Finite Group Databasebeta

← C13×#33560 #15719899

Subgroups — C13×#33560 #15719899

Order 3328.

1132 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3551C211yesmaximal, characteristic, complemented
2C13×#3028C211yesmaximal, characteristic, complemented
3C13×#3027C211yesmaximal, characteristic, complemented
4C13×#3018C211yesmaximal, characteristic, complemented
5C13×#2200C214yesmaximal, complemented
6C13×#2197C214yesmaximal, complemented
7C13×#2126C211yesmaximal, characteristic, complemented
8C13×#2123C211yesmaximal, characteristic, complemented
9C13×#2122C211yesmaximal, characteristic, complemented
10C13×#585C2211yescharacteristic
11C13×#575—21no—
12C13×#563—21no—
13C13×#560C2212yescomplemented
14C13×#555—21no—
15C13×#553—21no—
16C13×#552—21no—
17C13×#551C2212yescomplemented
18C13×#548—21no—
19C13×#546—21no—
20C13×#540—22no—
21C13×#538—22no—
22C13×#537—21no—
23C13×#536—21no—
24C13×#536C2211yescharacteristic
25C13×#535—21no—
26C13×#535C2211yescharacteristic
27C13×#532C2211yescharacteristic
28C13×#529—21no—
29C13×#458—22no—
30C13×#458C2214yes—
31C13×B(4,𝔽2)—22no—
32C13×B(4,𝔽2)C2214yes—
33C13×#456—21no—
34C13×#455C2212yes—
35C13×#454—21no—
36C13×#453C2212yes—
37C2×C13×#104—21no—
38C13×#413C2211yescharacteristic
39C13×#410—21no—
40C13×#410—21no—
41C13×#410C2211yescharacteristic
42C13×#410C2211yescharacteristic
43C13×#354C2212yescomplemented
44C13×#353C2212yescomplemented
45C13×#352C2214yescomplemented
46C13×AΣL(1,𝔽16)C2214yescomplemented
47C13×2−1+4—21no—
48C13×2−1+4—41no—
49C13×H(5,𝔽2)—21no—
50C13×H(5,𝔽2)—21no—
51C13×H(5,𝔽2)—41no—
52C13×H(5,𝔽2)C2312yes—
53C2×C13×#41—21no—
54C2×C13×#41—21no—
55C2×C13×#41—21no—
56C2×C13×#41—21no—
57C2×C13×#41—42no—
58C2×C13×#41D411yescharacteristic, complemented
59C2×C13×#41C2311yescharacteristic
60C22×Q8×C13D411yescharacteristic, complemented
61C22×D4×C13D411yescharacteristic
62C13×#137—22no—
63C13×#137—41no—
64C13×AGL(1,ℤ/8)—22no—
65C13×AGL(1,ℤ/8)—41no—
66C13×#135—42no—
67C2×C13×M16—21no—
68C13×C4⋊Q8—21no—
69C13×C4⋊Q8—41no—
70C13×C4⋊Q8D411yescharacteristic, complemented
71C13×#127—21no—
72C13×#127—41no—
73C13×#127C2311yescharacteristic
74C13×#126—22no—
75C13×#126—22no—
76C13×#126—22no—
77C13×#125—21no—
78C13×#125—22no—
79C13×#124—21no—
80C13×#124—22no—
81C13×#124—21no—
82C13×#124—21no—
83C13×#124—41no—
84C13×#124—41no—
85C13×#124D411yescharacteristic, complemented
86C13×#124C2311yescharacteristic
87C13×#123—22no—
88C13×#123—22no—
89C13×#123—22no—
90C13×#123—22no—
91C13×#123—24no—
92C13×#123D412yescomplemented
93C13×#123C2312yes—
94C13×C22⋊Q8—21no—
95C13×C22⋊Q8—22no—
96C13×C22⋊Q8—22no—
97C13×C22⋊Q8—21no—
98C13×C22⋊Q8—21no—
99C13×C22⋊Q8—42no—
100C13×#121—22no—
101C13×#121—22no—
102C13×#121—21no—
103C13×#121—22no—
104C13×#121—21no—
105C13×#121—21no—
106C13×#121—22no—
107C13×#121—21no—
108C13×#121—21no—
109C13×#121—22no—
110C13×#121—22no—
111C13×#121—42no—
112C13×#120—22no—
113C13×#120—24no—
114C13×#120D412yes—
115C13×#120C2312yes—
116C4×Q8×C13—21no—
117C4×D4×C13—22no—
118C4×D4×C13—21no—
119C4×D4×C13—22no—
120C4×D4×C13—21no—
121C4×D4×C13—21no—
122C4×D4×C13—22no—
123C13×#117—22no—
124C13×#117—22no—
125C13×#117—21no—
126C13×#117—21no—
127C13×#117D411yescharacteristic
128C13×#117D411yescharacteristic, complemented
129C2×C13×C4⋊C4—21no—
130C2×C13×C22⋊C4—22no—
131C2×C42×C13D411yescharacteristic, complemented
132C13×#104—22no—
133C13×#104—22no—
134C13×#101—21no—
135C13×#100C2312yes—
136C13×#99—21no—
137C13×#99—21no—
138C13×#99—24no—
139C13×#99—24no—
140C13×#99C2312yes—
141C13×#99C2312yes—
142#33560C1311yesmaximal, characteristic, direct product factor, Sylow
143C24×C13C2×D412yes—
144C13×#41—22no—
145C13×#41—22no—
146C13×#41—41no—
147C13×#41—41no—
148C13×#41—42no—
149C13×#41—41no—
150C13×#41—41no—
151C13×#41—41no—
152C13×#41—41no—
153C13×#41—41no—
154C13×#41—42no—
155C13×#41—42no—
156C13×#41—41no—
157C13×#41—41no—
158C13×#41—42no—
159C13×#41—41no—
160C13×#41—41no—
161C13×#41—41no—
162C13×#41—81no—
163C13×#41—81no—
164C2×Q8×C13—21no—
165C2×Q8×C13—21no—
166C2×Q8×C13—21no—
167C2×Q8×C13—21no—
168C2×Q8×C13—21no—
169C2×Q8×C13—41no—
170C2×Q8×C13—41no—
171C2×Q8×C13—42no—
172C2×Q8×C13C2×D411yescharacteristic
173C2×Q8×C13C2×D411yescharacteristic
174C2×D4×C13—21no—
175C2×D4×C13—21no—
176C2×D4×C13—21no—
177C2×D4×C13—22no—
178C2×D4×C13—22no—
179C2×D4×C13—22no—
180C2×D4×C13—22no—
181C2×D4×C13—22no—
182C2×D4×C13—21no—
183C2×D4×C13—21no—
184C2×D4×C13—22no—
185C2×D4×C13—21no—
186C2×D4×C13—21no—
187C2×D4×C13—21no—
188C2×D4×C13—41no—
189C2×D4×C13—41no—
190C2×D4×C13—42no—
191C2×D4×C13—42no—
192C2×D4×C13—42no—
193C2×D4×C13—41no—
194C2×D4×C13—44no—
195C2×D4×C13C2×D411yescharacteristic
196C2×D4×C13C2×D411yescharacteristic
197C2×D4×C13C2×D411yescharacteristic
198C2×D4×C13C2411yescharacteristic
199C22×C4×C13—22no—
200C22×C4×C13—22no—
201C22×C4×C13—22no—
202C22×C4×C13—22no—
203C22×C4×C13—22no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—41no—
207C22×C4×C13C2×D411yescharacteristic
208C22×C4×C13C2×D411yescharacteristic
209C22×C4×C13C2×D411yescharacteristic
210C22×C4×C13C2×D412yes—
211C13×Q16—42no—
212C13×SD16—42no—
213C13×SD16—42no—
214C13×D8—42no—
215C13×M16—22no—
216C13×M16—41no—
217C2×C8×C13—41no—
218C13×C4⋊C4—22no—
219C13×C4⋊C4—22no—
220C13×C4⋊C4—22no—
221C13×C4⋊C4—22no—
222C13×C4⋊C4—22no—
223C13×C4⋊C4—22no—
224C13×C4⋊C4—21no—
225C13×C4⋊C4—21no—
226C13×C4⋊C4—21no—
227C13×C4⋊C4—21no—
228C13×C4⋊C4—22no—
229C13×C4⋊C4—41no—
230C13×C4⋊C4—41no—
231C13×C4⋊C4—44no—
232C13×C22⋊C4—22no—
233C13×C22⋊C4—22no—
234C13×C22⋊C4—22no—
235C13×C22⋊C4—22no—
236C13×C22⋊C4—22no—
237C13×C22⋊C4—22no—
238C13×C22⋊C4—21no—
239C13×C22⋊C4—22no—
240C13×C22⋊C4—21no—
241C13×C22⋊C4—21no—
242C13×C22⋊C4—21no—
243C13×C22⋊C4—22no—
244C13×C22⋊C4—22no—
245C13×C22⋊C4—22no—
246C13×C22⋊C4—22no—
247C13×C22⋊C4—44no—
248C13×C22⋊C4—44no—
249C13×C22⋊C4C2×D412yes—
250C13×C22⋊C4C2×D412yes—
251C42×C13—22no—
252C42×C13—21no—
253C42×C13—21no—
254C42×C13—21no—
255C42×C13—41no—
256C42×C13—41no—
257C42×C13C2×D411yescharacteristic
258C42×C13C2×D411yescharacteristic
259#3551C2×C1311yescharacteristic, complemented
260#3028C2×C1311yescharacteristic, complemented
261#3027C2×C1311yescharacteristic, complemented
262#3018C2×C1311yescharacteristic, complemented
263#2200C2×C1314yescomplemented
264#2197C2×C1314yescomplemented
265#2126C2×C1311yescharacteristic, complemented
266#2123C2×C1311yescharacteristic, complemented
267#2122C2×C1311yescharacteristic, complemented
268C23×C13—22no—
269C23×C13—22no—
270C23×C13—22no—
271C23×C13—21no—
272C23×C13—41no—
273C23×C13—42no—
274C23×C13—82no—
275C23×C13#12011yescharacteristic
276C23×C13C22×D411yescharacteristic
277C23×C13C22×D411yescharacteristic
278Q8×C13—22no—
279Q8×C13—41no—
280Q8×C13—41no—
281Q8×C13—41no—
282Q8×C13—41no—
283Q8×C13—41no—
284Q8×C13—41no—
285Q8×C13—41no—
286Q8×C13—81no—
287D4×C13—22no—
288D4×C13—41no—
289D4×C13—41no—
290D4×C13—41no—
291D4×C13—41no—
292D4×C13—41no—
293D4×C13—41no—
294D4×C13—42no—
295D4×C13—42no—
296D4×C13—42no—
297D4×C13—42no—
298D4×C13—41no—
299D4×C13—41no—
300D4×C13—41no—
301D4×C13—81no—
302D4×C13—81no—
303D4×C13—82no—
304D4×C13—82no—
305D4×C13—82no—
306D4×C13—81no—
307D4×C13—81no—
308D4×C13—82no—
309D4×C13—164no—
310C2×C4×C13—21no—
311C2×C4×C13—21no—
312C2×C4×C13—21no—
313C2×C4×C13—21no—
314C2×C4×C13—21no—
315C2×C4×C13—21no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—21no—
319C2×C4×C13—22no—
320C2×C4×C13—21no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—21no—
324C2×C4×C13—42no—
325C2×C4×C13—42no—
326C2×C4×C13—42no—
327C2×C4×C13—41no—
328C2×C4×C13—42no—
329C2×C4×C13—41no—
330C2×C4×C13—41no—
331C2×C4×C13—42no—
332C2×C4×C13—42no—
333C2×C4×C13—42no—
334C2×C4×C13—82no—
335C2×C4×C13—81no—
336C2×C4×C13—82no—
337C2×C4×C13—82no—
338C2×C4×C13#12011yescharacteristic
339C2×C4×C13#12011yescharacteristic
340C2×C4×C13#12011yescharacteristic
341C2×C4×C13C22×D411yescharacteristic
342C8×C13—42no—
343#585C22×C1311yescharacteristic
344#575—21no—
345#563—21no—
346#560C22×C1312yescomplemented
347#555—21no—
348#553—21no—
349#552—21no—
350#551C22×C1312yescomplemented
351#548—21no—
352#546—21no—
353#540—22no—
354#538—22no—
355#537—21no—
356#536—21no—
357#536C22×C1311yescharacteristic
358#535—21no—
359#535C22×C1311yescharacteristic
360#532C22×C1311yescharacteristic
361#529—21no—
362#458—22no—
363#458C22×C1314yes—
364B(4,𝔽2)—22no—
365B(4,𝔽2)C22×C1314yes—
366#456—21no—
367#455C22×C1312yes—
368#454—21no—
369#453C22×C1312yes—
370C2×#104—21no—
371#413C22×C1311yescharacteristic
372#410—21no—
373#410—21no—
374#410C22×C1311yescharacteristic
375#410C22×C1311yescharacteristic
376#354C22×C1312yescomplemented
377#353C22×C1312yescomplemented
378#352C22×C1314yescomplemented
379AΣL(1,𝔽16)C22×C1314yescomplemented
380C22×C13—21no—
381C22×C13—21no—
382C22×C13—21no—
383C22×C13—41no—
384C22×C13—41no—
385C22×C13—41no—
386C22×C13—41no—
387C22×C13—42no—
388C22×C13—41no—
389C22×C13—42no—
390C22×C13—42no—
391C22×C13—41no—
392C22×C13—42no—
393C22×C13—82no—
394C22×C13—84no—
395C22×C13—82no—
396C22×C13—161no—
397C22×C13C2×#12011yescharacteristic
398C4×C13—21no—
399C4×C13—21no—
400C4×C13—21no—
401C4×C13—41no—
402C4×C13—42no—
403C4×C13—42no—
404C4×C13—41no—
405C4×C13—42no—
406C4×C13—41no—
407C4×C13—42no—
408C4×C13—82no—
409C4×C13—82no—
410C4×C13B(4,𝔽2)11yescharacteristic
411C4×C13B(4,𝔽2)11yescharacteristic
4122−1+4—21no—
4132−1+4—41no—
414H(5,𝔽2)—21no—
415H(5,𝔽2)—21no—
416H(5,𝔽2)—41no—
417H(5,𝔽2)C23×C1312yes—
418C2×#41—21no—
419C2×#41—21no—
420C2×#41—21no—
421C2×#41—21no—
422C2×#41—42no—
423C2×#41D4×C1311yescharacteristic, complemented
424C2×#41C23×C1311yescharacteristic
425C22×Q8D4×C1311yescharacteristic, complemented
426C22×D4D4×C1311yescharacteristic
427#137—22no—
428#137—41no—
429AGL(1,ℤ/8)—22no—
430AGL(1,ℤ/8)—41no—
431#135—42no—
432C2×M16—21no—
433C4⋊Q8—21no—
434C4⋊Q8—41no—
435C4⋊Q8D4×C1311yescharacteristic, complemented
436#127—21no—
437#127—41no—
438#127C23×C1311yescharacteristic
439#126—22no—
440#126—22no—
441#126—22no—
442#125—21no—
443#125—22no—
444#124—21no—
445#124—22no—
446#124—21no—
447#124—21no—
448#124—41no—
449#124—41no—
450#124D4×C1311yescharacteristic, complemented
451#124C23×C1311yescharacteristic
452#123—22no—
453#123—22no—
454#123—22no—
455#123—22no—
456#123—24no—
457#123D4×C1312yescomplemented
458#123C23×C1312yes—
459C22⋊Q8—21no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—21no—
463C22⋊Q8—21no—
464C22⋊Q8—42no—
465#121—22no—
466#121—22no—
467#121—21no—
468#121—22no—
469#121—21no—
470#121—21no—
471#121—22no—
472#121—21no—
473#121—21no—
474#121—22no—
475#121—22no—
476#121—42no—
477#120—22no—
478#120—24no—
479#120D4×C1312yes—
480#120C23×C1312yes—
481C4×Q8—21no—
482C4×D4—22no—
483C4×D4—21no—
484C4×D4—22no—
485C4×D4—21no—
486C4×D4—21no—
487C4×D4—22no—
488#117—22no—
489#117—22no—
490#117—21no—
491#117—21no—
492#117D4×C1311yescharacteristic
493#117D4×C1311yescharacteristic, complemented
494C2×C4⋊C4—21no—
495C2×C22⋊C4—22no—
496C2×C42D4×C1311yescharacteristic, complemented
497#104—22no—
498#104—22no—
499#101—21no—
500#100C23×C1312yes—
501#99—21no—
502#99—21no—
503#99—24no—
504#99—24no—
505#99C23×C1312yes—
506#99C23×C1312yes—
507C2×C13—21no—
508C2×C13—41no—
509C2×C13—41no—
510C2×C13—41no—
511C2×C13—81no—
512C2×C13—82no—
513C2×C13—82no—
514C2×C13C2×B(4,𝔽2)11yescharacteristic
515C24C2×D4×C1312yes—
516#41—22no—
517#41—22no—
518#41—41no—
519#41—41no—
520#41—42no—
521#41—41no—
522#41—41no—
523#41—41no—
524#41—41no—
525#41—41no—
526#41—42no—
527#41—42no—
528#41—41no—
529#41—41no—
530#41—42no—
531#41—41no—
532#41—41no—
533#41—41no—
534#41—81no—
535#41—81no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—41no—
542C2×Q8—41no—
543C2×Q8—42no—
544C2×Q8C2×D4×C1311yescharacteristic
545C2×Q8C2×D4×C1311yescharacteristic
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—41no—
566C2×D4—44no—
567C2×D4C2×D4×C1311yescharacteristic
568C2×D4C2×D4×C1311yescharacteristic
569C2×D4C2×D4×C1311yescharacteristic
570C2×D4C24×C1311yescharacteristic
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—41no—
579C22×C4C2×D4×C1311yescharacteristic
580C22×C4C2×D4×C1311yescharacteristic
581C22×C4C2×D4×C1311yescharacteristic
582C22×C4C2×D4×C1312yes—
583Q16—42no—
584SD16—42no—
585SD16—42no—
586D8—42no—
587M16—22no—
588M16—41no—
589C2×C8—41no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—22no—
601C4⋊C4—41no—
602C4⋊C4—41no—
603C4⋊C4—44no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—21no—
611C22⋊C4—22no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4C2×D4×C1312yes—
622C22⋊C4C2×D4×C1312yes—
623C42—22no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—41no—
628C42—41no—
629C42C2×D4×C1311yescharacteristic
630C42C2×D4×C1311yescharacteristic
631C13#3356011yescharacteristic, direct product factor, Sylow
632C23—22no—
633C23—22no—
634C23—22no—
635C23—21no—
636C23—41no—
637C23—42no—
638C23—82no—
639C23C13×#12011yescharacteristic
640C23C22×D4×C1311yescharacteristic
641C23C22×D4×C1311yescharacteristic
642Q8—22no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—81no—
651D4—22no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—42no—
659D4—42no—
660D4—42no—
661D4—42no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—81no—
666D4—81no—
667D4—82no—
668D4—82no—
669D4—82no—
670D4—81no—
671D4—81no—
672D4—82no—
673D4—164no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—82no—
699C2×C4—81no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4C13×#12011yescharacteristic
703C2×C4C13×#12011yescharacteristic
704C2×C4C13×#12011yescharacteristic
705C2×C4C22×D4×C1311yescharacteristic
706C8—42no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—42no—
715C22—41no—
716C22—42no—
717C22—42no—
718C22—41no—
719C22—42no—
720C22—82no—
721C22—84no—
722C22—82no—
723C22—161no—
724C22C2×C13×#12011yescharacteristic
725C4—21no—
726C4—21no—
727C4—21no—
728C4—41no—
729C4—42no—
730C4—42no—
731C4—41no—
732C4—42no—
733C4—41no—
734C4—42no—
735C4—82no—
736C4—82no—
737C4C13×B(4,𝔽2)11yescharacteristic
738C4C13×B(4,𝔽2)11yescharacteristic
739C2—21no—
740C2—41no—
741C2—41no—
742C2—41no—
743C2—82no—
744C2—81no—
745C2—82no—
746C2C2×C13×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C13C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C13
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3551C2semidirect
2. C13×#3028C2semidirect
3. C13×#3027C2semidirect
4. C13×#3018C2semidirect
5. C13×#2200C2semidirect
6. C13×#2197C2semidirect
7. C13×#2126C2semidirect
8. C13×#2123C2semidirect
9. C13×#2122C2semidirect
13. C13×#560C22semidirect
17. C13×#551C22semidirect
43. C13×#354C22semidirect
44. C13×#353C22semidirect
45. C13×#352C22semidirect
46. C13×AΣL(1,𝔽16)C22semidirect
58. C2×C13×#41D4semidirect
60. C22×Q8×C13D4semidirect
70. C13×C4⋊Q8D4semidirect
85. C13×#124D4semidirect
92. C13×#123D4semidirect
128. C13×#117D4semidirect
131. C2×C42×C13D4semidirect
142. #33560C13direct (N × H)
259. #3551C2×C13semidirect
260. #3028C2×C13semidirect
261. #3027C2×C13semidirect
262. #3018C2×C13semidirect
263. #2200C2×C13semidirect
264. #2197C2×C13semidirect
265. #2126C2×C13semidirect
266. #2123C2×C13semidirect
267. #2122C2×C13semidirect
346. #560C22×C13semidirect
350. #551C22×C13semidirect
376. #354C22×C13semidirect
377. #353C22×C13semidirect
378. #352C22×C13semidirect
379. AΣL(1,𝔽16)C22×C13semidirect
423. C2×#41D4×C13semidirect
425. C22×Q8D4×C13semidirect
435. C4⋊Q8D4×C13semidirect
450. #124D4×C13semidirect
457. #123D4×C13semidirect
493. #117D4×C13semidirect
496. C2×C42D4×C13semidirect
631. C13#33560direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35512
C13×#30282
C13×#30272
C13×#30182
C13×#22002
C13×#21972
C13×#21262
C13×#21232
C13×#21222
#3356013