Finite Group Databasebeta

← D13×#3504 #16771393

Subgroups — D13×#3504 #16771393

Order 3328.

6958 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128662C211yesmaximal, characteristic, complemented
2#13128661C214yesmaximal, complemented
3#13128660C213yesmaximal, complemented
4#13128659C216yesmaximal, complemented
5#13128658C212yesmaximal, complemented
6#13128657C213yesmaximal, complemented
7#13128656C2112yesmaximal, complemented
8D13×#557C214yesmaximal, complemented
9D13×#554C2112yesmaximal, complemented
10D13×#544C216yesmaximal, complemented
11D13×#533C213yesmaximal, complemented
12C2×D13×#125C213yesmaximal, complemented
13D13×#520C212yesmaximal
14C4×#41×D13C211yesmaximal, characteristic
15C13×#3504C211yesmaximal, characteristic, complemented
16C2×#41×D13C2211yescharacteristic
17C13×#557C2214yescomplemented
18C13×#554C22112yescomplemented
19C13×#544C2216yescomplemented
20C13×#533C2213yescomplemented
21C2×C13×#125C2213yescomplemented
22C13×#520C2212yes—
23C4×C13×#41C2211yescharacteristic
24#11719532C2212yes—
25#41×Dic13C2211yescharacteristic
26#11719435C22112yescomplemented
27#11719434C22112yescomplemented
28#11719434C22112yescomplemented
29#11719433C2216yescomplemented
30D13×C4⋊Q8C2216yes—
31D13×C4⋊Q8C22112yes—
32#11719426C22112yescomplemented
33#11719395C22112yescomplemented
34#11719395C22112yescomplemented
35#11719394C22112yescomplemented
36#11719394C22112yescomplemented
37#11719393C2213yescomplemented
38#11719393C2213yescomplemented
39D13×#125C2216yes—
40D13×#125C22112yes—
41D13×#125C2213yes—
42D13×#125C22112yes—
43D13×#125C2211yescharacteristic
44D13×#125C22112yescomplemented
45D13×#125C2216yescomplemented
46D13×#125C2216yescomplemented
47#11719390C22112yescomplemented
48#11719390C22112yescomplemented
49#11719341C22124yescomplemented
50#11719341C22124yescomplemented
51#11719340C22124yescomplemented
52D13×C22⋊Q8C22124yes—
53D13×C22⋊Q8C22112yes—
54#11719328C22124yescomplemented
55#11719327C22112yescomplemented
56#11719284C22112yescomplemented
57#11719283C22112yescomplemented
58#11719279C2214yes—
59C4×#6131C2212yes—
60C4×Q8×D13C2212yes—
61C4×Q8×D13C2214yes—
62C4×Q8×D13C22112yes—
63#11719275C2214yescomplemented
64#11719274C2214yescomplemented
65#11719274C2214yescomplemented
66#11719272C22112yescomplemented
67#11719251C22112yes—
68C4×D4×D13C2216yes—
69C4×D4×D13C22112yes—
70#11719248C22112yescomplemented
71#11719244C22112yescomplemented
72#11719244C22112yescomplemented
73C4×#6129C2216yes—
74#11719228C2216yes—
75#11719227C2213yes—
76D13×#117C2213yes—
77D13×#117C2216yes—
78#11719224C2216yescomplemented
79#11719224C2216yescomplemented
80#11719222C2216yescomplemented
81#11719216C22124yescomplemented
82#11719209C2216yes—
83C2×C4⋊C4×D13C2216yes—
84C2×C4⋊C4×D13C22112yes—
85#11719205C2216yescomplemented
86C2×#88144C2216yescomplemented
87C2×#88143C22112yescomplemented
88C4×#6127C2213yes—
89C2×C42×D13C2213yes—
90#11719175C2213yescomplemented
91C2×#88124C2213yescomplemented
92C2×C13×#41C2311yescharacteristic
93#41×D13Q8116yescomplemented
94C2×#6131C2311yescharacteristic
95C2×Q8×D13C23112yes—
96C2×Q8×D13C2311yescharacteristic
97C2×#6129C2313yes—
98C2×D4×D13C2313yes—
99C2×#6127C2313yes—
100C22×C4×D13C2316yes—
101C22×C4×D13C23112yes—
102C22×C4×D13C2313yes—
103C13×C4⋊Q8C23112yes—
104C13×C4⋊Q8C2316yes—
105C13×#125C2313yes—
106C13×#125C2316yes—
107C13×#125C23112yes—
108C13×#125C2311yescharacteristic
109C13×#125C23112yes—
110C13×C22⋊Q8C23112yes—
111C13×C22⋊Q8C23124yes—
112C4×Q8×C13C23112yes—
113C4×Q8×C13C2312yes—
114C4×Q8×C13C2314yes—
115C4×D4×C13C2316yes—
116C4×D4×C13C23112yes—
117C13×#117C2316yes—
118C13×#117C2313yes—
119C2×C13×C4⋊C4C23112yes—
120C2×C13×C4⋊C4C2316yes—
121C2×C42×C13C2313yes—
122#88200C23112yes—
123#88200C23124yes—
124Q8×Dic13C23112yes—
125Q8×Dic13C2314yes—
126Q8×Dic13C2312yes—
127#88198C23124yes—
128#88198C23112yes—
129D4×Dic13C2316yes—
130D4×Dic13C23112yes—
131C4×C22⋊D13C23112yes—
132C4×C22⋊D13C23124yes—
133#88180C2316yes—
134#88180C2313yes—
135C2×C4⋊Dic13C2316yes—
136C2×C4⋊Dic13C23112yes—
137#88178C23112yes—
138#88178C23124yes—
139C2×#6101C23112yes—
140C2×#6101C23112yes—
141C2×#6101C23112yes—
142C2×C4×Dic13C2316yes—
143C2×C4×Dic13C2313yes—
144#88151C23112yes—
145#88151C23124yes—
146#88150C23124yes—
147#88150C23124yes—
148#88150C23112yes—
149#88150C23112yes—
150#88147C2316yes—
151#88147C23112yes—
152#88146C2316yes—
153#88146C2316yes—
154#88146C2316yes—
155C4⋊C4×D13C2312yes—
156C4⋊C4×D13C2316yes—
157C4⋊C4×D13C2316yes—
158C4⋊C4×D13C23112yes—
159C4⋊C4×D13C23124yes—
160C4⋊C4×D13C23112yes—
161C4⋊C4×D13C23112yes—
162C4⋊C4×D13C23112yes—
163C4⋊C4×D13C23124yes—
164C4⋊C4×D13C23112yes—
165C4⋊C4×D13C23124yes—
166C4⋊C4×D13C2314yes—
167#88144C23112yes—
168#88144C23112yes—
169#88144C2312yes—
170#88144C2316yes—
171#88144C23112yes—
172#88144C23112yes—
173#88144C23112yes—
174#88143C23124yes—
175#88143C23124yes—
176#88143C23124yes—
177#88143C23124yes—
178#88143C23112yes—
179#88143C23124yes—
180#88143C2314yes—
181#88142C2316yes—
182#88142C23112yes—
183#88142C2316yes—
184#88142C23112yes—
185#88142C23124yes—
186#88142C23112yes—
187#88141C2316yes—
188#88141C23112yes—
189#88141C23112yes—
190#88141C23112yes—
191#88141C23112yes—
192#88135C23112yes—
193#88135C23124yes—
194C22⋊C4×D13C23112yes—
195C22⋊C4×D13C2316yes—
196#88132C23112yes—
197#88132C23112yes—
198#88132C23124yes—
199#88132C23124yes—
200#88131C2316yes—
201#88131C23112yes—
202C4×D52C2316yes—
203C4×D52C23112yes—
204#88126C2316yes—
205#88126C23112yes—
206C42×D13C2313yes—
207C42×D13C23112yes—
208C42×D13C2311yescharacteristic
209C42×D13C2313yes—
210C42×D13C2313yes—
211C42×D13C2316yes—
212C42×D13C2316yes—
213#88124C2313yes—
214#88124C2316yes—
215#88124C23112yes—
216#88124C2311yescharacteristic
217#88124C23112yes—
218#88123C2316yes—
219#88123C23112yes—
220C4×Dic26C23112yes—
221C4×Dic26C23112yes—
222C4×Dic26C23112yes—
223C4×Dic26C2316yes—
224C4×Dic26C23112yes—
225C2×#3504—131nomaximal, Sylow
226C23×D13C2413yes—
227C13×#41C2×Q818yescomplemented
228C2×Q8×C13C24112yes—
229C2×Q8×C13C2411yescharacteristic
230C2×D4×C13C2413yes—
231C22×C4×C13C2416yes—
232C22×C4×C13C24112yes—
233C22×C4×C13C2413yes—
234C2×C22⋊D13C2416yes—
235C22×Dic13C2416yes—
236C22×Dic13C24112yes—
237C22×Dic13C2413yes—
238#6131C2×Q818yescomplemented
239Q8×D13—424no—
240Q8×D13C2×Q818yes—
241#6129C2×Q8124yescomplemented
242D4×D13C2×Q8124yes—
243#6127C2×Q8124yescomplemented
244C2×D52C2413yes—
245C2×C4×D13—412no—
246C2×C4×D13—424no—
247C2×C4×D13C2×Q8124yes—
248C2×C4×D13C2412yes—
249C2×C4×D13C2414yes—
250C2×C4×D13C2416yes—
251C2×C4×D13C24112yes—
252C2×C4×D13C2416yes—
253C2×C4×D13C2416yes—
254C2×C4×D13C24124yes—
255C2×C4×D13C2413yes—
256C2×C4×D13C2411yescharacteristic
257C2×C4×D13C2413yes—
258C2×C4×D13C2413yes—
259C2×Dic26C24112yes—
260C2×Dic26C24112yes—
261C2×Dic26C24112yes—
262C2×Dic26C2413yes—
263C13×C4⋊C4C2414yes—
264C13×C4⋊C4C2416yes—
265C13×C4⋊C4C24112yes—
266C13×C4⋊C4C24112yes—
267C13×C4⋊C4C24112yes—
268C13×C4⋊C4C2412yes—
269C13×C4⋊C4C24124yes—
270C13×C4⋊C4C2416yes—
271C13×C22⋊C4C24112yes—
272C13×C22⋊C4C2416yes—
273C42×C13C24112yes—
274C42×C13C2416yes—
275C42×C13C2413yes—
276C42×C13C2411yescharacteristic
277C22⋊Dic13C24112yes—
278C22⋊Dic13C2416yes—
279#6103C24112yes—
280#6103C24112yes—
281#6103C24112yes—
282C4⋊Dic13C2414yes—
283C4⋊Dic13C2416yes—
284C4⋊Dic13C24112yes—
285C4⋊Dic13C24112yes—
286C4⋊Dic13C24112yes—
287C4⋊Dic13C2412yes—
288C4⋊Dic13C2416yes—
289C4⋊Dic13C24124yes—
290#6101C2414yes—
291#6101C2414yes—
292#6101C24112yes—
293#6101C24112yes—
294#6101C24112yes—
295#6101C24112yes—
296#6101C24112yes—
297#6101C24124yes—
298#6101C24124yes—
299#6101C24124yes—
300#6101C2414yes—
301#6101C24112yes—
302C4×Dic13C2416yes—
303C4×Dic13C24112yes—
304C4×Dic13C2416yes—
305C4×Dic13C24112yes—
306C4×Dic13C2412yes—
307C4×Dic13C2411yescharacteristic
308C4×Dic13C2413yes—
309C4×Dic13C2416yes—
310C4×Dic13C2416yes—
311C4×Dic13C24112yes—
312#3504—134no—
313#3504—1312no—
314#3504—136no—
315#3504—133no—
316#3504—133no—
317#3504—132no—
318#3504—131no—
319#3504D1311yescharacteristic, direct product factor
320C2×#557—134no—
321C2×#554—1312no—
322C2×#544—136no—
323C2×#533—133no—
324C22×#125—133no—
325C2×#520—132no—
326C2×C4×#41—131no—
327C23×C13C2513yes—
328C22×D13—212no—
329C22×D13C22×Q8112yes—
330C22×D13C2513yes—
331C22×D13C2511yescharacteristic
332Q8×C13—412no—
333Q8×C13C22×Q814yes—
334D4×C13C22×Q8112yes—
335C2×C4×C13—46no—
336C2×C4×C13—412no—
337C2×C4×C13C22×Q8112yes—
338C2×C4×C13C2512yes—
339C2×C4×C13C2514yes—
340C2×C4×C13C2516yes—
341C2×C4×C13C25112yes—
342C2×C4×C13C2513yes—
343C2×C4×C13C2511yescharacteristic
344C22⋊D13C22×Q8124yes—
345C2×Dic13—46no—
346C2×Dic13—412no—
347C2×Dic13C22×Q8112yes—
348C2×Dic13C2512yes—
349C2×Dic13C2514yes—
350C2×Dic13C2516yes—
351C2×Dic13C25112yes—
352C2×Dic13C2513yes—
353C2×Dic13C2511yescharacteristic
354D52C22×Q8112yes—
355C4×D13—24no—
356C4×D13—224no—
357C4×D13—212no—
358C4×D13—28no—
359C4×D13—46no—
360C4×D13—424no—
361C4×D13—46no—
362C4×D13C22×Q814yes—
363C4×D13C22×Q8112yes—
364C4×D13C22×Q8112yes—
365C4×D13C22×Q8112yes—
366Dic26—412no—
367Dic26—412no—
368Dic26—412no—
369Dic26C22×Q8112yes—
370C22×#41—131no—
371#557—1312no—
372#557—1312no—
373#557—1312no—
374#557—1312no—
375#557—134no—
376#557—134no—
377#557—134no—
378#557C2×D1314yescomplemented
379#554—1312no—
380#554—1312no—
381#554—1312no—
382#554—1324no—
383#554—1324no—
384#554—1324no—
385#554—1312no—
386#554—1312no—
387#554—1312no—
388#554—1312no—
389#554—1324no—
390#554C2×D13112yescomplemented
391#544—1312no—
392#544—1312no—
393#544—1312no—
394#544—1312no—
395#544—1324no—
396#544—136no—
397#544—136no—
398#544—136no—
399#544C2×D1316yescomplemented
400#533—136no—
401#533—133no—
402#533—133no—
403#533—1312no—
404#533—1312no—
405#533—136no—
406#533—133no—
407#533C2×D1313yescomplemented
408C2×C4⋊Q8—136no—
409C2×C4⋊Q8—1312no—
410C2×#125—133no—
411C2×#125—136no—
412C2×#125—1312no—
413C2×#125—1312no—
414C2×#125—136no—
415C2×#125—136no—
416C2×#125—131no—
417C2×#125—1312no—
418C2×#125—1312no—
419C2×#125—136no—
420C2×#125—133no—
421C2×#125C2×D1313yescomplemented
422C2×C22⋊Q8—1312no—
423C2×C22⋊Q8—1324no—
424#520—132no—
425#520—134no—
426#520—1312no—
427#520—136no—
428#520—136no—
429#520C2×D1312yes—
430C4×#41—131no—
431C4×#41—132no—
432C4×#41—136no—
433C4×#41—133no—
434C4×#41—133no—
435C4×#41C2×D1311yescharacteristic
436C2×C4×Q8—132no—
437C2×C4×Q8—134no—
438C2×C4×Q8—1312no—
439C2×C4×D4—136no—
440C2×C4×D4—1312no—
441C2×#117—133no—
442C2×#117—136no—
443C22×C4⋊C4—136no—
444C22×C4⋊C4—1312no—
445C22×C42—133no—
446C22×C13—26no—
447C22×C13C23×Q816yes—
448C22×C13C2611yescharacteristic
449C2×D13—26no—
450C2×D13—224no—
451C2×D13C23×Q816yes—
452C2×D13C23×Q812yes—
453C2×D13#58514yes—
454C4×C13—24no—
455C4×C13—26no—
456C4×C13—212no—
457C4×C13—22no—
458C4×C13C23×Q816yes—
459C4×C13C23×Q812yes—
460Dic13—24no—
461Dic13—26no—
462Dic13—212no—
463Dic13—22no—
464Dic13C23×Q816yes—
465Dic13C23×Q812yes—
466C2×#41—1316no—
467C2×#41—131no—
468C2×#41—133no—
469C2×#41—133no—
470C2×#41C22×D1311yescharacteristic
471C22×Q8—131no—
472C22×Q8—1312no—
473C22×D4—133no—
474C23×C4—133no—
475C23×C4—1312no—
476C23×C4—136no—
477C4⋊Q8—1312no—
478C4⋊Q8—1324no—
479C4⋊Q8—1312no—
480C4⋊Q8—136no—
481C4⋊Q8—136no—
482C4⋊Q8—1324no—
483C4⋊Q8—1312no—
484C4⋊Q8—1312no—
485C4⋊Q8—136no—
486C4⋊Q8—1312no—
487C4⋊Q8C22×D1316yes—
488C4⋊Q8C22×D13112yes—
489#125—1312no—
490#125—136no—
491#125—1324no—
492#125—1312no—
493#125—1324no—
494#125—1324no—
495#125—1312no—
496#125—1312no—
497#125—134no—
498#125—132no—
499#125—1324no—
500#125—1324no—
501#125—1312no—
502#125—1312no—
503#125—133no—
504#125—136no—
505#125—1312no—
506#125—131no—
507#125—1312no—
508#125C22×D1313yes—
509#125C22×D1316yes—
510#125C22×D13112yes—
511#125C22×D1311yescharacteristic
512#125C22×D13112yes—
513C22⋊Q8—1312no—
514C22⋊Q8—1324no—
515C22⋊Q8—1312no—
516C22⋊Q8—1324no—
517C22⋊Q8—1312no—
518C22⋊Q8—1312no—
519C22⋊Q8—1312no—
520C22⋊Q8—1324no—
521C22⋊Q8—1324no—
522C22⋊Q8—1324no—
523C22⋊Q8—1312no—
524C22⋊Q8—1312no—
525C22⋊Q8—1324no—
526C22⋊Q8—1324no—
527C22⋊Q8C22×D13112yes—
528C22⋊Q8C22×D13124yes—
529C4×Q8—132no—
530C4×Q8—134no—
531C4×Q8—1312no—
532C4×Q8—136no—
533C4×Q8—1312no—
534C4×Q8—1312no—
535C4×Q8—1312no—
536C4×Q8—1312no—
537C4×Q8—136no—
538C4×Q8—1312no—
539C4×Q8—1312no—
540C4×Q8—1312no—
541C4×Q8—1312no—
542C4×Q8C22×D1312yes—
543C4×Q8C22×D1314yes—
544C4×Q8C22×D13112yes—
545C4×D4—136no—
546C4×D4—1312no—
547C4×D4—1312no—
548C4×D4—1324no—
549C4×D4—136no—
550C4×D4—1312no—
551C4×D4—1312no—
552C4×D4—1324no—
553C4×D4—136no—
554C4×D4—1312no—
555C4×D4C22×D1316yes—
556C4×D4C22×D13112yes—
557#117—133no—
558#117—136no—
559#117—136no—
560#117—136no—
561#117—136no—
562#117—136no—
563#117—1312no—
564#117—136no—
565#117—1312no—
566#117C22×D1313yes—
567#117C22×D1316yes—
568C2×C4⋊C4—1312no—
569C2×C4⋊C4—136no—
570C2×C4⋊C4—1312no—
571C2×C4⋊C4—1312no—
572C2×C4⋊C4—1312no—
573C2×C4⋊C4—136no—
574C2×C4⋊C4—1312no—
575C2×C4⋊C4—1312no—
576C2×C4⋊C4—1312no—
577C2×C4⋊C4—1312no—
578C2×C4⋊C4—1324no—
579C2×C4⋊C4—1324no—
580C2×C4⋊C4—1324no—
581C2×C4⋊C4—132no—
582C2×C4⋊C4—136no—
583C2×C4⋊C4—134no—
584C2×C4⋊C4—1312no—
585C2×C4⋊C4C22×D1316yes—
586C2×C4⋊C4C22×D13112yes—
587C2×C22⋊C4—1312no—
588C2×C22⋊C4—136no—
589C2×C42—136no—
590C2×C42—133no—
591C2×C42—133no—
592C2×C42—1312no—
593C2×C42—136no—
594C2×C42—136no—
595C2×C42—133no—
596C2×C42—133no—
597C2×C42—131no—
598C2×C42C22×D1313yes—
599C2×C13—26no—
600C2×C13C24×Q811yescharacteristic
601C2×C13C2×#58512yes—
602D13—26no—
603D13#350414yesdirect product factor
604C24—133no—
605#41—138no—
606#41—1324no—
607#41—1324no—
608#41Q8×D1318yescomplemented
609C2×Q8—138no—
610C2×Q8—133no—
611C2×Q8—1312no—
612C2×Q8—1312no—
613C2×Q8—1312no—
614C2×Q8—5224no—
615C2×Q8C23×D13112yes—
616C2×Q8C23×D1311yescharacteristic
617C2×D4—136no—
618C2×D4—1324no—
619C2×D4—133no—
620C2×D4C23×D1313yes—
621C22×C4—133no—
622C22×C4—1324no—
623C22×C4—133no—
624C22×C4—131no—
625C22×C4—133no—
626C22×C4—133no—
627C22×C4—136no—
628C22×C4—1312no—
629C22×C4—132no—
630C22×C4—134no—
631C22×C4—136no—
632C22×C4—1312no—
633C22×C4—136no—
634C22×C4—136no—
635C22×C4—1324no—
636C22×C4—5212no—
637C22×C4—5224no—
638C22×C4C23×D1316yes—
639C22×C4C23×D13112yes—
640C22×C4C23×D1313yes—
641C4⋊C4—1312no—
642C4⋊C4—136no—
643C4⋊C4—1312no—
644C4⋊C4—1312no—
645C4⋊C4—1312no—
646C4⋊C4—1324no—
647C4⋊C4—1312no—
648C4⋊C4—1324no—
649C4⋊C4—1324no—
650C4⋊C4—1324no—
651C4⋊C4—134no—
652C4⋊C4—132no—
653C4⋊C4—1312no—
654C4⋊C4—136no—
655C4⋊C4—134no—
656C4⋊C4—134no—
657C4⋊C4—134no—
658C4⋊C4—1312no—
659C4⋊C4—1312no—
660C4⋊C4—1312no—
661C4⋊C4C23×D1316yes—
662C4⋊C4C23×D13112yes—
663C4⋊C4C23×D13112yes—
664C4⋊C4C23×D13124yes—
665C4⋊C4C23×D1312yes—
666C4⋊C4C23×D1316yes—
667C4⋊C4C23×D1314yes—
668C4⋊C4C23×D13112yes—
669C22⋊C4—1312no—
670C22⋊C4—136no—
671C22⋊C4—1312no—
672C22⋊C4—1312no—
673C22⋊C4—1312no—
674C22⋊C4C23×D13112yes—
675C22⋊C4C23×D1316yes—
676C42—132no—
677C42—131no—
678C42—136no—
679C42—133no—
680C42—136no—
681C42—136no—
682C42—136no—
683C42—1312no—
684C42—1312no—
685C42—1312no—
686C42C23×D1311yescharacteristic
687C42C23×D1313yes—
688C42C23×D1316yes—
689C42C23×D13112yes—
690C13C2×#350411yescharacteristic, complemented, Sylow
691C23—131no—
692C23—1312no—
693C23—133no—
694C23—2612no—
695C23C24×D1313yes—
696Q8—412no—
697Q8—1312no—
698Q8—5212no—
699Q8—5212no—
700Q8—5212no—
701Q8C2×Q8×D1314yes—
702D4—1324no—
703D4—1312no—
704D4C2×Q8×D13112yes—
705C2×C4—46no—
706C2×C4—412no—
707C2×C4—1312no—
708C2×C4—133no—
709C2×C4—131no—
710C2×C4—134no—
711C2×C4—1312no—
712C2×C4—1312no—
713C2×C4—1312no—
714C2×C4—132no—
715C2×C4—134no—
716C2×C4—136no—
717C2×C4—1312no—
718C2×C4—264no—
719C2×C4—2624no—
720C2×C4—2612no—
721C2×C4—268no—
722C2×C4—526no—
723C2×C4—5224no—
724C2×C4—526no—
725C2×C4—526no—
726C2×C4—5212no—
727C2×C4C2×Q8×D13112yes—
728C2×C4C24×D1312yes—
729C2×C4C24×D1314yes—
730C2×C4C24×D1316yes—
731C2×C4C24×D13112yes—
732C2×C4C24×D1313yes—
733C2×C4C24×D1311yescharacteristic
734C22—26no—
735C22—132no—
736C22—134no—
737C22—136no—
738C22—2624no—
739C22—266no—
740C22C22×Q8×D1316yes—
741C22C25×D1311yescharacteristic
742C4—22no—
743C4—212no—
744C4—26no—
745C4—24no—
746C4—132no—
747C4—136no—
748C4—262no—
749C4—2612no—
750C4—266no—
751C4—264no—
752C4C22×Q8×D1312yes—
753C4C22×Q8×D1316yes—
754C2—26no—
755C2—134no—
756C2—266no—
757C2C23×Q8×D1311yescharacteristic
758C2D13×#58512yes—
subgroupG/H
center, FrattiniC22C25×D13
commutator, socle, cosocleC22×C13C26
FittingC13×#3504C2
prime radicalC2×#41×D13C22
hypercenter#3504D13
hypocenterC13C2×#3504
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #3504

Complements

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

NH ≅ G/Ntype
1. #13128662C2semidirect
2. #13128661C2semidirect
3. #13128660C2semidirect
4. #13128659C2semidirect
5. #13128658C2semidirect
6. #13128657C2semidirect
7. #13128656C2semidirect
8. D13×#557C2semidirect
9. D13×#554C2semidirect
10. D13×#544C2semidirect
11. D13×#533C2semidirect
12. C2×D13×#125C2semidirect
15. C13×#3504C2semidirect
17. C13×#557C22semidirect
18. C13×#554C22semidirect
19. C13×#544C22semidirect
20. C13×#533C22semidirect
21. C2×C13×#125C22semidirect
26. #11719435C22semidirect
27. #11719434C22semidirect
28. #11719434C22semidirect
29. #11719433C22semidirect
32. #11719426C22semidirect
33. #11719395C22semidirect
34. #11719395C22semidirect
35. #11719394C22semidirect
36. #11719394C22semidirect
37. #11719393C22semidirect
38. #11719393C22semidirect
44. D13×#125C22semidirect
45. D13×#125C22semidirect
46. D13×#125C22semidirect
47. #11719390C22semidirect
48. #11719390C22semidirect
49. #11719341C22semidirect
50. #11719341C22semidirect
51. #11719340C22semidirect
54. #11719328C22semidirect
55. #11719327C22semidirect
56. #11719284C22semidirect
57. #11719283C22semidirect
63. #11719275C22semidirect
64. #11719274C22semidirect
65. #11719274C22semidirect
66. #11719272C22semidirect
70. #11719248C22semidirect
71. #11719244C22semidirect
72. #11719244C22semidirect
78. #11719224C22semidirect
79. #11719224C22semidirect
80. #11719222C22semidirect
81. #11719216C22semidirect
85. #11719205C22semidirect
86. C2×#88144C22semidirect
87. C2×#88143C22semidirect
90. #11719175C22semidirect
91. C2×#88124C22semidirect
93. #41×D13Q8semidirect
227. C13×#41C2×Q8semidirect
238. #6131C2×Q8semidirect
241. #6129C2×Q8semidirect
243. #6127C2×Q8semidirect
319. #3504D13direct (N × H)
378. #557C2×D13semidirect
390. #554C2×D13semidirect
399. #544C2×D13semidirect
407. #533C2×D13semidirect
421. C2×#125C2×D13semidirect
603. D13#3504direct (N × H)
608. #41Q8×D13semidirect
690. C13C2×#3504semidirect

Maximal subgroups

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

subgroupindex
#131286622
#131286612
#131286602
#131286592
#131286582
#131286572
#131286562
D13×#5572
D13×#5542
D13×#5442
D13×#5332
C2×D13×#1252
D13×#5202
C4×#41×D132
C13×#35042
C2×#350413