Finite Group Databasebeta

← C13×#33558 #15719897

Subgroups — C13×#33558 #15719897

Order 3328.

1158 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×#3545C211yesmaximal, characteristic, complemented
2C13×#3026C212yesmaximal, complemented
3C2×C13×#455C211yesmaximal, characteristic, complemented
4C13×#2201C212yesmaximal, complemented
5C13×#2199C212yesmaximal, complemented
6C13×#2197C214yesmaximal, complemented
7C2×C13×#354C211yesmaximal, characteristic, complemented
8C13×#2121C212yesmaximal, complemented
9C2×C13×H(5,𝔽2)C2211yescharacteristic
10C2×C13×#137—21no—
11C13×#563C2211yescharacteristic, complemented
12C13×#562—21no—
13C13×H(3,𝔽4)C2211yescharacteristic, complemented
14C13×#555—21no—
15C13×#551—22no—
16C13×#551C2212yescomplemented
17C13×#546—22no—
18C13×#542—22no—
19C13×#538—22no—
20C13×#536—21no—
21C13×#534—22no—
22C13×#534C2212yes—
23C13×#529—21no—
24C2×C13×#124C2211yescharacteristic
25C13×#458—22no—
26C13×#458C2214yes—
27C13×B(4,𝔽2)—22no—
28C13×B(4,𝔽2)C2214yes—
29C13×#455—21no—
30C13×#455—21no—
31C13×#455C2212yes—
32C13×#455C2212yes—
33C2×C13×#104—21no—
34C2×C13×#100C2211yescharacteristic
35C2×C13×#99—22no—
36C2×C13×#99C2212yes—
37C13×#354C2212yescomplemented
38C13×#354C2212yescomplemented
39C13×#352C2214yescomplemented
40C13×AΣL(1,𝔽16)C2214yescomplemented
41C13×H(5,𝔽2)—22no—
42C13×H(5,𝔽2)—21no—
43C13×H(5,𝔽2)—42no—
44C13×H(5,𝔽2)C2312yes—
45C2×C13×#41—21no—
46C2×C13×#41—21no—
47C2×C13×#41—41no—
48C22×Q8×C13D411yescharacteristic, complemented
49C22×D4×C13—22no—
50C22×D4×C13—41no—
51C22×D4×C13D412yescomplemented
52C22×D4×C13C2311yescharacteristic
53C13×#137—22no—
54C13×#137—22no—
55C13×#137—42no—
56C2×C13×Q16—41no—
57C2×C13×SD16—41no—
58C2×C13×M16—21no—
59C13×C4⋊Q8—21no—
60C13×C4⋊Q8—21no—
61C13×#126—22no—
62C13×#126—22no—
63C13×#126—22no—
64C13×#125—21no—
65C13×#124—21no—
66C13×#124—22no—
67C13×#124—21no—
68C13×#124—22no—
69C13×#124—22no—
70C13×#124—21no—
71C13×#124D411yescharacteristic, complemented
72C13×#124D411yescharacteristic, complemented
73C13×#124C2311yescharacteristic
74C13×#124C2311yescharacteristic
75C13×#123—22no—
76C13×#123—22no—
77C13×#123—22no—
78C13×#123—22no—
79C13×#123—22no—
80C13×#123—24no—
81C13×#123—42no—
82C13×#123D412yescomplemented
83C13×#123C2312yes—
84C13×C22⋊Q8—21no—
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8—22no—
87C13×C22⋊Q8—22no—
88C13×C22⋊Q8—22no—
89C13×#121—21no—
90C13×#121—22no—
91C13×#121—22no—
92C13×#121—22no—
93C13×#121—22no—
94C13×#121—44no—
95C13×#120—22no—
96C13×#120—22no—
97C13×#120—24no—
98C13×#120—42no—
99C13×#120D412yescomplemented
100C13×#120C2312yes—
101C4×Q8×C13—21no—
102C4×D4×C13—21no—
103C4×D4×C13—22no—
104C4×D4×C13—22no—
105C4×D4×C13—22no—
106C13×#117—21no—
107C13×#117—22no—
108C13×#117—22no—
109C2×C13×C22⋊C4—22no—
110C2×C13×C22⋊C4—22no—
111C2×C13×C22⋊C4—22no—
112C2×C13×C22⋊C4D412yescomplemented
113C2×C42×C13D411yescharacteristic, complemented
114C13×#104—22no—
115C13×#104—22no—
116C13×#100—21no—
117C13×#100C2312yes—
118C13×#99—22no—
119C13×#99—24no—
120C13×#99—24no—
121C13×#99C2314yes—
122#33558C1311yesmaximal, characteristic, direct product factor, Sylow
123C24×C13—22no—
124C24×C13C2×D412yes—
125C24×C13C2×D412yes—
126C13×#41—22no—
127C13×#41—22no—
128C13×#41—42no—
129C13×#41—41no—
130C13×#41—44no—
131C13×#41—42no—
132C13×#41—41no—
133C13×#41—81no—
134C13×#41—81no—
135C2×Q8×C13—21no—
136C2×Q8×C13—21no—
137C2×Q8×C13—21no—
138C2×Q8×C13—21no—
139C2×Q8×C13—41no—
140C2×Q8×C13—41no—
141C2×Q8×C13C2×D411yescharacteristic
142C2×Q8×C13C2×D411yescharacteristic
143C2×D4×C13—21no—
144C2×D4×C13—24no—
145C2×D4×C13—22no—
146C2×D4×C13—24no—
147C2×D4×C13—21no—
148C2×D4×C13—21no—
149C2×D4×C13—22no—
150C2×D4×C13—22no—
151C2×D4×C13—22no—
152C2×D4×C13—41no—
153C2×D4×C13—41no—
154C2×D4×C13—42no—
155C2×D4×C13—42no—
156C2×D4×C13—42no—
157C2×D4×C13—42no—
158C2×D4×C13—44no—
159C2×D4×C13—42no—
160C2×D4×C13—41no—
161C2×D4×C13—42no—
162C2×D4×C13—42no—
163C2×D4×C13—44no—
164C2×D4×C13C2×D412yes—
165C2×D4×C13C2×D411yescharacteristic
166C2×D4×C13C2411yescharacteristic
167C22×C4×C13—22no—
168C22×C4×C13—21no—
169C22×C4×C13—22no—
170C22×C4×C13—22no—
171C22×C4×C13—22no—
172C22×C4×C13—21no—
173C22×C4×C13—41no—
174C22×C4×C13—42no—
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13C2×D412yes—
177C13×Q16—42no—
178C13×Q16—42no—
179C13×SD16—42no—
180C13×SD16—42no—
181C13×M16—22no—
182C13×M16—41no—
183C2×C8×C13—41no—
184C13×C4⋊C4—22no—
185C13×C4⋊C4—22no—
186C13×C4⋊C4—22no—
187C13×C4⋊C4—22no—
188C13×C4⋊C4—22no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—22no—
192C13×C4⋊C4—22no—
193C13×C4⋊C4—44no—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—22no—
196C13×C22⋊C4—22no—
197C13×C22⋊C4—22no—
198C13×C22⋊C4—22no—
199C13×C22⋊C4—22no—
200C13×C22⋊C4—22no—
201C13×C22⋊C4—22no—
202C13×C22⋊C4—22no—
203C13×C22⋊C4—22no—
204C13×C22⋊C4—22no—
205C13×C22⋊C4—22no—
206C13×C22⋊C4—22no—
207C13×C22⋊C4—24no—
208C13×C22⋊C4—44no—
209C13×C22⋊C4—42no—
210C13×C22⋊C4—44no—
211C13×C22⋊C4C2×D412yes—
212C13×C22⋊C4C2×D412yes—
213C42×C13—21no—
214C42×C13—22no—
215C42×C13—21no—
216C42×C13—21no—
217C42×C13C2×D411yescharacteristic
218C42×C13C2×D411yescharacteristic
219#3545C2×C1311yescharacteristic, complemented
220#3026C2×C1312yescomplemented
221C2×#455C2×C1311yescharacteristic, complemented
222#2201C2×C1312yescomplemented
223#2199C2×C1312yescomplemented
224#2197C2×C1314yescomplemented
225C2×#354C2×C1311yescharacteristic, complemented
226#2121C2×C1312yescomplemented
227C23×C13—22no—
228C23×C13—22no—
229C23×C13—24no—
230C23×C13—22no—
231C23×C13—42no—
232C23×C13—42no—
233C23×C13—41no—
234C23×C13—82no—
235C23×C13—82no—
236C23×C13—162no—
237C23×C13#12012yes—
238C23×C13#12011yescharacteristic
239C23×C13C22×D412yes—
240Q8×C13—22no—
241Q8×C13—41no—
242Q8×C13—41no—
243Q8×C13—41no—
244Q8×C13—81no—
245Q8×C13—81no—
246Q8×C13—81no—
247D4×C13—22no—
248D4×C13—41no—
249D4×C13—42no—
250D4×C13—41no—
251D4×C13—41no—
252D4×C13—44no—
253D4×C13—44no—
254D4×C13—42no—
255D4×C13—42no—
256D4×C13—42no—
257D4×C13—42no—
258D4×C13—82no—
259D4×C13—82no—
260D4×C13—82no—
261D4×C13—81no—
262D4×C13—81no—
263D4×C13—164no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
266C2×C4×C13—24no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—22no—
270C2×C4×C13—21no—
271C2×C4×C13—22no—
272C2×C4×C13—22no—
273C2×C4×C13—21no—
274C2×C4×C13—42no—
275C2×C4×C13—42no—
276C2×C4×C13—42no—
277C2×C4×C13—41no—
278C2×C4×C13—41no—
279C2×C4×C13—41no—
280C2×C4×C13—42no—
281C2×C4×C13—44no—
282C2×C4×C13—82no—
283C2×C4×C13—81no—
284C2×C4×C13—82no—
285C2×C4×C13—82no—
286C2×C4×C13—162no—
287C2×C4×C13#12011yescharacteristic
288C2×C4×C13C22×D411yescharacteristic
289C8×C13—42no—
290C2×H(5,𝔽2)C22×C1311yescharacteristic
291C2×#137—21no—
292#563C22×C1311yescharacteristic, complemented
293#562—21no—
294H(3,𝔽4)C22×C1311yescharacteristic, complemented
295#555—21no—
296#551—22no—
297#551C22×C1312yescomplemented
298#546—22no—
299#542—22no—
300#538—22no—
301#536—21no—
302#534—22no—
303#534C22×C1312yes—
304#529—21no—
305C2×#124C22×C1311yescharacteristic
306#458—22no—
307#458C22×C1314yes—
308B(4,𝔽2)—22no—
309B(4,𝔽2)C22×C1314yes—
310#455—21no—
311#455—21no—
312#455C22×C1312yes—
313#455C22×C1312yes—
314C2×#104—21no—
315C2×#100C22×C1311yescharacteristic
316C2×#99—22no—
317C2×#99C22×C1312yes—
318#354C22×C1312yescomplemented
319#354C22×C1312yescomplemented
320#352C22×C1314yescomplemented
321AΣL(1,𝔽16)C22×C1314yescomplemented
322C22×C13—22no—
323C22×C13—22no—
324C22×C13—41no—
325C22×C13—42no—
326C22×C13—42no—
327C22×C13—42no—
328C22×C13—42no—
329C22×C13—42no—
330C22×C13—42no—
331C22×C13—82no—
332C22×C13—82no—
333C22×C13—82no—
334C22×C13—84no—
335C22×C13—84no—
336C22×C13—162no—
337C22×C13B(4,𝔽2)11yescharacteristic
338C22×C13B(4,𝔽2)11yescharacteristic
339C22×C13C2×#12011yescharacteristic
340C4×C13—21no—
341C4×C13—21no—
342C4×C13—41no—
343C4×C13—42no—
344C4×C13—42no—
345C4×C13—41no—
346C4×C13—42no—
347C4×C13—41no—
348C4×C13—41no—
349C4×C13—42no—
350C4×C13—84no—
351H(5,𝔽2)—22no—
352H(5,𝔽2)—21no—
353H(5,𝔽2)—42no—
354H(5,𝔽2)C23×C1312yes—
355C2×#41—21no—
356C2×#41—21no—
357C2×#41—41no—
358C22×Q8D4×C1311yescharacteristic, complemented
359C22×D4—22no—
360C22×D4—41no—
361C22×D4D4×C1312yescomplemented
362C22×D4C23×C1311yescharacteristic
363#137—22no—
364#137—22no—
365#137—42no—
366C2×Q16—41no—
367C2×SD16—41no—
368C2×M16—21no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371#126—22no—
372#126—22no—
373#126—22no—
374#125—21no—
375#124—21no—
376#124—22no—
377#124—21no—
378#124—22no—
379#124—22no—
380#124—21no—
381#124D4×C1311yescharacteristic, complemented
382#124D4×C1311yescharacteristic, complemented
383#124C23×C1311yescharacteristic
384#124C23×C1311yescharacteristic
385#123—22no—
386#123—22no—
387#123—22no—
388#123—22no—
389#123—22no—
390#123—24no—
391#123—42no—
392#123D4×C1312yescomplemented
393#123C23×C1312yes—
394C22⋊Q8—21no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399#121—21no—
400#121—22no—
401#121—22no—
402#121—22no—
403#121—22no—
404#121—44no—
405#120—22no—
406#120—22no—
407#120—24no—
408#120—42no—
409#120D4×C1312yescomplemented
410#120C23×C1312yes—
411C4×Q8—21no—
412C4×D4—21no—
413C4×D4—22no—
414C4×D4—22no—
415C4×D4—22no—
416#117—21no—
417#117—22no—
418#117—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4D4×C1312yescomplemented
423C2×C42D4×C1311yescharacteristic, complemented
424#104—22no—
425#104—22no—
426#100—21no—
427#100C23×C1312yes—
428#99—22no—
429#99—24no—
430#99—24no—
431#99C23×C1314yes—
432C2×C13—21no—
433C2×C13—21no—
434C2×C13—21no—
435C2×C13—42no—
436C2×C13—42no—
437C2×C13—82no—
438C2×C13—82no—
439C2×C13C2×B(4,𝔽2)11yescharacteristic
440C24—22no—
441C24C2×D4×C1312yes—
442C24C2×D4×C1312yes—
443#41—22no—
444#41—22no—
445#41—42no—
446#41—41no—
447#41—44no—
448#41—42no—
449#41—41no—
450#41—81no—
451#41—81no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—41no—
457C2×Q8—41no—
458C2×Q8C2×D4×C1311yescharacteristic
459C2×Q8C2×D4×C1311yescharacteristic
460C2×D4—21no—
461C2×D4—24no—
462C2×D4—22no—
463C2×D4—24no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—44no—
476C2×D4—41no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—44no—
481C2×D4C2×D4×C1312yes—
482C2×D4C2×D4×C1311yescharacteristic
483C2×D4C24×C1311yescharacteristic
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—41no—
491C22×C4—42no—
492C22×C4C2×D4×C1311yescharacteristic
493C22×C4C2×D4×C1312yes—
494Q16—42no—
495Q16—42no—
496SD16—42no—
497SD16—42no—
498M16—22no—
499M16—41no—
500C2×C8—41no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—44no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—24no—
525C22⋊C4—44no—
526C22⋊C4—42no—
527C22⋊C4—44no—
528C22⋊C4C2×D4×C1312yes—
529C22⋊C4C2×D4×C1312yes—
530C42—21no—
531C42—22no—
532C42—21no—
533C42—21no—
534C42C2×D4×C1311yescharacteristic
535C42C2×D4×C1311yescharacteristic
536C13#3355811yescharacteristic, direct product factor, Sylow
537C23—22no—
538C23—22no—
539C23—24no—
540C23—22no—
541C23—42no—
542C23—42no—
543C23—41no—
544C23—82no—
545C23—82no—
546C23—162no—
547C23C13×#12012yes—
548C23C13×#12011yescharacteristic
549C23C22×D4×C1312yes—
550Q8—22no—
551Q8—41no—
552Q8—41no—
553Q8—41no—
554Q8—81no—
555Q8—81no—
556Q8—81no—
557D4—22no—
558D4—41no—
559D4—42no—
560D4—41no—
561D4—41no—
562D4—44no—
563D4—44no—
564D4—42no—
565D4—42no—
566D4—42no—
567D4—42no—
568D4—82no—
569D4—82no—
570D4—82no—
571D4—81no—
572D4—81no—
573D4—164no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—24no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—44no—
592C2×C4—82no—
593C2×C4—81no—
594C2×C4—82no—
595C2×C4—82no—
596C2×C4—162no—
597C2×C4C13×#12011yescharacteristic
598C2×C4C22×D4×C1311yescharacteristic
599C8—42no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22—84no—
613C22—84no—
614C22—162no—
615C22C13×B(4,𝔽2)11yescharacteristic
616C22C13×B(4,𝔽2)11yescharacteristic
617C22C2×C13×#12011yescharacteristic
618C4—21no—
619C4—21no—
620C4—41no—
621C4—42no—
622C4—42no—
623C4—41no—
624C4—42no—
625C4—41no—
626C4—41no—
627C4—42no—
628C4—84no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—42no—
633C2—42no—
634C2—82no—
635C2—82no—
636C2C2×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 ◁ C23×C13 ◁ C22×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3545C2semidirect
2. C13×#3026C2semidirect
3. C2×C13×#455C2semidirect
4. C13×#2201C2semidirect
5. C13×#2199C2semidirect
6. C13×#2197C2semidirect
7. C2×C13×#354C2semidirect
8. C13×#2121C2semidirect
11. C13×#563C22semidirect
13. C13×H(3,𝔽4)C22semidirect
16. C13×#551C22semidirect
37. C13×#354C22semidirect
38. C13×#354C22semidirect
39. C13×#352C22semidirect
40. C13×AΣL(1,𝔽16)C22semidirect
48. C22×Q8×C13D4semidirect
51. C22×D4×C13D4semidirect
71. C13×#124D4semidirect
72. C13×#124D4semidirect
82. C13×#123D4semidirect
99. C13×#120D4semidirect
112. C2×C13×C22⋊C4D4semidirect
113. C2×C42×C13D4semidirect
122. #33558C13direct (N × H)
219. #3545C2×C13semidirect
220. #3026C2×C13semidirect
221. C2×#455C2×C13semidirect
222. #2201C2×C13semidirect
223. #2199C2×C13semidirect
224. #2197C2×C13semidirect
225. C2×#354C2×C13semidirect
226. #2121C2×C13semidirect
292. #563C22×C13semidirect
294. H(3,𝔽4)C22×C13semidirect
297. #551C22×C13semidirect
318. #354C22×C13semidirect
319. #354C22×C13semidirect
320. #352C22×C13semidirect
321. AΣL(1,𝔽16)C22×C13semidirect
358. C22×Q8D4×C13semidirect
361. C22×D4D4×C13semidirect
381. #124D4×C13semidirect
382. #124D4×C13semidirect
392. #123D4×C13semidirect
409. #120D4×C13semidirect
422. C2×C22⋊C4D4×C13semidirect
423. C2×C42D4×C13semidirect
536. C13#33558direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35452
C13×#30262
C2×C13×#4552
C13×#22012
C13×#21992
C13×#21972
C2×C13×#3542
C13×#21212
#3355813