—
1043C22×C4—262no—
1044C22×C4—262no—
1045C22×C4—262no—
1046C22×C4—262no—
1047C22×C4—262no—
1048C22×C4—262no—
1049C22×C4—262no—
1050C22×C4—262no—
1051C22×C4—262no—
1052C22×C4—262no—
1053C22×C4—262no—
1054C22×C4—262no—
1055C22×C4—262no—
1056C22×C4—262no—
1057C22×C4—262no—
1058C22×C4—262no—
1059C22×C4—262no—
1060C22×C4—262no—
1061C22×C4—262no—
1062C22×C4—262no—
1063C22×C4—262no—
1064C22×C4—262no—
1065C22×C4—262no—
1066C22×C4—262no—
1067C22×C4—262no—
1068C22×C4—262no—
1069C22×C4—262no—
1070C22×C4—262no—
1071C22×C4—262no—
1072C22×C4—262no—
1073C22×C4—262no—
1074C22×C4—262no—
1075C22×C4—262no—
1076C22×C4C23×D1311yescharacteristic
1077C22×C4C23×D1311yescharacteristic
1078C22×C4C23×D1311yescharacteristic
1079C22×C4C23×D1311yescharacteristic
1080C22×C4C23×D1311yescharacteristic
1081C22×C4C23×D1311yescharacteristic
1082C22×C4C23×D1311yescharacteristic
1083C22×C4C23×D1311yescharacteristic
1084C22×C4C23×D1311yescharacteristic
1085C22×C4C23×D1311yescharacteristic
1086C22×C4C23×D1311yescharacteristic
1087C22×C4C23×D1311yescharacteristic
1088C22×C4C23×D1311yescharacteristic
1089C22×C4C23×D1311yescharacteristic
1090C22×C4C23×D1311yescharacteristic
1091C4⋊C4—22no—
1092C4⋊C4—22no—
1093C4⋊C4—22no—
1094C4⋊C4—22no—
1095C4⋊C4—22no—
1096C4⋊C4—22no—
1097C4⋊C4—22no—
1098C4⋊C4—22no—
1099C4⋊C4—41no—
1100C4⋊C4—41no—
1101C4⋊C4—41no—
1102C4⋊C4—41no—
1103C4⋊C4—262no—
1104C4⋊C4—262no—
1105C4⋊C4—262no—
1106C4⋊C4—262no—
1107C4⋊C4—262no—
1108C4⋊C4—262no—
1109C4⋊C4—262no—
1110C4⋊C4—262no—
1111C4⋊C4—262no—
1112C4⋊C4—262no—
1113C4⋊C4—262no—
1114C4⋊C4—262no—
1115C4⋊C4—262no—
1116C4⋊C4—262no—
1117C4⋊C4—262no—
1118C4⋊C4—262no—
1119C4⋊C4—262no—
1120C4⋊C4—262no—
1121C4⋊C4—262no—
1122C4⋊C4—262no—
1123C4⋊C4—262no—
1124C4⋊C4—262no—
1125C4⋊C4—262no—
1126C4⋊C4—262no—
1127C4⋊C4—521no—
1128C4⋊C4—521no—
1129C4⋊C4—521no—
1130C4⋊C4—521no—
1131C4⋊C4—521no—
1132C4⋊C4—521no—
1133C4⋊C4—521no—
1134C4⋊C4—521no—
1135C4⋊C4—521no—
1136C4⋊C4—521no—
1137C4⋊C4—521no—
1138C4⋊C4—521no—
1139C42—22no—
1140C42—41no—
1141C42—41no—
1142C42—262no—
1143C42—262no—
1144C42—262no—
1145C42—521no—
1146C42—521no—
1147C42—521no—
1148C42—521no—
1149C42—521no—
1150C42—521no—
1151C13C2×#265511yescharacteristic, complemented, Sylow
1152C23—132no—
1153C23—132no—
1154C23—132no—
1155C23—132no—
1156C23—132no—
1157C23—132no—
1158C23—132no—
1159C23C24×D1311yescharacteristic
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—132no—
1203C2×C4—132no—
1204C2×C4—132no—
1205C2×C4—268no—
1206C2×C4—268no—
1207C2×C4—268no—
1208C2×C4—261no—
1209C2×C4—261no—
1210C2×C4—261no—
1211C2×C4—261no—
1212C2×C4—261no—
1213C2×C4—261no—
1214C2×C4—261no—
1215C2×C4—261no—
1216C2×C4—261no—
1217C2×C4—261no—
1218C2×C4—261no—
1219C2×C4—261no—
1220C2×C4—261no—
1221C2×C4—261no—
1222C2×C4—261no—
1223C2×C4—261no—
1224C2×C4—261no—
1225C2×C4—261no—
1226C2×C4—261no—
1227C2×C4—261no—
1228C2×C4—261no—
1229C2×C4—261no—
1230C2×C4—261no—
1231C2×C4—261no—
1232C2×C4—261no—
1233C2×C4—261no—
1234C2×C4—261no—
1235C2×C4—261no—
1236C2×C4—261no—
1237C2×C4—261no—
1238C2×C4—261no—
1239C2×C4—261no—
1240C2×C4—261no—
1241C2×C4—261no—
1242C2×C4—261no—
1243C2×C4—261no—
1244C2×C4—261no—
1245C2×C4—261no—
1246C2×C4—261no—
1247C2×C4—261no—
1248C2×C4—261no—
1249C2×C4—261no—
1250C2×C4—524no—
1251C2×C4—524no—
1252C2×C4—524no—
1253C2×C4—524no—
1254C2×C4—524no—
1255C2×C4—524no—
1256C2×C4—524no—
1257C2×C4—524no—
1258C2×C4—524no—
1259C2×C4—524no—
1260C2×C4—524no—
1261C2×C4—524no—
1262C2×C4#41×D1312yes—
1263C2×C4#41×D1312yes—
1264C2×C4#41×D1312yes—
1265C22—134no—
1266C22—134no—
1267C22—134no—
1268C22—134no—
1269C22—134no—
1270C22—134no—
1271C22—134no—
1272C22C2×#41×D1311yescharacteristic
1273C22C2×#41×D1311yescharacteristic
1274C22C2×#41×D1311yescharacteristic
1275C22D13×H(5,𝔽2)11yescharacteristic
1276C22D13×2−1+411yescharacteristic
1277C22D13×2−1+411yescharacteristic
1278C22D13×2−1+411yescharacteristic
1279C4—22no—
1280C4—22no—
1281C4—22no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—262no—
1295C4—262no—
1296C4—262no—
1297C4—521no—
1298C4—521no—
1299C4—521no—
1300C4—521no—
1301C4—521no—
1302C4—521no—
1303C4—521no—
1304C4—521no—
1305C4—521no—
1306C4—521no—
1307C4—521no—
1308C4—521no—
1309C2—138no—
1310C2D13×#52911yescharacteristic
1311C2D13×#53911yescharacteristic
1312C2D13×#53911yescharacteristic
1313C2D13×#54111yescharacteristic
1314C2D13×#54111yescharacteristic
1315C2D13×#54111yescharacteristic
1316C2D13×#54211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutator, socle, cosocleC23×C13C25
FittingC13×#2655C2
prime radicalC23×D13C24
hypercenter#2655D13
hypocenterC13C2×#2655
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2655

Complements

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

NH ≅ G/Ntype
1. #13120936C2semidirect
2. #13120935C2semidirect
3. #13120934C2semidirect
4. #13120933C2semidirect
5. #13120932C2semidirect
6. #13120931C2semidirect
7. #13120930C2semidirect
8. #13120929C2semidirect
9. #13120928C2semidirect
10. #13120927C2semidirect
11. #13120926C2semidirect
12. #13120925C2semidirect
13. #13120924C2semidirect
14. #13120923C2semidirect
15. #13120922C2semidirect
31. C13×#2655C2semidirect
509. #2655D13direct (N × H)
1014. D13#2655direct (N × H)
1151. C13C2×#2655semidirect

Maximal subgroups

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

subgroupindex
#131209362
#131209352
#131209342
#131209332
#131209322
#131209312
#131209302
#131209292
#131209282
#131209272
#131209262
#131209252
#131209242
#131209232
#131209222
D13×#4012
D13×#4002
D13×#3982
D13×#3892
D13×#3872
C4×C4⋊C4×D132
C13×#26552
C2×#265513