Finite Group Databasebeta

← C13×#33546 #15719885

Subgroups — C13×#33546 #15719885

Order 3328.

1236 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3481C211yesmaximal, characteristic, complemented
2C13×#3025C212yesmaximal, complemented
3C13×#3018C211yesmaximal, characteristic, complemented
4C13×#2198C212yesmaximal, complemented
5C13×#2197C214yesmaximal, complemented
6C13×#2196C212yesmaximal, complemented
7C13×#2126C211yesmaximal, characteristic, complemented
8C13×#2120C212yesmaximal, complemented
9C13×#585C2211yescharacteristic, complemented
10C13×#575—21no—
11C13×#559C2211yescharacteristic, complemented
12C13×#554—21no—
13C13×#553—22no—
14C13×#551—21no—
15C13×#551C2212yescomplemented
16C13×#546—22no—
17D42×C13C2211yescharacteristic, complemented
18C13×#532C2211yescharacteristic
19C13×#529—22no—
20C13×#525—21no—
21C13×#525—22no—
22C13×#525C2212yes—
23C4×C13×#41—21no—
24C2×C4×D4×C13—22no—
25C13×#458—22no—
26C13×#458C2214yescomplemented
27C13×B(4,𝔽2)—22no—
28C13×B(4,𝔽2)C2214yes—
29C13×#456—21no—
30C13×#455C2212yescomplemented
31C13×#454—21no—
32C13×#453C2212yes—
33C2×C13×#104—21no—
34C13×#413C2211yescharacteristic, complemented
35C13×#410—22no—
36C13×#410C2212yescomplemented
37C13×#354C2212yescomplemented
38C13×#353C2212yescomplemented
39C13×#352C2214yescomplemented
40C13×AΣL(1,𝔽16)C2214yescomplemented
41C13×2−1+4—21no—
42C13×2−1+4—41no—
43C13×H(5,𝔽2)—22no—
44C13×H(5,𝔽2)—41no—
45C13×H(5,𝔽2)C2312yes—
46C2×C13×#41—21no—
47C2×C13×#41—22no—
48C2×C13×#41—21no—
49C2×C13×#41—42no—
50C2×C13×#41D411yescharacteristic, complemented
51C2×C13×#41C2311yescharacteristic
52C22×D4×C13—22no—
53C23×C4×C13—21no—
54C23×C4×C13D412yescomplemented
55C13×#137—22no—
56C13×#137—41no—
57C13×AGL(1,ℤ/8)—22no—
58C13×AGL(1,ℤ/8)—41no—
59C13×#135—42no—
60C2×C13×M16—21no—
61C13×C4⋊Q8D411yescharacteristic, complemented
62C13×#127C2311yescharacteristic
63C13×#126—22no—
64C13×#126—22no—
65C13×#125—22no—
66C13×#124—22no—
67C13×#124D411yescharacteristic, complemented
68C13×#124C2311yescharacteristic
69C13×#123—21no—
70C13×#123—22no—
71C13×#123—21no—
72C13×#123—22no—
73C13×#123—24no—
74C13×#123D412yescomplemented
75C13×#123C2312yes—
76C13×C22⋊Q8—22no—
77C13×C22⋊Q8—22no—
78C13×C22⋊Q8—22no—
79C13×C22⋊Q8—42no—
80C13×#121—22no—
81C13×#121—22no—
82C13×#121—22no—
83C13×#121—22no—
84C13×#121—42no—
85C13×#120—21no—
86C13×#120—21no—
87C13×#120—24no—
88C13×#120D412yescomplemented
89C13×#120C2312yes—
90C4×Q8×C13—21no—
91C4×Q8×C13—21no—
92C4×D4×C13—21no—
93C4×D4×C13—22no—
94C4×D4×C13—22no—
95C4×D4×C13—22no—
96C4×D4×C13—22no—
97C4×D4×C13—22no—
98C4×D4×C13—22no—
99C4×D4×C13—22no—
100C4×D4×C13—22no—
101C4×D4×C13—22no—
102C4×D4×C13—21no—
103C4×D4×C13—44no—
104C13×#117—21no—
105C13×#117—21no—
106C13×#117—22no—
107C13×#117—22no—
108C13×#117D412yescomplemented
109C2×C13×C4⋊C4—22no—
110C2×C13×C22⋊C4—22no—
111C2×C13×C22⋊C4—22no—
112C2×C42×C13—22no—
113C2×C42×C13D411yescharacteristic, complemented
114C13×#104—22no—
115C13×#104—22no—
116C13×#101—21no—
117C13×#100C2312yes—
118C13×#99—22no—
119C13×#99—24no—
120C13×#99—24no—
121C13×#99C2314yes—
122#33546C1311yesmaximal, characteristic, direct product factor, Sylow
123C24×C13—21no—
124C24×C13C2×D412yes—
125C13×#41—22no—
126C13×#41—22no—
127C13×#41—41no—
128C13×#41—41no—
129C13×#41—42no—
130C13×#41—42no—
131C13×#41—42no—
132C13×#41—41no—
133C13×#41—44no—
134C13×#41—41no—
135C13×#41—41no—
136C13×#41—44no—
137C13×#41—42no—
138C13×#41—42no—
139C13×#41—41no—
140C2×Q8×C13—21no—
141C2×Q8×C13—22no—
142C2×Q8×C13—21no—
143C2×Q8×C13—42no—
144C2×Q8×C13C2×D411yescharacteristic
145C2×Q8×C13C2×D411yescharacteristic
146C2×D4×C13—21no—
147C2×D4×C13—21no—
148C2×D4×C13—22no—
149C2×D4×C13—22no—
150C2×D4×C13—22no—
151C2×D4×C13—24no—
152C2×D4×C13—22no—
153C2×D4×C13—22no—
154C2×D4×C13—21no—
155C2×D4×C13—42no—
156C2×D4×C13—48no—
157C2×D4×C13—44no—
158C2×D4×C13—41no—
159C2×D4×C13—44no—
160C2×D4×C13C2×D412yes—
161C2×D4×C13C2×D411yescharacteristic
162C2×D4×C13C2411yescharacteristic
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—24no—
166C22×C4×C13—21no—
167C22×C4×C13—22no—
168C22×C4×C13—21no—
169C22×C4×C13—22no—
170C22×C4×C13—21no—
171C22×C4×C13—22no—
172C22×C4×C13—41no—
173C22×C4×C13—42no—
174C22×C4×C13—42no—
175C22×C4×C13—81no—
176C22×C4×C13—81no—
177C22×C4×C13C2×D412yes—
178C22×C4×C13C2×D411yescharacteristic
179C22×C4×C13C2×D412yes—
180C13×Q16—42no—
181C13×SD16—42no—
182C13×SD16—42no—
183C13×D8—42no—
184C13×M16—22no—
185C13×M16—41no—
186C2×C8×C13—41no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—22no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—22no—
191C13×C4⋊C4—22no—
192C13×C4⋊C4—22no—
193C13×C4⋊C4—22no—
194C13×C4⋊C4—22no—
195C13×C4⋊C4—22no—
196C13×C4⋊C4—42no—
197C13×C4⋊C4—44no—
198C13×C22⋊C4—22no—
199C13×C22⋊C4—22no—
200C13×C22⋊C4—22no—
201C13×C22⋊C4—21no—
202C13×C22⋊C4—21no—
203C13×C22⋊C4—22no—
204C13×C22⋊C4—22no—
205C13×C22⋊C4—22no—
206C13×C22⋊C4—22no—
207C13×C22⋊C4—22no—
208C13×C22⋊C4—22no—
209C13×C22⋊C4—24no—
210C13×C22⋊C4—44no—
211C13×C22⋊C4—44no—
212C13×C22⋊C4C2×D412yes—
213C13×C22⋊C4C2×D412yes—
214C42×C13—22no—
215C42×C13—22no—
216C42×C13—21no—
217C42×C13—22no—
218C42×C13—42no—
219C42×C13C2×D411yescharacteristic
220C42×C13C2×D411yescharacteristic
221#3481C2×C1311yescharacteristic, complemented
222#3025C2×C1312yescomplemented
223#3018C2×C1311yescharacteristic, complemented
224#2198C2×C1312yescomplemented
225#2197C2×C1314yescomplemented
226#2196C2×C1312yescomplemented
227#2126C2×C1311yescharacteristic, complemented
228#2120C2×C1312yescomplemented
229C23×C13—22no—
230C23×C13—24no—
231C23×C13—21no—
232C23×C13—42no—
233C23×C13—44no—
234C23×C13—44no—
235C23×C13—41no—
236C23×C13—81no—
237C23×C13#12011yescharacteristic
238C23×C13C22×D412yes—
239Q8×C13—22no—
240Q8×C13—41no—
241Q8×C13—42no—
242Q8×C13—42no—
243Q8×C13—41no—
244Q8×C13—41no—
245D4×C13—24no—
246D4×C13—22no—
247D4×C13—42no—
248D4×C13—41no—
249D4×C13—44no—
250D4×C13—42no—
251D4×C13—41no—
252D4×C13—44no—
253D4×C13—44no—
254D4×C13—44no—
255D4×C13—44no—
256D4×C13—42no—
257D4×C13—42no—
258D4×C13—41no—
259D4×C13—81no—
260D4×C13—88no—
261C2×C4×C13—21no—
262C2×C4×C13—22no—
263C2×C4×C13—21no—
264C2×C4×C13—22no—
265C2×C4×C13—21no—
266C2×C4×C13—24no—
267C2×C4×C13—21no—
268C2×C4×C13—22no—
269C2×C4×C13—22no—
270C2×C4×C13—22no—
271C2×C4×C13—21no—
272C2×C4×C13—44no—
273C2×C4×C13—44no—
274C2×C4×C13—42no—
275C2×C4×C13—42no—
276C2×C4×C13—44no—
277C2×C4×C13—41no—
278C2×C4×C13—42no—
279C2×C4×C13—41no—
280C2×C4×C13—42no—
281C2×C4×C13—42no—
282C2×C4×C13—41no—
283C2×C4×C13—42no—
284C2×C4×C13—44no—
285C2×C4×C13—82no—
286C2×C4×C13—81no—
287C2×C4×C13—82no—
288C2×C4×C13#12012yes—
289C2×C4×C13#12011yescharacteristic
290C2×C4×C13C22×D411yescharacteristic
291C8×C13—42no—
292#585C22×C1311yescharacteristic, complemented
293#575—21no—
294#559C22×C1311yescharacteristic, complemented
295#554—21no—
296#553—22no—
297#551—21no—
298#551C22×C1312yescomplemented
299#546—22no—
300D42C22×C1311yescharacteristic, complemented
301#532C22×C1311yescharacteristic
302#529—22no—
303#525—21no—
304#525—22no—
305#525C22×C1312yes—
306C4×#41—21no—
307C2×C4×D4—22no—
308#458—22no—
309#458C22×C1314yescomplemented
310B(4,𝔽2)—22no—
311B(4,𝔽2)C22×C1314yes—
312#456—21no—
313#455C22×C1312yescomplemented
314#454—21no—
315#453C22×C1312yes—
316C2×#104—21no—
317#413C22×C1311yescharacteristic, complemented
318#410—22no—
319#410C22×C1312yescomplemented
320#354C22×C1312yescomplemented
321#353C22×C1312yescomplemented
322#352C22×C1314yescomplemented
323AΣL(1,𝔽16)C22×C1314yescomplemented
324C22×C13—24no—
325C22×C13—22no—
326C22×C13—21no—
327C22×C13—41no—
328C22×C13—42no—
329C22×C13—42no—
330C22×C13—42no—
331C22×C13—44no—
332C22×C13—42no—
333C22×C13—42no—
334C22×C13—41no—
335C22×C13—82no—
336C22×C13—84no—
337C22×C13—84no—
338C22×C13—161no—
339C22×C13C2×#12011yescharacteristic
340C4×C13—22no—
341C4×C13—21no—
342C4×C13—22no—
343C4×C13—41no—
344C4×C13—42no—
345C4×C13—42no—
346C4×C13—42no—
347C4×C13—42no—
348C4×C13—41no—
349C4×C13—84no—
350C4×C13B(4,𝔽2)11yescharacteristic
351C4×C13B(4,𝔽2)11yescharacteristic
3522−1+4—21no—
3532−1+4—41no—
354H(5,𝔽2)—22no—
355H(5,𝔽2)—41no—
356H(5,𝔽2)C23×C1312yes—
357C2×#41—21no—
358C2×#41—22no—
359C2×#41—21no—
360C2×#41—42no—
361C2×#41D4×C1311yescharacteristic, complemented
362C2×#41C23×C1311yescharacteristic
363C22×D4—22no—
364C23×C4—21no—
365C23×C4D4×C1312yescomplemented
366#137—22no—
367#137—41no—
368AGL(1,ℤ/8)—22no—
369AGL(1,ℤ/8)—41no—
370#135—42no—
371C2×M16—21no—
372C4⋊Q8D4×C1311yescharacteristic, complemented
373#127C23×C1311yescharacteristic
374#126—22no—
375#126—22no—
376#125—22no—
377#124—22no—
378#124D4×C1311yescharacteristic, complemented
379#124C23×C1311yescharacteristic
380#123—21no—
381#123—22no—
382#123—21no—
383#123—22no—
384#123—24no—
385#123D4×C1312yescomplemented
386#123C23×C1312yes—
387C22⋊Q8—22no—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390C22⋊Q8—42no—
391#121—22no—
392#121—22no—
393#121—22no—
394#121—22no—
395#121—42no—
396#120—21no—
397#120—21no—
398#120—24no—
399#120D4×C1312yescomplemented
400#120C23×C1312yes—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×D4—21no—
404C4×D4—22no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—22no—
412C4×D4—22no—
413C4×D4—21no—
414C4×D4—44no—
415#117—21no—
416#117—21no—
417#117—22no—
418#117—22no—
419#117D4×C1312yescomplemented
420C2×C4⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C42—22no—
424C2×C42D4×C1311yescharacteristic, complemented
425#104—22no—
426#104—22no—
427#101—21no—
428#100C23×C1312yes—
429#99—22no—
430#99—24no—
431#99—24no—
432#99C23×C1314yes—
433C2×C13—21no—
434C2×C13—42no—
435C2×C13—44no—
436C2×C13—41no—
437C2×C13—81no—
438C2×C13—82no—
439C2×C13C2×B(4,𝔽2)11yescharacteristic
440C24—21no—
441C24C2×D4×C1312yes—
442#41—22no—
443#41—22no—
444#41—41no—
445#41—41no—
446#41—42no—
447#41—42no—
448#41—42no—
449#41—41no—
450#41—44no—
451#41—41no—
452#41—41no—
453#41—44no—
454#41—42no—
455#41—41no—
456#41—42no—
457C2×Q8—21no—
458C2×Q8—22no—
459C2×Q8—21no—
460C2×Q8—42no—
461C2×Q8C2×D4×C1311yescharacteristic
462C2×Q8C2×D4×C1311yescharacteristic
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—24no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—42no—
473C2×D4—48no—
474C2×D4—44no—
475C2×D4—41no—
476C2×D4—44no—
477C2×D4C2×D4×C1312yes—
478C2×D4C2×D4×C1311yescharacteristic
479C2×D4C24×C1311yescharacteristic
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—41no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—81no—
493C22×C4—81no—
494C22×C4C2×D4×C1312yes—
495C22×C4C2×D4×C1311yescharacteristic
496C22×C4C2×D4×C1312yes—
497Q16—42no—
498SD16—42no—
499SD16—42no—
500D8—42no—
501M16—22no—
502M16—41no—
503C2×C8—41no—
504C4⋊C4—21no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—42no—
514C4⋊C4—44no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—24no—
527C22⋊C4—44no—
528C22⋊C4—44no—
529C22⋊C4C2×D4×C1312yes—
530C22⋊C4C2×D4×C1312yes—
531C42—22no—
532C42—22no—
533C42—21no—
534C42—22no—
535C42—42no—
536C42C2×D4×C1311yescharacteristic
537C42C2×D4×C1311yescharacteristic
538C13#3354611yescharacteristic, direct product factor, Sylow
539C23—22no—
540C23—24no—
541C23—21no—
542C23—42no—
543C23—44no—
544C23—44no—
545C23—41no—
546C23—81no—
547C23C13×#12011yescharacteristic
548C23C22×D4×C1312yes—
549Q8—22no—
550Q8—41no—
551Q8—41no—
552Q8—42no—
553Q8—42no—
554Q8—41no—
555D4—24no—
556D4—22no—
557D4—42no—
558D4—41no—
559D4—41no—
560D4—44no—
561D4—42no—
562D4—44no—
563D4—44no—
564D4—44no—
565D4—44no—
566D4—42no—
567D4—42no—
568D4—41no—
569D4—81no—
570D4—88no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—24no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—44no—
583C2×C4—44no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—44no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—44no—
595C2×C4—82no—
596C2×C4—81no—
597C2×C4—82no—
598C2×C4C13×#12012yes—
599C2×C4C13×#12011yescharacteristic
600C2×C4C22×D4×C1311yescharacteristic
601C8—42no—
602C22—24no—
603C22—22no—
604C22—21no—
605C22—41no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—44no—
610C22—42no—
611C22—42no—
612C22—41no—
613C22—82no—
614C22—84no—
615C22—84no—
616C22—161no—
617C22C2×C13×#12011yescharacteristic
618C4—22no—
619C4—21no—
620C4—22no—
621C4—41no—
622C4—42no—
623C4—42no—
624C4—42no—
625C4—42no—
626C4—41no—
627C4—84no—
628C4C13×B(4,𝔽2)11yescharacteristic
629C4C13×B(4,𝔽2)11yescharacteristic
630C2—21no—
631C2—42no—
632C2—44no—
633C2—41no—
634C2—81no—
635C2—82no—
636C2C2×C13×B(4,𝔽2)11yescharacteristic
subgroupG/H
centerC4×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C13
socleC2×C13C2×B(4,𝔽2)
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C13 ◁ C2×C4×C13 ◁ C2×C13×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3481C2semidirect
2. C13×#3025C2semidirect
3. C13×#3018C2semidirect
4. C13×#2198C2semidirect
5. C13×#2197C2semidirect
6. C13×#2196C2semidirect
7. C13×#2126C2semidirect
8. C13×#2120C2semidirect
9. C13×#585C22semidirect
11. C13×#559C22semidirect
15. C13×#551C22semidirect
17. D42×C13C22semidirect
26. C13×#458C22semidirect
30. C13×#455C22semidirect
34. C13×#413C22semidirect
36. C13×#410C22semidirect
37. C13×#354C22semidirect
38. C13×#353C22semidirect
39. C13×#352C22semidirect
40. C13×AΣL(1,𝔽16)C22semidirect
50. C2×C13×#41D4semidirect
54. C23×C4×C13D4semidirect
61. C13×C4⋊Q8D4semidirect
67. C13×#124D4semidirect
74. C13×#123D4semidirect
88. C13×#120D4semidirect
108. C13×#117D4semidirect
113. C2×C42×C13D4semidirect
122. #33546C13direct (N × H)
221. #3481C2×C13semidirect
222. #3025C2×C13semidirect
223. #3018C2×C13semidirect
224. #2198C2×C13semidirect
225. #2197C2×C13semidirect
226. #2196C2×C13semidirect
227. #2126C2×C13semidirect
228. #2120C2×C13semidirect
292. #585C22×C13semidirect
294. #559C22×C13semidirect
298. #551C22×C13semidirect
300. D42C22×C13semidirect
309. #458C22×C13semidirect
313. #455C22×C13semidirect
317. #413C22×C13semidirect
319. #410C22×C13semidirect
320. #354C22×C13semidirect
321. #353C22×C13semidirect
322. #352C22×C13semidirect
323. AΣL(1,𝔽16)C22×C13semidirect
361. C2×#41D4×C13semidirect
365. C23×C4D4×C13semidirect
372. C4⋊Q8D4×C13semidirect
378. #124D4×C13semidirect
385. #123D4×C13semidirect
399. #120D4×C13semidirect
419. #117D4×C13semidirect
424. C2×C42D4×C13semidirect
538. C13#33546direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34812
C13×#30252
C13×#30182
C13×#21982
C13×#21972
C13×#21962
C13×#21262
C13×#21202
#3354613