Finite Group Databasebeta

← D13×#3550 #16770723

Subgroups — D13×#3550 #16770723

Order 3328.

7074 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13129250C211yesmaximal, characteristic, complemented
2#13129249C214yesmaximal, complemented
3#13129248C212yesmaximal, complemented
4#13129247C212yesmaximal, complemented
5#13129246C214yesmaximal, complemented
6#13129245C214yesmaximal, complemented
7#13129244C218yesmaximal, complemented
8#13129243C214yesmaximal, complemented
9#13129242C212yesmaximal, complemented
10D13×#563C214yesmaximal, complemented
11D13×#559C212yesmaximal, complemented
12Q82×D13C212yesmaximal, complemented
13D13×#556C214yesmaximal, complemented
14D4×Q8×D13C214yesmaximal, complemented
15D13×#542C218yesmaximal, complemented
16D13×#536C214yesmaximal, complemented
17D13×#533C212yesmaximal, complemented
18D13×#532C211yesmaximal, characteristic
19C13×#3550C211yesmaximal, characteristic, complemented
20C2×#41×D13C2212yes—
21C22×Q8×D13C2214yes—
22C13×#563C2214yescomplemented
23C13×#559C2212yescomplemented
24Q82×C13C2212yescomplemented
25C13×#556C2214yescomplemented
26D4×Q8×C13C2214yescomplemented
27C13×#542C2218yescomplemented
28C13×#536C2214yescomplemented
29C13×#533C2212yescomplemented
30C13×#532C2211yescharacteristic
31#11719537C2212yes—
32#11719530C2214yescomplemented
33#11719521C2214yescomplemented
34Q8×C22⋊D13C2218yescomplemented
35#11719440C2218yescomplemented
36#11719438C2218yescomplemented
37#11719437C2214yescomplemented
38#11719433C2212yescomplemented
39#11719433C2212yescomplemented
40#11719432C2218yescomplemented
41#11719432C2214yescomplemented
42#11719430C2211yescharacteristic
43#11719429C2218yescomplemented
44D13×C4⋊Q8C2218yes—
45D13×C4⋊Q8C2218yes—
46D13×C4⋊Q8C2212yes—
47D13×C4⋊Q8C2211yescharacteristic
48D13×C4⋊Q8C2212yes—
49#11719427C2212yescomplemented
50#11719427C2218yescomplemented
51#11719427C2218yescomplemented
52#11719421C2211yescharacteristic
53D13×#127C2211yescharacteristic
54#11719418C2212yescomplemented
55#11719417C22116yescomplemented
56#11719415C22116yescomplemented
57D13×#126C22116yes—
58#11719407C22116yescomplemented
59#11719404C2218yescomplemented
60#11719393C2214yescomplemented
61D13×#125C2214yes—
62#11719387C2218yescomplemented
63#11719386C2218yescomplemented
64#11719380C2218yescomplemented
65D13×#124C2212yes—
66D13×#124C2218yes—
67D13×#124C2218yes—
68#11719377C2214yescomplemented
69#11719376C2218yescomplemented
70#11719374C22116yescomplemented
71#11719373C2212yes—
72#11719369C2218yescomplemented
73#11719367C22116yescomplemented
74D13×#123C2218yes—
75D13×#123C2218yes—
76#11719356C2218yescomplemented
77#11719353C2218yescomplemented
78#11719353C2218yescomplemented
79#11719351C22116yescomplemented
80#11719348C2218yescomplemented
81#11719346C2218yescomplemented
82#11719345C22116yescomplemented
83#11719337C22116yescomplemented
84#11719337C2218yescomplemented
85#11719333C2218yescomplemented
86#11719333C2218yescomplemented
87D13×C22⋊Q8C22116yes—
88D13×C22⋊Q8C2214yes—
89D13×C22⋊Q8C2218yes—
90D13×C22⋊Q8C2214yes—
91#11719327C2214yescomplemented
92#11719327C2214yescomplemented
93D13×#121C2214yes—
94#11719308C2218yescomplemented
95#11719301C2214yes—
96#11719290C2214yescomplemented
97#11719289C2214yescomplemented
98#11719287C2218yescomplemented
99#11719283C2214yescomplemented
100#11719283C2214yescomplemented
101Q8×D52C2214yescomplemented
102C4×Q8×D13C2218yes—
103C4×Q8×D13C2214yes—
104C4×Q8×D13C2214yes—
105#11719273C2218yescomplemented
106Q8×Dic26C2218yescomplemented
107Q8×Dic26C2214yescomplemented
108#11719266C2218yescomplemented
109#11719264C2218yescomplemented
110#11719253C2214yes—
111C4×D4×D13C2218yes—
112C4×D4×D13C2214yes—
113#11719247C2214yescomplemented
114D4×Dic26C2218yescomplemented
115D4×Dic26C2214yescomplemented
116#11719239C2218yescomplemented
117#11719238C2218yescomplemented
118#11719231C2214yescomplemented
119D13×#117C2214yes—
120D13×#117C2214yes—
121#11719222C2214yescomplemented
122#11719182C2211yescharacteristic
123C2×C42×D13C2211yescharacteristic
124#11719175C2212yescomplemented
125C2×C13×#41C2312yes—
126C22×Q8×C13C2314yes—
127#41×D13—48no—
128C2×#6131C2312yes—
129C2×Q8×D13—416no—
130C2×Q8×D13C2314yes—
131C2×Q8×D13C2314yes—
132C2×Q8×D13C2312yes—
133C2×Q8×D13C2318yes—
134C2×Q8×D13C2318yes—
135C2×Q8×D13C2318yes—
136C2×#6129C2314yes—
137C2×#6129C2312yes—
138C2×D4×D13C2314yes—
139C2×D4×D13C2314yes—
140C2×D4×D13C2312yes—
141C2×#6127C2312yes—
142C2×#6127C2314yes—
143C22×C4×D13C2312yes—
144C22×C4×D13C2311yescharacteristic
145C22×C4×D13C2314yes—
146C22×C4×D13C2318yes—
147C22×Dic26C2314yes—
148C22×Dic26C2318yes—
149C13×C4⋊Q8C2311yescharacteristic
150C13×C4⋊Q8C2318yes—
151C13×C4⋊Q8C2318yes—
152C13×C4⋊Q8C2312yes—
153C13×C4⋊Q8C2312yes—
154C13×#127C2311yescharacteristic
155C13×#126C23116yes—
156C13×#125C2314yes—
157C13×#124C2312yes—
158C13×#124C2318yes—
159C13×#124C2318yes—
160C13×#123C2318yes—
161C13×#123C2318yes—
162C13×C22⋊Q8C2314yes—
163C13×C22⋊Q8C2314yes—
164C13×C22⋊Q8C2318yes—
165C13×C22⋊Q8C23116yes—
166C13×#121C2314yes—
167C4×Q8×C13C2318yes—
168C4×Q8×C13C2314yes—
169C4×Q8×C13C2314yes—
170C4×D4×C13C2314yes—
171C4×D4×C13C2318yes—
172C13×#117C2314yes—
173C13×#117C2314yes—
174C2×C42×C13C2311yescharacteristic
175#88201C2318yes—
176#88201C2312yes—
177#88201C2318yes—
178#88200C23116yes—
179#88200C2318yes—
180#88200C2314yes—
181#88200C2314yes—
182Q8×Dic13C2314yes—
183Q8×Dic13C2314yes—
184Q8×Dic13C2318yes—
185#88198C2312yes—
186#88198C2318yes—
187#88198C23116yes—
188#88198C2318yes—
189#88198C2314yes—
190#88198C2314yes—
191#88194C2314yes—
192#88194C2312yes—
193#88193C2318yes—
194#88192C2314yes—
195#88190C2318yes—
196#88190C2318yes—
197#88190C2312yes—
198#88189C2318yes—
199#88189C2318yes—
200D4×Dic13C2314yes—
201D4×Dic13C2318yes—
202#88184C2314yes—
203#88183C2318yes—
204#88183C2318yes—
205C4×C22⋊D13C2318yes—
206C4×C22⋊D13C23116yes—
207#88180C2314yes—
208#88180C2314yes—
209#88178C2314yes—
210#88178C2314yes—
211#88178C2318yes—
212#88178C23116yes—
213C2×C4×Dic13C2312yes—
214C2×C4×Dic13C2311yescharacteristic
215#88152C23116yes—
216#88152C23116yes—
217#88152C23116yes—
218#88151C2314yes—
219#88151C2314yes—
220#88151C2318yes—
221#88151C23116yes—
222#88150C2318yes—
223#88150C23116yes—
224#88150C23116yes—
225#88150C23116yes—
226#88150C2318yes—
227#88149C2314yes—
228#88148C23116yes—
229#88148C23116yes—
230#88147C2314yes—
231#88147C2318yes—
232#88146C2314yes—
233#88146C2314yes—
234#88146C2318yes—
235C4⋊C4×D13C2314yes—
236C4⋊C4×D13C2314yes—
237C4⋊C4×D13C23116yes—
238C4⋊C4×D13C2318yes—
239C4⋊C4×D13C2314yes—
240C4⋊C4×D13C2314yes—
241C4⋊C4×D13C2314yes—
242C4⋊C4×D13C2318yes—
243#88144C2314yes—
244#88144C2314yes—
245#88143C2318yes—
246#88143C2318yes—
247#88142C2314yes—
248#88142C2318yes—
249#88142C2318yes—
250#88142C23116yes—
251#88142C23116yes—
252#88142C23116yes—
253#88142C2314yes—
254#88142C2314yes—
255#88142C2314yes—
256#88142C2314yes—
257#88141C2314yes—
258#88141C2318yes—
259#88141C2318yes—
260#88141C23116yes—
261#88141C2314yes—
262#88141C2318yes—
263#88140C2318yes—
264#88140C2318yes—
265#88139C23116yes—
266#88139C23116yes—
267#88139C2318yes—
268#88139C23116yes—
269#88139C23116yes—
270#88138C2318yes—
271#88137C23116yes—
272#88137C23116yes—
273#88135C2318yes—
274#88135C23116yes—
275C22⋊C4×D13C2318yes—
276C22⋊C4×D13C2318yes—
277C22⋊C4×D13C2318yes—
278C22⋊C4×D13C23116yes—
279#88133C23116yes—
280#88133C23116yes—
281#88133C23116yes—
282#88132C2318yes—
283#88132C2318yes—
284#88132C23116yes—
285#88132C23116yes—
286#88132C23116yes—
287#88131C2318yes—
288#88131C2318yes—
289#88130C23116yes—
290#88129C2318yes—
291#88129C2312yes—
292#88129C2318yes—
293#88128C2311yescharacteristic
294C4×D52C2314yes—
295C4×D52C2318yes—
296#88126C2318yes—
297#88126C2318yes—
298C42×D13C2312yes—
299C42×D13C2311yescharacteristic
300C42×D13C2318yes—
301C42×D13C2318yes—
302C42×D13C2311yescharacteristic
303C42×D13C2312yes—
304C42×D13C2311yescharacteristic
305C42×D13C2311yescharacteristic
306#88124C2314yes—
307#88123C2312yes—
308#88123C2312yes—
309#88123C2311yescharacteristic
310#88123C2318yes—
311#88123C2318yes—
312C4×Dic26C2314yes—
313C4×Dic26C2318yes—
314C4×Dic26C23116yes—
315C4×Dic26C2318yes—
316C4×Dic26C2314yes—
317C4×Dic26C2318yes—
318C2×#3550—131nomaximal, Sylow
319C23×D13C2414yes—
320C23×D13C2411yescharacteristic
321C13×#41—44no—
322C2×Q8×C13—48no—
323C2×Q8×C13C2414yes—
324C2×Q8×C13C2414yes—
325C2×Q8×C13C2412yes—
326C2×Q8×C13C2418yes—
327C2×D4×C13C2414yes—
328C2×D4×C13C2412yes—
329C2×D4×C13C2414yes—
330C22×C4×C13C2411yescharacteristic
331C22×C4×C13C2412yes—
332C22×C4×C13C2414yes—
333C22×C4×C13C2418yes—
334C2×C22⋊D13C2418yes—
335C2×C22⋊D13C2414yes—
336C2×C22⋊D13C2414yes—
337C2×C22⋊D13C2414yes—
338C22×Dic13C2412yes—
339C22×Dic13C2414yes—
340C22×Dic13C2411yescharacteristic
341C22×Dic13C2418yes—
342#6131—44no—
343Q8×D13—216no—
344Q8×D13—216no—
345Q8×D13—416no—
346Q8×D13—416no—
347Q8×D13—416no—
348Q8×D13—44no—
349#6129—44no—
350#6129—48no—
351D4×D13—216no—
352D4×D13—44no—
353D4×D13—48no—
354#6127—48no—
355#6127—44no—
356C2×D52C2414yes—
357C2×D52C2412yes—
358C2×D52C2414yes—
359C2×C4×D13—216no—
360C2×C4×D13—24no—
361C2×C4×D13—28no—
362C2×C4×D13—416no—
363C2×C4×D13C2418yes—
364C2×C4×D13C2412yes—
365C2×C4×D13C2412yes—
366C2×C4×D13C2414yes—
367C2×C4×D13C2412yes—
368C2×C4×D13C2411yescharacteristic
369C2×C4×D13C2411yescharacteristic
370C2×C4×D13C2411yescharacteristic
371C2×C4×D13C2418yes—
372C2×C4×D13C2414yes—
373C2×C4×D13C2414yes—
374C2×C4×D13C24116yes—
375C2×C4×D13C2411yescharacteristic
376C2×C4×D13C2412yes—
377C2×Dic26—416no—
378C2×Dic26—48no—
379C2×Dic26C2414yes—
380C2×Dic26C2418yes—
381C2×Dic26C2414yes—
382C2×Dic26C2418yes—
383C2×Dic26C2414yes—
384C2×Dic26C2418yes—
385C2×Dic26C2412yes—
386C2×Dic26C24116yes—
387C13×C4⋊C4C2414yes—
388C13×C4⋊C4C2414yes—
389C13×C4⋊C4C2418yes—
390C13×C4⋊C4C24116yes—
391C13×C4⋊C4C2414yes—
392C13×C4⋊C4C2418yes—
393C13×C4⋊C4C2414yes—
394C13×C4⋊C4C2414yes—
395C13×C22⋊C4C2418yes—
396C13×C22⋊C4C2418yes—
397C13×C22⋊C4C2418yes—
398C13×C22⋊C4C24116yes—
399C42×C13C2411yescharacteristic
400C42×C13C2418yes—
401C42×C13C2412yes—
402C42×C13C2418yes—
403C42×C13C2411yescharacteristic
404C22⋊Dic13C2418yes—
405C22⋊Dic13C2418yes—
406C22⋊Dic13C2418yes—
407C22⋊Dic13C24116yes—
408#6103C2418yes—
409#6103C24116yes—
410#6103C2418yes—
411#6103C24116yes—
412#6103C2418yes—
413#6103C24116yes—
414#6103C2418yes—
415C4⋊Dic13C2414yes—
416C4⋊Dic13C2414yes—
417C4⋊Dic13C24116yes—
418C4⋊Dic13C2418yes—
419C4⋊Dic13C2414yes—
420C4⋊Dic13C2418yes—
421C4⋊Dic13C2414yes—
422C4⋊Dic13C2414yes—
423#6101C2418yes—
424#6101C2418yes—
425#6101C2418yes—
426#6101C2418yes—
427#6101C2418yes—
428#6101C24116yes—
429#6101C24116yes—
430#6101C2418yes—
431#6101C2418yes—
432#6101C2418yes—
433#6101C2418yes—
434C4×Dic13C2412yes—
435C4×Dic13C2412yes—
436C4×Dic13C2418yes—
437C4×Dic13C24116yes—
438C4×Dic13C2418yes—
439C4×Dic13C2412yes—
440C4×Dic13C2412yes—
441C4×Dic13C2411yescharacteristic
442C4×Dic13C2412yes—
443C4×Dic13C2411yescharacteristic
444C4×Dic13C2418yes—
445C4×Dic13C2418yes—
446#3550—134no—
447#3550—132no—
448#3550—132no—
449#3550—134no—
450#3550—134no—
451#3550—138no—
452#3550—134no—
453#3550—132no—
454#3550—131no—
455#3550D1311yescharacteristic, direct product factor
456C2×#563—134no—
457C2×#559—132no—
458C2×Q82—132no—
459C2×#556—134no—
460C2×D4×Q8—134no—
461C2×#542—138no—
462C2×#536—134no—
463C2×#533—132no—
464C2×#532—131no—
465C23×C13C2514yes—
466C23×C13C2511yescharacteristic
467C22×D13—28no—
468C22×D13—22no—
469C22×D13—24no—
470C22×D13—216no—
471C22×D13C2514yes—
472C22×D13C2511yescharacteristic
473C22×D13C2511yescharacteristic
474Q8×C13—28no—
475Q8×C13—28no—
476Q8×C13—48no—
477Q8×C13—42no—
478D4×C13—28no—
479D4×C13—44no—
480D4×C13—42no—
481C2×C4×C13—28no—
482C2×C4×C13—22no—
483C2×C4×C13—24no—
484C2×C4×C13—48no—
485C2×C4×C13C2518yes—
486C2×C4×C13C2511yescharacteristic
487C2×C4×C13C2514yes—
488C2×C4×C13C2512yes—
489C2×C4×C13C2518yes—
490C2×C4×C13C2511yescharacteristic
491C2×C4×C13C2512yes—
492C22⋊D13—216no—
493C22⋊D13—44no—
494C22⋊D13—44no—
495C22⋊D13—44no—
496C2×Dic13—28no—
497C2×Dic13—22no—
498C2×Dic13—24no—
499C2×Dic13—48no—
500C2×Dic13C2518yes—
501C2×Dic13C2512yes—
502C2×Dic13C2511yescharacteristic
503C2×Dic13C2514yes—
504C2×Dic13C2518yes—
505C2×Dic13C2511yescharacteristic
506C2×Dic13C2512yes—
507D52—28no—
508D52—44no—
509D52—42no—
510C4×D13—22no—
511C4×D13—28no—
512C4×D13—216no—
513C4×D13—24no—
514C4×D13—216no—
515C4×D13—22no—
516C4×D13—28no—
517C4×D13—24no—
518C4×D13—22no—
519C4×D13—28no—
520C4×D13—24no—
521C4×D13—416no—
522C4×D13H(5,𝔽2)14yes—
523C4×D132−1+418yes—
524Dic26—28no—
525Dic26—28no—
526Dic26—216no—
527Dic26—216no—
528Dic26—48no—
529Dic26—416no—
530Dic26—42no—
531Dic26—44no—
532C22×#41—132no—
533C23×Q8—134no—
534#563—138no—
535#563—1316no—
536#563—138no—
537#563—134no—
538#563—138no—
539#563—1316no—
540#563C2×D1314yescomplemented
541#559—132no—
542#559—138no—
543#559—138no—
544#559—134no—
545#559—138no—
546#559C2×D1312yescomplemented
547Q82—138no—
548Q82—138no—
549Q82—132no—
550Q82—138no—
551Q82—134no—
552Q82C2×D1312yescomplemented
553#556—134no—
554#556—1316no—
555#556—138no—
556#556—138no—
557#556—138no—
558#556—134no—
559#556—134no—
560#556—138no—
561#556C2×D1314yescomplemented
562D4×Q8—138no—
563D4×Q8—138no—
564D4×Q8—134no—
565D4×Q8—138no—
566D4×Q8—1316no—
567D4×Q8—134no—
568D4×Q8—138no—
569D4×Q8—134no—
570D4×Q8C2×D1314yescomplemented
571#542—138no—
572#542—1316no—
573#542—1316no—
574#542—138no—
575#542—1316no—
576#542—1316no—
577#542—138no—
578#542—138no—
579#542—138no—
580#542—138no—
581#542—138no—
582#542C2×D1318yescomplemented
583#536—134no—
584#536—134no—
585#536—138no—
586#536—138no—
587#536—138no—
588#536—138no—
589#536—138no—
590#536—138no—
591#536—134no—
592#536C2×D1314yescomplemented
593#533—132no—
594#533—132no—
595#533—134no—
596#533—134no—
597#533—134no—
598#533—134no—
599#533—134no—
600#533—134no—
601#533—132no—
602#533C2×D1312yescomplemented
603#532—132no—
604#532—131no—
605#532—131no—
606#532—132no—
607#532—134no—
608#532—134no—
609#532—131no—
610#532C2×D1311yescharacteristic
611C2×C4⋊Q8—131no—
612C2×C4⋊Q8—132no—
613C2×C4⋊Q8—132no—
614C2×C4⋊Q8—138no—
615C2×C4⋊Q8—138no—
616C2×#127—131no—
617C2×#126—1316no—
618C2×#125—134no—
619C2×#124—132no—
620C2×#124—138no—
621C2×#124—138no—
622C2×#123—138no—
623C2×#123—138no—
624C2×C22⋊Q8—134no—
625C2×C22⋊Q8—134no—
626C2×C22⋊Q8—138no—
627C2×C22⋊Q8—1316no—
628C2×#121—134no—
629C2×C4×Q8—134no—
630C2×C4×Q8—134no—
631C2×C4×Q8—138no—
632C2×C4×D4—134no—
633C2×C4×D4—138no—
634C2×#117—134no—
635C2×#117—134no—
636C22×C42—131no—
637C22×C13—24no—
638C22×C13—21no—
639C22×C13—22no—
640C22×C13—28no—
641C22×C13C2611yescharacteristic
642C2×D13—24no—
643C2×D13—21no—
644C2×D13—22no—
645C2×D13—28no—
646C2×D13—416no—
647C2×D13—44no—
648C2×D13C2×H(5,𝔽2)12yes—
649C2×D13C2×2−1+414yes—
650C4×C13—28no—
651C4×C13—24no—
652C4×C13—21no—
653C4×C13—28no—
654C4×C13—22no—
655C4×C13C2×H(5,𝔽2)12yes—
656C4×C13C2×2−1+414yes—
657Dic13—28no—
658Dic13—24no—
659Dic13—21no—
660Dic13—28no—
661Dic13—22no—
662Dic13C2×H(5,𝔽2)12yes—
663Dic13C2×2−1+414yes—
664C2×#41—132no—
665C2×#41—134no—
666C2×#41—132no—
667C2×#41—134no—
668C2×#41—132no—
669C2×#41—528no—
670C2×#41C22×D1312yes—
671C22×Q8—134no—
672C22×Q8—134no—
673C22×Q8—138no—
674C22×Q8—132no—
675C22×Q8—138no—
676C22×Q8—138no—
677C22×Q8—138no—
678C22×Q8—134no—
679C22×Q8—5216no—
680C22×Q8C22×D1314yes—
681C22×D4—134no—
682C22×D4—134no—
683C22×D4—132no—
684C23×C4—132no—
685C23×C4—134no—
686C23×C4—131no—
687C23×C4—138no—
688C4⋊Q8—132no—
689C4⋊Q8—134no—
690C4⋊Q8—134no—
691C4⋊Q8—138no—
692C4⋊Q8—138no—
693C4⋊Q8—1316no—
694C4⋊Q8—134no—
695C4⋊Q8—134no—
696C4⋊Q8—134no—
697C4⋊Q8—134no—
698C4⋊Q8—134no—
699C4⋊Q8—1316no—
700C4⋊Q8—1316no—
701C4⋊Q8—1316no—
702C4⋊Q8—138no—
703C4⋊Q8—138no—
704C4⋊Q8—131no—
705C4⋊Q8—132no—
706C4⋊Q8—132no—
707C4⋊Q8—138no—
708C4⋊Q8—138no—
709C4⋊Q8C22×D1311yescharacteristic
710C4⋊Q8C22×D1312yes—
711C4⋊Q8C22×D1312yes—
712C4⋊Q8C22×D1318yes—
713C4⋊Q8C22×D1318yes—
714#127—132no—
715#127—134no—
716#127—131no—
717#127C22×D1311yescharacteristic
718#126—1316no—
719#126—1316no—
720#126—1316no—
721#126—1316no—
722#126—1316no—
723#126—1316no—
724#126—1316no—
725#126C22×D13116yes—
726#125—138no—
727#125—138no—
728#125—134no—
729#125—134no—
730#125—134no—
731#125C22×D1314yes—
732#124—132no—
733#124—138no—
734#124—138no—
735#124—132no—
736#124—138no—
737#124—138no—
738#124—138no—
739#124—1316no—
740#124—1316no—
741#124—1316no—
742#124—1316no—
743#124—132no—
744#124—138no—
745#124—138no—
746#124C22×D1312yes—
747#124C22×D1318yes—
748#124C22×D1318yes—
749#123—138no—
750#123—138no—
751#123—138no—
752#123—138no—
753#123—1316no—
754#123—1316no—
755#123—1316no—
756#123—138no—
757#123—1316no—
758#123—138no—
759#123C22×D1318yes—
760#123C22×D1318yes—
761C22⋊Q8—134no—
762C22⋊Q8—134no—
763C22⋊Q8—138no—
764C22⋊Q8—1316no—
765C22⋊Q8—134no—
766C22⋊Q8—134no—
767C22⋊Q8—138no—
768C22⋊Q8—1316no—
769C22⋊Q8—138no—
770C22⋊Q8—134no—
771C22⋊Q8—138no—
772C22⋊Q8—134no—
773C22⋊Q8—1316no—
774C22⋊Q8—138no—
775C22⋊Q8—1316no—
776C22⋊Q8—1316no—
777C22⋊Q8—1316no—
778C22⋊Q8—138no—
779C22⋊Q8—138no—
780C22⋊Q8—1316no—
781C22⋊Q8—1316no—
782C22⋊Q8—1316no—
783C22⋊Q8C22×D1314yes—
784C22⋊Q8C22×D1314yes—
785C22⋊Q8C22×D1318yes—
786C22⋊Q8C22×D13116yes—
787#121—134no—
788#121—138no—
789#121—134no—
790#121—134no—
791#121—138no—
792#121C22×D1314yes—
793C4×Q8—134no—
794C4×Q8—134no—
795C4×Q8—138no—
796C4×Q8—138no—
797C4×Q8—134no—
798C4×Q8—138no—
799C4×Q8—134no—
800C4×Q8—1316no—
801C4×Q8—138no—
802C4×Q8—138no—
803C4×Q8—134no—
804C4×Q8—138no—
805C4×Q8—134no—
806C4×Q8—1316no—
807C4×Q8—138no—
808C4×Q8C22×D1314yes—
809C4×Q8C22×D1314yes—
810C4×Q8C22×D1318yes—
811C4×D4—134no—
812C4×D4—138no—
813C4×D4—138no—
814C4×D4—1316no—
815C4×D4—134no—
816C4×D4—138no—
817C4×D4—138no—
818C4×D4—1316no—
819C4×D4—134no—
820C4×D4—138no—
821C4×D4C22×D1314yes—
822C4×D4C22×D1318yes—
823#117—134no—
824#117—134no—
825#117—134no—
826#117—134no—
827#117—138no—
828#117—138no—
829#117—138no—
830#117—138no—
831#117—138no—
832#117C22×D1314yes—
833#117C22×D1314yes—
834C2×C4⋊C4—134no—
835C2×C4⋊C4—134no—
836C2×C4⋊C4—134no—
837C2×C4⋊C4—134no—
838C2×C4⋊C4—134no—
839C2×C4⋊C4—138no—
840C2×C4⋊C4—1316no—
841C2×C4⋊C4—138no—
842C2×C22⋊C4—138no—
843C2×C22⋊C4—138no—
844C2×C22⋊C4—138no—
845C2×C22⋊C4—1316no—
846C2×C42—131no—
847C2×C42—132no—
848C2×C42—138no—
849C2×C42—138no—
850C2×C42—132no—
851C2×C42—131no—
852C2×C42—131no—
853C2×C42—131no—
854C2×C42—131no—
855C2×C42—132no—
856C2×C42C22×D1311yescharacteristic
857C2×C13—44no—
858C2×C13—41no—
859C2×C13C22×H(5,𝔽2)11yescharacteristic
860C2×C13C22×2−1+412yes—
861D13—44no—
862D13—41no—
863D13#355014yesdirect product factor
864C24—134no—
865C24—131no—
866#41—44no—
867#41—528no—
868#41—524no—
869#41—528no—
870#41—524no—
871#41—524no—
872C2×Q8—48no—
873C2×Q8—138no—
874C2×Q8—134no—
875C2×Q8—138no—
876C2×Q8—134no—
877C2×Q8—1316no—
878C2×Q8—138no—
879C2×Q8—132no—
880C2×Q8—134no—
881C2×Q8—2616no—
882C2×Q8—2616no—
883C2×Q8—528no—
884C2×Q8—5216no—
885C2×Q8—5216no—
886C2×Q8—524no—
887C2×Q8—5216no—
888C2×Q8—5216no—
889C2×Q8C23×D1314yes—
890C2×Q8C23×D1314yes—
891C2×Q8C23×D1318yes—
892C2×Q8C23×D1312yes—
893C2×D4—138no—
894C2×D4—134no—
895C2×D4—134no—
896C2×D4—134no—
897C2×D4—134no—
898C2×D4—134no—
899C2×D4—132no—
900C2×D4—2616no—
901C2×D4—524no—
902C2×D4—528no—
903C2×D4C23×D1314yes—
904C2×D4C23×D1314yes—
905C2×D4C23×D1312yes—
906C22×C4—132no—
907C22×C4—131no—
908C22×C4—132no—
909C22×C4—131no—
910C22×C4—134no—
911C22×C4—138no—
912C22×C4—138no—
913C22×C4—132no—
914C22×C4—134no—
915C22×C4—131no—
916C22×C4—132no—
917C22×C4—132no—
918C22×C4—131no—
919C22×C4—131no—
920C22×C4—138no—
921C22×C4—134no—
922C22×C4—134no—
923C22×C4—1316no—
924C22×C4—2616no—
925C22×C4—264no—
926C22×C4—268no—
927C22×C4—5216no—
928C22×C4C23×D1312yes—
929C22×C4C23×D1311yescharacteristic
930C22×C4C23×D1314yes—
931C22×C4C23×D1318yes—
932C4⋊C4—138no—
933C4⋊C4—134no—
934C4⋊C4—138no—
935C4⋊C4—134no—
936C4⋊C4—138no—
937C4⋊C4—134no—
938C4⋊C4—138no—
939C4⋊C4—134no—
940C4⋊C4—138no—
941C4⋊C4—134no—
942C4⋊C4—138no—
943C4⋊C4—138no—
944C4⋊C4—138no—
945C4⋊C4—1316no—
946C4⋊C4—1316no—
947C4⋊C4—1316no—
948C4⋊C4—138no—
949C4⋊C4—138no—
950C4⋊C4—138no—
951C4⋊C4C23×D1314yes—
952C4⋊C4C23×D1314yes—
953C4⋊C4C23×D1314yes—
954C4⋊C4C23×D1314yes—
955C4⋊C4C23×D1314yes—
956C4⋊C4C23×D1318yes—
957C4⋊C4C23×D13116yes—
958C4⋊C4C23×D1318yes—
959C22⋊C4—138no—
960C22⋊C4—138no—
961C22⋊C4—138no—
962C22⋊C4—1316no—
963C22⋊C4—138no—
964C22⋊C4—138no—
965C22⋊C4—1316no—
966C22⋊C4—138no—
967C22⋊C4—138no—
968C22⋊C4—1316no—
969C22⋊C4—1316no—
970C22⋊C4C23×D1318yes—
971C22⋊C4C23×D1318yes—
972C22⋊C4C23×D1318yes—
973C22⋊C4C23×D13116yes—
974C42—132no—
975C42—132no—
976C42—132no—
977C42—131no—
978C42—132no—
979C42—131no—
980C42—132no—
981C42—138no—
982C42—138no—
983C42—138no—
984C42—138no—
985C42—1316no—
986C42C23×D1312yes—
987C42C23×D1311yescharacteristic
988C42C23×D1311yescharacteristic
989C42C23×D1318yes—
990C42C23×D1318yes—
991C13C2×#355011yescharacteristic, complemented, Sylow
992C23—131no—
993C23—134no—
994C23—131no—
995C23—268no—
996C23—262no—
997C23—264no—
998C23—2616no—
999C23C24×D1314yes—
1000C23C24×D1311yescharacteristic
1001Q8—28no—
1002Q8—28no—
1003Q8—48no—
1004Q8—42no—
1005Q8—2616no—
1006Q8—2616no—
1007Q8—268no—
1008Q8—268no—
1009Q8—528no—
1010Q8—5216no—
1011Q8—522no—
1012Q8—524no—
1013D4—28no—
1014D4—42no—
1015D4—44no—
1016D4—2616no—
1017D4—268no—
1018D4—522no—
1019D4—524no—
1020D4—524no—
1021D4—524no—
1022D4—524no—
1023C2×C4—28no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—48no—
1027C2×C4—132no—
1028C2×C4—131no—
1029C2×C4—134no—
1030C2×C4—138no—
1031C2×C4—138no—
1032C2×C4—132no—
1033C2×C4—134no—
1034C2×C4—131no—
1035C2×C4—138no—
1036C2×C4—264no—
1037C2×C4—268no—
1038C2×C4—262no—
1039C2×C4—264no—
1040C2×C4—262no—
1041C2×C4—268no—
1042C2×C4—2616no—
1043C2×C4—2616no—
1044C2×C4—264no—
1045C2×C4—268no—
1046C2×C4—262no—
1047C2×C4—268no—
1048C2×C4—262no—
1049C2×C4—264no—
1050C2×C4—5216no—
1051C2×C4—528no—
1052C2×C4C24×D1318yes—
1053C2×C4C24×D1312yes—
1054C2×C4C24×D1314yes—
1055C2×C4C24×D1311yescharacteristic
1056C2×C4C24×D1318yes—
1057C2×C4C24×D1311yescharacteristic
1058C2×C4C24×D1312yes—
1059C22—24no—
1060C22—21no—
1061C22—22no—
1062C22—28no—
1063C22—132no—
1064C22—134no—
1065C22—264no—
1066C22—261no—
1067C22—262no—
1068C22—268no—
1069C22—5216no—
1070C22—524no—
1071C22C25×D1311yescharacteristic
1072C4—21no—
1073C4—24no—
1074C4—28no—
1075C4—22no—
1076C4—28no—
1077C4—132no—
1078C4—134no—
1079C4—261no—
1080C4—264no—
1081C4—268no—
1082C4—262no—
1083C4—268no—
1084C4D13×H(5,𝔽2)12yes—
1085C4D13×2−1+414yes—
1086C2—44no—
1087C2—41no—
1088C2—134no—
1089C2—524no—
1090C2—521no—
1091C2C2×D13×H(5,𝔽2)11yescharacteristic
1092C2C2×D13×2−1+412yes—
subgroupG/H
center, FrattiniC22C25×D13
commutator, socle, cosocleC22×C13C26
FittingC13×#3550C2
prime radicalD13×#532C2
hypercenter#3550D13
hypocenterC13C2×#3550
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #3550

Complements

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

NH ≅ G/Ntype
1. #13129250C2semidirect
2. #13129249C2semidirect
3. #13129248C2semidirect
4. #13129247C2semidirect
5. #13129246C2semidirect
6. #13129245C2semidirect
7. #13129244C2semidirect
8. #13129243C2semidirect
9. #13129242C2semidirect
10. D13×#563C2semidirect
11. D13×#559C2semidirect
12. Q82×D13C2semidirect
13. D13×#556C2semidirect
14. D4×Q8×D13C2semidirect
15. D13×#542C2semidirect
16. D13×#536C2semidirect
17. D13×#533C2semidirect
19. C13×#3550C2semidirect
22. C13×#563C22semidirect
23. C13×#559C22semidirect
24. Q82×C13C22semidirect
25. C13×#556C22semidirect
26. D4×Q8×C13C22semidirect
27. C13×#542C22semidirect
28. C13×#536C22semidirect
29. C13×#533C22semidirect
32. #11719530C22semidirect
33. #11719521C22semidirect
34. Q8×C22⋊D13C22semidirect
35. #11719440C22semidirect
36. #11719438C22semidirect
37. #11719437C22semidirect
38. #11719433C22semidirect
39. #11719433C22semidirect
40. #11719432C22semidirect
41. #11719432C22semidirect
43. #11719429C22semidirect
49. #11719427C22semidirect
50. #11719427C22semidirect
51. #11719427C22semidirect
54. #11719418C22semidirect
55. #11719417C22semidirect
56. #11719415C22semidirect
58. #11719407C22semidirect
59. #11719404C22semidirect
60. #11719393C22semidirect
62. #11719387C22semidirect
63. #11719386C22semidirect
64. #11719380C22semidirect
68. #11719377C22semidirect
69. #11719376C22semidirect
70. #11719374C22semidirect
72. #11719369C22semidirect
73. #11719367C22semidirect
76. #11719356C22semidirect
77. #11719353C22semidirect
78. #11719353C22semidirect
79. #11719351C22semidirect
80. #11719348C22semidirect
81. #11719346C22semidirect
82. #11719345C22semidirect
83. #11719337C22semidirect
84. #11719337C22semidirect
85. #11719333C22semidirect
86. #11719333C22semidirect
91. #11719327C22semidirect
92. #11719327C22semidirect
94. #11719308C22semidirect
96. #11719290C22semidirect
97. #11719289C22semidirect
98. #11719287C22semidirect
99. #11719283C22semidirect
100. #11719283C22semidirect
101. Q8×D52C22semidirect
105. #11719273C22semidirect
106. Q8×Dic26C22semidirect
107. Q8×Dic26C22semidirect
108. #11719266C22semidirect
109. #11719264C22semidirect
113. #11719247C22semidirect
114. D4×Dic26C22semidirect
115. D4×Dic26C22semidirect
116. #11719239C22semidirect
117. #11719238C22semidirect
118. #11719231C22semidirect
121. #11719222C22semidirect
124. #11719175C22semidirect
455. #3550D13direct (N × H)
540. #563C2×D13semidirect
546. #559C2×D13semidirect
552. Q82C2×D13semidirect
561. #556C2×D13semidirect
570. D4×Q8C2×D13semidirect
582. #542C2×D13semidirect
592. #536C2×D13semidirect
602. #533C2×D13semidirect
863. D13#3550direct (N × H)
991. C13C2×#3550semidirect

Maximal subgroups

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

subgroupindex
#131292502
#131292492
#131292482
#131292472
#131292462
#131292452
#131292442
#131292432
#131292422
D13×#5632
D13×#5592
Q82×D132
D13×#5562
D4×Q8×D132
D13×#5422
D13×#5362
D13×#5332
D13×#5322
C13×#35502
C2×#355013