Finite Group Databasebeta

← C13×#62596 #15748935

Subgroups — C13×#62596 #15748935

Order 3328.

1776 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3563C211yesmaximal, characteristic, complemented
2C13×#3543C211yesmaximal, characteristic
3C13×#3371C212yesmaximal, complemented
4C13×#3368C212yesmaximal, complemented
5C13×#3317C212yesmaximal, complemented
6C13×#3314C212yesmaximal, complemented
7C13×#3310C212yesmaximal, complemented
8C13×#3310C212yesmaximal, complemented
9C13×#3296C212yesmaximal, complemented
10C13×#3295C212yesmaximal, complemented
11C13×#3241C212yesmaximal, complemented
12C13×#3232C211yesmaximal, characteristic, complemented
13C13×#3222C212yesmaximal, complemented
14C13×#3208C211yesmaximal, characteristic, complemented
15C13×#3181C211yesmaximal, characteristic, complemented
16C13×#3174C212yesmaximal, complemented
17C13×#3136C212yesmaximal, complemented
18C2×C13×#490C211yesmaximal, characteristic, complemented
19C13×#2968C211yesmaximal, characteristic, complemented
20C13×#564—21no—
21C13×#563—21no—
22C13×#560—22no—
23C13×#559C2211yescharacteristic
24C13×#557C2212yescomplemented
25C13×#554C2212yescomplemented
26C13×#552—22no—
27C13×#552C2212yescomplemented
28C13×#552C2212yescomplemented
29C13×#550C2211yescharacteristic
30C13×#550C2211yescharacteristic
31C13×#546—21no—
32C13×#546C2212yes—
33D42×C13—21no—
34D42×C13C2212yes—
35D42×C13C2211yescharacteristic
36C13×#544—21no—
37C13×#544C2212yescomplemented
38C13×#541—22no—
39C13×#541C2212yescomplemented
40C13×#540—21no—
41C13×#540C2212yes—
42C13×#539—21no—
43C13×#535—21no—
44C13×#535C2212yes—
45C13×#534—22no—
46C13×#533C2211yescharacteristic, complemented
47C2×C13×#127C2211yescharacteristic
48C13×#529C2211yescharacteristic
49C13×#529C2211yescharacteristic
50C2×C13×#125C2211yescharacteristic, complemented
51C13×#501C2211yescharacteristic, complemented
52C13×#499C2212yescomplemented
53C13×#497C2211yescharacteristic, complemented
54C13×#492C2212yescomplemented
55C13×#491C2211yescharacteristic, complemented
56C13×#490C2212yes—
57C13×#490C2212yescomplemented
58C13×#490C2212yescomplemented
59C13×#490C2212yescomplemented
60C13×#490C2212yescomplemented
61C13×#489C2212yescomplemented
62C13×#489C2211yescharacteristic, complemented
63C13×#488C2212yescomplemented
64C13×#488C2212yescomplemented
65C13×#486C2212yescomplemented
66C13×#486C2212yescomplemented
67C13×#484C2211yescharacteristic, complemented
68C13×#483C2211yescharacteristic, complemented
69C13×#482C2212yescomplemented
70C13×#482C2212yescomplemented
71C13×#481C2211yescharacteristic
72C13×#481C2212yescomplemented
73C13×#480C2211yescharacteristic
74C13×#480C2212yescomplemented
75C13×#479C2212yescomplemented
76C13×#478C2212yescomplemented
77C13×#478C2212yescomplemented
78C13×#478C2212yescomplemented
79C13×#476C2212yescomplemented
80C13×#474C2212yescomplemented
81C13×#468C2212yescomplemented
82C13×#468C2212yescomplemented
83C13×#467C2212yescomplemented
84C13×#465C2212yes—
85C13×#465C2212yescomplemented
86C13×#465C2212yescomplemented
87C13×#464C2212yescomplemented
88C13×#464C2212yescomplemented
89C13×#460C2212yes—
90C13×#460C2212yescomplemented
91C13×#460C2212yescomplemented
92C13×#460C2212yescomplemented
93C13×#452C2212yescomplemented
94C13×#452C2212yescomplemented
95C13×#450C2212yescomplemented
96C13×#450C2212yescomplemented
97C13×#450C2212yescomplemented
98C13×#450C2212yescomplemented
99C13×#446C2212yescomplemented
100C13×#441C2212yescomplemented
101C13×#440C2212yescomplemented
102C13×#440C2212yescomplemented
103C13×#440C2212yescomplemented
104C4×C13×SD16C2212yescomplemented
105C4×C13×SD16C2212yescomplemented
106C13×#435C2212yescomplemented
107C13×#435C2212yescomplemented
108C8×D4×C13C2212yescomplemented
109C13×#433C2212yescomplemented
110C13×#431C2211yescharacteristic, complemented
111C13×#418C2212yescomplemented
112C13×#417C2212yescomplemented
113C13×#416C2212yescomplemented
114C2×C13×#102C2212yescomplemented
115C2×C13×#102C2212yescomplemented
116C2×C13×#102C2212yescomplemented
117C13×#405C2212yescomplemented
118C2×C13×#97C2211yescharacteristic, complemented
119C2×C13×#41—21no—
120C2×C13×#41C2312yes—
121C22×D4×C13—22no—
122C22×D4×C13—21no—
123C22×D4×C13—21no—
124C22×D4×C13—21no—
125C22×D4×C13C2312yes—
126C22×D4×C13C2312yes—
127C2×C13×Q16C2312yes—
128C2×C13×SD16C2312yes—
129C2×C13×SD16C2312yes—
130C2×C13×SD16C2312yes—
131C2×C13×SD16C2312yes—
132C2×C13×SD16C2312yes—
133C2×C13×M16C2312yes—
134C22×C8×C13C2312yes—
135C22×C8×C13C2312yes—
136C13×C4⋊Q8—22no—
137C13×C4⋊Q8—22no—
138C13×C4⋊Q8C2311yescharacteristic
139C13×C4⋊Q8C2312yes—
140C13×C4⋊Q8C2311yescharacteristic
141C13×#127—21no—
142C13×#127—21no—
143C13×#127—21no—
144C13×#127C2311yescharacteristic
145C13×#127C2312yes—
146C13×#127C2311yescharacteristic
147C13×#127C2312yes—
148C13×#126—22no—
149C13×#126—22no—
150C13×#126—22no—
151C13×#126—22no—
152C13×#126—21no—
153C13×#126D412yes—
154C13×#125—22no—
155C13×#125—22no—
156C13×#125—22no—
157C13×#125—22no—
158C13×#125—22no—
159C13×#125—22no—
160C13×#125—22no—
161C13×#125—22no—
162C13×#125—21no—
163C13×#125—21no—
164C13×#125—21no—
165C13×#125D411yescharacteristic
166C13×#125C2312yes—
167C13×#125C2312yes—
168C13×#125C2312yes—
169C13×#125C2311yescharacteristic
170C13×#124—21no—
171C13×#124D411yescharacteristic
172C13×#124C2312yes—
173C13×#124C2311yescharacteristic
174C13×#123—22no—
175C13×#123—22no—
176C13×#123—21no—
177C13×#123—22no—
178C13×#123—22no—
179C13×#123—22no—
180C13×#123—22no—
181C13×#123D412yes—
182C13×C22⋊Q8—21no—
183C13×C22⋊Q8—22no—
184C13×C22⋊Q8—22no—
185C13×C22⋊Q8—22no—
186C13×C22⋊Q8—22no—
187C13×C22⋊Q8D411yescharacteristic
188C13×C22⋊Q8C2312yes—
189C13×C22⋊Q8C2312yes—
190C13×C22⋊Q8C2312yes—
191C13×C22⋊Q8C2311yescharacteristic
192C13×#121—22no—
193C13×#121—22no—
194C13×#121—22no—
195C13×#121—21no—
196C13×#121—21no—
197C13×#121—22no—
198C13×#121—22no—
199C13×#121—22no—
200C13×#121—22no—
201C13×#121—22no—
202C13×#121D411yescharacteristic
203C13×#121C2311yescharacteristic
204C13×#121C2312yes—
205C13×#121C2312yes—
206C13×#120—22no—
207C13×#120—22no—
208C13×#120—22no—
209C13×#120—22no—
210C13×#120—22no—
211C13×#120—22no—
212C4×Q8×C13—22no—
213C4×Q8×C13—21no—
214C4×Q8×C13C2312yes—
215C4×Q8×C13C2312yes—
216C4×Q8×C13C2312yes—
217C4×Q8×C13C2311yescharacteristic
218C4×Q8×C13C2311yescharacteristic
219C4×D4×C13—22no—
220C4×D4×C13—21no—
221C4×D4×C13—21no—
222C4×D4×C13—21no—
223C4×D4×C13C2312yes—
224C4×D4×C13C2312yes—
225C4×D4×C13C2311yescharacteristic
226C4×D4×C13C2312yes—
227C4×D4×C13C2311yescharacteristic
228C13×#117—21no—
229C13×#117—22no—
230C13×#117—22no—
231C13×#117—21no—
232C13×#117C2312yes—
233C13×#117C2312yes—
234C2×C13×C4⋊C4—21no—
235C2×C13×C4⋊C4—21no—
236C2×C13×C4⋊C4C2311yescharacteristic
237C2×C13×C4⋊C4C2311yescharacteristic
238C2×C13×C4⋊C4C2312yes—
239C2×C13×C22⋊C4—22no—
240C2×C42×C13C2311yescharacteristic
241C13×#107C2312yes—
242C13×#107C2312yes—
243C13×#107C2312yes—
244C13×#106C2312yes—
245C13×#106C2312yes—
246C13×#106C2312yes—
247C13×C4⋊C8C2312yes—
248C13×C4⋊C8C2312yes—
249C13×C4⋊C8C2312yes—
250C13×#103C2312yes—
251C13×#103C2312yes—
252C13×#103C2312yes—
253C13×#103C2312yes—
254C13×#103C2312yes—
255C13×#102C2312yes—
256C13×#102C2312yes—
257C13×#102C2312yes—
258C13×#102C2312yes—
259C13×#102C2312yes—
260C13×#102C2312yes—
261C13×#102C2312yes—
262C13×#102C2312yes—
263C13×#102C2312yes—
264C13×#102C2312yes—
265C13×#102C2312yes—
266C13×#102C2312yes—
267C13×#102C2312yes—
268C13×#102C2312yes—
269C13×#102C2312yes—
270C13×C22⋊C8C2311yescharacteristic
271C13×C22⋊C8C2311yescharacteristic
272C13×C22⋊C8C2312yes—
273C13×C22⋊C8C2312yes—
274C13×#97C2311yescharacteristic
275C13×#97C2311yescharacteristic
276C13×#97C2312yes—
277C13×#97C2312yes—
278C4×C8×C13C2312yes—
279C4×C8×C13C2312yes—
280#62596C1311yesmaximal, characteristic, direct product factor, Sylow
281C24×C13—22no—
282C24×C13—22no—
283C13×#41—42no—
284C13×#41—42no—
285C13×#41—82no—
286C2×Q8×C13—21no—
287C2×Q8×C13—22no—
288C2×Q8×C13C2×D411yescharacteristic
289C2×Q8×C13C2411yescharacteristic
290C2×Q8×C13C2412yes—
291C2×D4×C13—21no—
292C2×D4×C13—22no—
293C2×D4×C13—22no—
294C2×D4×C13—22no—
295C2×D4×C13—21no—
296C2×D4×C13—21no—
297C2×D4×C13—22no—
298C2×D4×C13—22no—
299C2×D4×C13—21no—
300C2×D4×C13—22no—
301C2×D4×C13—22no—
302C2×D4×C13—22no—
303C2×D4×C13—22no—
304C2×D4×C13—21no—
305C2×D4×C13—42no—
306C2×D4×C13—42no—
307C2×D4×C13—42no—
308C2×D4×C13—42no—
309C2×D4×C13—82no—
310C2×D4×C13—82no—
311C2×D4×C13—82no—
312C2×D4×C13—84no—
313C2×D4×C13C2×D412yes—
314C2×D4×C13C2×D411yescharacteristic
315C2×D4×C13C2412yes—
316C2×D4×C13C2411yescharacteristic
317C2×D4×C13C2412yes—
318C22×C4×C13—21no—
319C22×C4×C13—21no—
320C22×C4×C13—22no—
321C22×C4×C13—21no—
322C22×C4×C13—22no—
323C22×C4×C13—22no—
324C22×C4×C13—22no—
325C22×C4×C13C2×D411yescharacteristic
326C22×C4×C13C2×D411yescharacteristic
327C22×C4×C13C2411yescharacteristic
328C22×C4×C13C2412yes—
329C13×Q16—42no—
330C13×SD16—42no—
331C13×SD16—42no—
332C13×SD16—42no—
333C13×SD16—42no—
334C13×SD16—42no—
335C13×M16—42no—
336C2×C8×C13—42no—
337C2×C8×C13—42no—
338C2×C8×C13C2412yes—
339C2×C8×C13C2412yes—
340C2×C8×C13C2412yes—
341C2×C8×C13C2412yes—
342C13×C4⋊C4—22no—
343C13×C4⋊C4—22no—
344C13×C4⋊C4—22no—
345C13×C4⋊C4—22no—
346C13×C4⋊C4—21no—
347C13×C4⋊C4—22no—
348C13×C4⋊C4—21no—
349C13×C4⋊C4—21no—
350C13×C4⋊C4—21no—
351C13×C4⋊C4—21no—
352C13×C4⋊C4—22no—
353C13×C4⋊C4—22no—
354C13×C4⋊C4—22no—
355C13×C4⋊C4—21no—
356C13×C4⋊C4—21no—
357C13×C4⋊C4—22no—
358C13×C4⋊C4—22no—
359C13×C4⋊C4—22no—
360C13×C4⋊C4—21no—
361C13×C4⋊C4—21no—
362C13×C4⋊C4—22no—
363C13×C4⋊C4—22no—
364C13×C4⋊C4—22no—
365C13×C4⋊C4C2×D412yes—
366C13×C4⋊C4C2×D412yes—
367C13×C4⋊C4C2×D411yescharacteristic
368C13×C4⋊C4C2×D411yescharacteristic
369C13×C4⋊C4C2×D412yes—
370C13×C4⋊C4C2×D412yes—
371C13×C4⋊C4C2412yes—
372C13×C4⋊C4C2412yes—
373C13×C4⋊C4C2412yes—
374C13×C4⋊C4C2411yescharacteristic
375C13×C4⋊C4C2411yescharacteristic
376C13×C22⋊C4—21no—
377C13×C22⋊C4—22no—
378C13×C22⋊C4—22no—
379C13×C22⋊C4—22no—
380C13×C22⋊C4—22no—
381C13×C22⋊C4—22no—
382C13×C22⋊C4—22no—
383C13×C22⋊C4—21no—
384C13×C22⋊C4—21no—
385C13×C22⋊C4—21no—
386C13×C22⋊C4—22no—
387C13×C22⋊C4—22no—
388C13×C22⋊C4—21no—
389C13×C22⋊C4—22no—
390C13×C22⋊C4—22no—
391C13×C22⋊C4C2×D412yes—
392C13×C22⋊C4C2×D412yes—
393C13×C22⋊C4C2×D412yes—
394C13×C22⋊C4C2×D412yes—
395C13×C22⋊C4C2×D412yes—
396C42×C13—22no—
397C42×C13—22no—
398C42×C13—21no—
399C42×C13—22no—
400C42×C13—22no—
401C42×C13C2×D411yescharacteristic
402C42×C13C2×D411yescharacteristic
403C42×C13C2411yescharacteristic
404C42×C13C2412yes—
405C42×C13C2411yescharacteristic
406#3563C2×C1311yescharacteristic, complemented
407#3543C2×C1311yescharacteristic
408#3371C2×C1312yescomplemented
409#3368C2×C1312yescomplemented
410#3317C2×C1312yescomplemented
411#3314C2×C1312yescomplemented
412#3310C2×C1312yescomplemented
413#3310C2×C1312yescomplemented
414#3296C2×C1312yescomplemented
415#3295C2×C1312yescomplemented
416#3241C2×C1312yescomplemented
417#3232C2×C1311yescharacteristic, complemented
418#3222C2×C1312yescomplemented
419#3208C2×C1311yescharacteristic, complemented
420#3181C2×C1311yescharacteristic, complemented
421#3174C2×C1312yescomplemented
422#3136C2×C1312yescomplemented
423C2×#490C2×C1311yescharacteristic, complemented
424#2968C2×C1311yescharacteristic, complemented
425C23×C13—21no—
426C23×C13—22no—
427C23×C13—22no—
428C23×C13—44no—
429C23×C13—82no—
430C23×C13—82no—
431C23×C13—82no—
432C23×C13—82no—
433C23×C13—82no—
434C23×C13C22×D412yes—
435C23×C13C22×D411yescharacteristic
436Q8×C13—22no—
437Q8×C13—22no—
438Q8×C13—22no—
439Q8×C13—41no—
440Q8×C13—81no—
441Q8×C13—82no—
442D4×C13—24no—
443D4×C13—22no—
444D4×C13—22no—
445D4×C13—22no—
446D4×C13—22no—
447D4×C13—22no—
448D4×C13—41no—
449D4×C13—42no—
450D4×C13—42no—
451D4×C13—42no—
452D4×C13—82no—
453D4×C13—82no—
454D4×C13—82no—
455D4×C13—81no—
456D4×C13—82no—
457D4×C13—81no—
458D4×C13—82no—
459D4×C13—82no—
460D4×C13—82no—
461D4×C13—82no—
462D4×C13—82no—
463C2×C4×C13—22no—
464C2×C4×C13—22no—
465C2×C4×C13—22no—
466C2×C4×C13—22no—
467C2×C4×C13—22no—
468C2×C4×C13—22no—
469C2×C4×C13—22no—
470C2×C4×C13—21no—
471C2×C4×C13—21no—
472C2×C4×C13—22no—
473C2×C4×C13—21no—
474C2×C4×C13—41no—
475C2×C4×C13—42no—
476C2×C4×C13—42no—
477C2×C4×C13—82no—
478C2×C4×C13—82no—
479C2×C4×C13—82no—
480C2×C4×C13—81no—
481C2×C4×C13—82no—
482C2×C4×C13C22×D411yescharacteristic
483C2×C4×C13C22×D411yescharacteristic
484C2×C4×C13C22×D412yes—
485C2×C4×C13C22×D412yes—
486C2×C4×C13C22×D412yes—
487C2×C4×C13C22×D411yescharacteristic
488C2×C4×C13C22×D411yescharacteristic
489C2×C4×C13C22×D411yescharacteristic
490C2×C4×C13C2511yescharacteristic
491C8×C13—22no—
492C8×C13—22no—
493C8×C13—22no—
494C8×C13—22no—
495#564—21no—
496#563—21no—
497#560—22no—
498#559C22×C1311yescharacteristic
499#557C22×C1312yescomplemented
500#554C22×C1312yescomplemented
501#552—22no—
502#552C22×C1312yescomplemented
503#552C22×C1312yescomplemented
504#550C22×C1311yescharacteristic
505#550C22×C1311yescharacteristic
506#546—21no—
507#546C22×C1312yes—
508D42—21no—
509D42C22×C1312yes—
510D42C22×C1311yescharacteristic
511#544—21no—
512#544C22×C1312yescomplemented
513#541—22no—
514#541C22×C1312yescomplemented
515#540—21no—
516#540C22×C1312yes—
517#539—21no—
518#535—21no—
519#535C22×C1312yes—
520#534—22no—
521#533C22×C1311yescharacteristic, complemented
522C2×#127C22×C1311yescharacteristic
523#529C22×C1311yescharacteristic
524#529C22×C1311yescharacteristic
525C2×#125C22×C1311yescharacteristic, complemented
526#501C22×C1311yescharacteristic, complemented
527#499C22×C1312yescomplemented
528#497C22×C1311yescharacteristic, complemented
529#492C22×C1312yescomplemented
530#491C22×C1311yescharacteristic, complemented
531#490C22×C1312yes—
532#490C22×C1312yescomplemented
533#490C22×C1312yescomplemented
534#490C22×C1312yescomplemented
535#490C22×C1312yescomplemented
536#489C22×C1312yescomplemented
537#489C22×C1311yescharacteristic, complemented
538#488C22×C1312yescomplemented
539#488C22×C1312yescomplemented
540#486C22×C1312yescomplemented
541#486C22×C1312yescomplemented
542#484C22×C1311yescharacteristic, complemented
543#483C22×C1311yescharacteristic, complemented
544#482C22×C1312yescomplemented
545#482C22×C1312yescomplemented
546#481C22×C1311yescharacteristic
547#481C22×C1312yescomplemented
548#480C22×C1311yescharacteristic
549#480C22×C1312yescomplemented
550#479C22×C1312yescomplemented
551#478C22×C1312yescomplemented
552#478C22×C1312yescomplemented
553#478C22×C1312yescomplemented
554#476C22×C1312yescomplemented
555#474C22×C1312yescomplemented
556#468C22×C1312yescomplemented
557#468C22×C1312yescomplemented
558#467C22×C1312yescomplemented
559#465C22×C1312yes—
560#465C22×C1312yescomplemented
561#465C22×C1312yescomplemented
562#464C22×C1312yescomplemented
563#464C22×C1312yescomplemented
564#460C22×C1312yes—
565#460C22×C1312yescomplemented
566#460C22×C1312yescomplemented
567#460C22×C1312yescomplemented
568#452C22×C1312yescomplemented
569#452C22×C1312yescomplemented
570#450C22×C1312yescomplemented
571#450C22×C1312yescomplemented
572#450C22×C1312yescomplemented
573#450C22×C1312yescomplemented
574#446C22×C1312yescomplemented
575#441C22×C1312yescomplemented
576#440C22×C1312yescomplemented
577#440C22×C1312yescomplemented
578#440C22×C1312yescomplemented
579C4×SD16C22×C1312yescomplemented
580C4×SD16C22×C1312yescomplemented
581#435C22×C1312yescomplemented
582#435C22×C1312yescomplemented
583C8×D4C22×C1312yescomplemented
584#433C22×C1312yescomplemented
585#431C22×C1311yescharacteristic, complemented
586#418C22×C1312yescomplemented
587#417C22×C1312yescomplemented
588#416C22×C1312yescomplemented
589C2×#102C22×C1312yescomplemented
590C2×#102C22×C1312yescomplemented
591C2×#102C22×C1312yescomplemented
592#405C22×C1312yescomplemented
593C2×#97C22×C1311yescharacteristic, complemented
594C22×C13—21no—
595C22×C13—21no—
596C22×C13—22no—
597C22×C13—22no—
598C22×C13—22no—
599C22×C13—41no—
600C22×C13—42no—
601C22×C13—42no—
602C22×C13—42no—
603C22×C13—41no—
604C22×C13—42no—
605C22×C13—42no—
606C22×C13—41no—
607C22×C13—42no—
608C22×C13—164no—
609C22×C13—164no—
610C22×C13#57712yes—
611C22×C13C23×D411yescharacteristic
612C4×C13—21no—
613C4×C13—21no—
614C4×C13—22no—
615C4×C13—22no—
616C4×C13—21no—
617C4×C13—21no—
618C4×C13—21no—
619C4×C13—22no—
620C4×C13—41no—
621C4×C13—42no—
622C4×C13—42no—
623C4×C13—41no—
624C4×C13—42no—
625C4×C13—42no—
626C4×C13—41no—
627C4×C13#58512yes—
628C2×#41—21no—
629C2×#41C23×C1312yes—
630C22×D4—22no—
631C22×D4—21no—
632C22×D4—21no—
633C22×D4—21no—
634C22×D4C23×C1312yes—
635C22×D4C23×C1312yes—
636C2×Q16C23×C1312yes—
637C2×SD16C23×C1312yes—
638C2×SD16C23×C1312yes—
639C2×SD16C23×C1312yes—
640C2×SD16C23×C1312yes—
641C2×SD16C23×C1312yes—
642C2×M16C23×C1312yes—
643C22×C8C23×C1312yes—
644C22×C8C23×C1312yes—
645C4⋊Q8—22no—
646C4⋊Q8—22no—
647C4⋊Q8C23×C1311yescharacteristic
648C4⋊Q8C23×C1311yescharacteristic
649C4⋊Q8C23×C1312yes—
650#127—21no—
651#127—21no—
652#127—21no—
653#127C23×C1312yes—
654#127C23×C1311yescharacteristic
655#127C23×C1311yescharacteristic
656#127C23×C1312yes—
657#126—22no—
658#126—22no—
659#126—22no—
660#126—22no—
661#126—21no—
662#126D4×C1312yes—
663#125—22no—
664#125—22no—
665#125—22no—
666#125—22no—
667#125—22no—
668#125—22no—
669#125—22no—
670#125—22no—
671#125—21no—
672#125—21no—
673#125—21no—
674#125D4×C1311yescharacteristic
675#125C23×C1312yes—
676#125C23×C1312yes—
677#125C23×C1311yescharacteristic
678#125C23×C1312yes—
679#124—21no—
680#124D4×C1311yescharacteristic
681#124C23×C1311yescharacteristic
682#124C23×C1312yes—
683#123—22no—
684#123—22no—
685#123—21no—
686#123—22no—
687#123—22no—
688#123—22no—
689#123—22no—
690#123D4×C1312yes—
691C22⋊Q8—21no—
692C22⋊Q8—22no—
693C22⋊Q8—22no—
694C22⋊Q8—22no—
695C22⋊Q8—22no—
696C22⋊Q8D4×C1311yescharacteristic
697C22⋊Q8C23×C1311yescharacteristic
698C22⋊Q8C23×C1312yes—
699C22⋊Q8C23×C1312yes—
700C22⋊Q8C23×C1312yes—
701#121—22no—
702#121—22no—
703#121—22no—
704#121—21no—
705#121—21no—
706#121—22no—
707#121—22no—
708#121—22no—
709#121—22no—
710#121—22no—
711#121D4×C1311yescharacteristic
712#121C23×C1311yescharacteristic
713#121C23×C1312yes—
714#121C23×C1312yes—
715#120—22no—
716#120—22no—
717#120—22no—
718#120—22no—
719#120—22no—
720#120—22no—
721C4×Q8—22no—
722C4×Q8—21no—
723C4×Q8C23×C1311yescharacteristic
724C4×Q8C23×C1312yes—
725C4×Q8C23×C1312yes—
726C4×Q8C23×C1312yes—
727C4×Q8C23×C1311yescharacteristic
728C4×D4—22no—
729C4×D4—21no—
730C4×D4—21no—
731C4×D4—21no—
732C4×D4C23×C1311yescharacteristic
733C4×D4C23×C1312yes—
734C4×D4C23×C1312yes—
735C4×D4C23×C1312yes—
736C4×D4C23×C1311yescharacteristic
737#117—21no—
738#117—22no—
739#117—22no—
740#117—21no—
741#117C23×C1312yes—
742#117C23×C1312yes—
743C2×C4⋊C4—21no—
744C2×C4⋊C4—21no—
745C2×C4⋊C4C23×C1311yescharacteristic
746C2×C4⋊C4C23×C1311yescharacteristic
747C2×C4⋊C4C23×C1312yes—
748C2×C22⋊C4—22no—
749C2×C42C23×C1311yescharacteristic
750#107C23×C1312yes—
751#107C23×C1312yes—
752#107C23×C1312yes—
753#106C23×C1312yes—
754#106C23×C1312yes—
755#106C23×C1312yes—
756C4⋊C8C23×C1312yes—
757C4⋊C8C23×C1312yes—
758C4⋊C8C23×C1312yes—
759#103C23×C1312yes—
760#103C23×C1312yes—
761#103C23×C1312yes—
762#103C23×C1312yes—
763#103C23×C1312yes—
764#102C23×C1312yes—
765#102C23×C1312yes—
766#102C23×C1312yes—
767#102C23×C1312yes—
768#102C23×C1312yes—
769#102C23×C1312yes—
770#102C23×C1312yes—
771#102C23×C1312yes—
772#102C23×C1312yes—
773#102C23×C1312yes—
774#102C23×C1312yes—
775#102C23×C1312yes—
776#102C23×C1312yes—
777#102C23×C1312yes—
778#102C23×C1312yes—
779C22⋊C8C23×C1311yescharacteristic
780C22⋊C8C23×C1311yescharacteristic
781C22⋊C8C23×C1312yes—
782C22⋊C8C23×C1312yes—
783#97C23×C1311yescharacteristic
784#97C23×C1311yescharacteristic
785#97C23×C1312yes—
786#97C23×C1312yes—
787C4×C8C23×C1312yes—
788C4×C8C23×C1312yes—
789C2×C13—22no—
790C2×C13—42no—
791C2×C13—82no—
792C2×C13—81no—
793C2×C13—82no—
794C2×C13#350011yescharacteristic
795C2×C13C2×#57711yescharacteristic
796C2×C13#358511yescharacteristic
797C24—22no—
798C24—22no—
799#41—42no—
800#41—42no—
801#41—82no—
802C2×Q8—21no—
803C2×Q8—22no—
804C2×Q8C2×D4×C1311yescharacteristic
805C2×Q8C24×C1311yescharacteristic
806C2×Q8C24×C1312yes—
807C2×D4—21no—
808C2×D4—22no—
809C2×D4—22no—
810C2×D4—22no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—22no—
814C2×D4—22no—
815C2×D4—21no—
816C2×D4—22no—
817C2×D4—22no—
818C2×D4—22no—
819C2×D4—22no—
820C2×D4—21no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—82no—
826C2×D4—82no—
827C2×D4—82no—
828C2×D4—84no—
829C2×D4C2×D4×C1312yes—
830C2×D4C2×D4×C1311yescharacteristic
831C2×D4C24×C1312yes—
832C2×D4C24×C1311yescharacteristic
833C2×D4C24×C1312yes—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—22no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4C2×D4×C1311yescharacteristic
842C22×C4C2×D4×C1311yescharacteristic
843C22×C4C24×C1311yescharacteristic
844C22×C4C24×C1312yes—
845Q16—42no—
846SD16—42no—
847SD16—42no—
848SD16—42no—
849SD16—42no—
850SD16—42no—
851M16—42no—
852C2×C8—42no—
853C2×C8—42no—
854C2×C8C24×C1312yes—
855C2×C8C24×C1312yes—
856C2×C8C24×C1312yes—
857C2×C8C24×C1312yes—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—21no—
863C4⋊C4—22no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—22no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4C2×D4×C1312yes—
882C4⋊C4C2×D4×C1312yes—
883C4⋊C4C2×D4×C1311yescharacteristic
884C4⋊C4C2×D4×C1311yescharacteristic
885C4⋊C4C2×D4×C1312yes—
886C4⋊C4C2×D4×C1312yes—
887C4⋊C4C24×C1312yes—
888C4⋊C4C24×C1312yes—
889C4⋊C4C24×C1312yes—
890C4⋊C4C24×C1311yescharacteristic
891C4⋊C4C24×C1311yescharacteristic
892C22⋊C4—21no—
893C22⋊C4—22no—
894C22⋊C4—22no—
895C22⋊C4—22no—
896C22⋊C4—22no—
897C22⋊C4—22no—
898C22⋊C4—22no—
899C22⋊C4—21no—
900C22⋊C4—21no—
901C22⋊C4—21no—
902C22⋊C4—22no—
903C22⋊C4—22no—
904C22⋊C4—21no—
905C22⋊C4—22no—
906C22⋊C4—22no—
907C22⋊C4C2×D4×C1312yes—
908C22⋊C4C2×D4×C1312yes—
909C22⋊C4C2×D4×C1312yes—
910C22⋊C4C2×D4×C1312yes—
911C22⋊C4C2×D4×C1312yes—
912C42—22no—
913C42—22no—
914C42—21no—
915C42—22no—
916C42—22no—
917C42C2×D4×C1311yescharacteristic
918C42C2×D4×C1311yescharacteristic
919C42C24×C1311yescharacteristic
920C42C24×C1312yes—
921C42C24×C1311yescharacteristic
922C13#6259611yescharacteristic, direct product factor, Sylow
923C23—22no—
924C23—21no—
925C23—22no—
926C23—44no—
927C23—82no—
928C23—82no—
929C23—82no—
930C23—82no—
931C23—82no—
932C23C22×D4×C1312yes—
933C23C22×D4×C1311yescharacteristic
934Q8—22no—
935Q8—22no—
936Q8—22no—
937Q8—41no—
938Q8—81no—
939Q8—82no—
940D4—24no—
941D4—22no—
942D4—22no—
943D4—22no—
944D4—22no—
945D4—22no—
946D4—41no—
947D4—42no—
948D4—42no—
949D4—42no—
950D4—82no—
951D4—82no—
952D4—81no—
953D4—82no—
954D4—81no—
955D4—82no—
956D4—82no—
957D4—82no—
958D4—82no—
959D4—82no—
960D4—82no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—41no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—82no—
976C2×C4—82no—
977C2×C4—82no—
978C2×C4—81no—
979C2×C4—82no—
980C2×C4C22×D4×C1311yescharacteristic
981C2×C4C22×D4×C1311yescharacteristic
982C2×C4C22×D4×C1312yes—
983C2×C4C22×D4×C1312yes—
984C2×C4C22×D4×C1312yes—
985C2×C4C22×D4×C1311yescharacteristic
986C2×C4C22×D4×C1311yescharacteristic
987C2×C4C22×D4×C1311yescharacteristic
988C2×C4C25×C1311yescharacteristic
989C8—22no—
990C8—22no—
991C8—22no—
992C8—22no—
993C22—21no—
994C22—21no—
995C22—22no—
996C22—22no—
997C22—22no—
998C22—42no—
999C22—41no—
1000C22—42no—
1001C22—41no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—42no—
1006C22—41no—
1007C22—164no—
1008C22—164no—
1009C22C13×#57712yes—
1010C22C23×D4×C1311yescharacteristic
1011C4—21no—
1012C4—21no—
1013C4—22no—
1014C4—21no—
1015C4—21no—
1016C4—22no—
1017C4—22no—
1018C4—21no—
1019C4—42no—
1020C4—41no—
1021C4—41no—
1022C4—42no—
1023C4—42no—
1024C4—41no—
1025C4—42no—
1026C4C13×#58512yes—
1027C2—22no—
1028C2—42no—
1029C2—82no—
1030C2—81no—
1031C2—82no—
1032C2C13×#350011yescharacteristic
1033C2C2×C13×#57711yescharacteristic
1034C2C13×#358511yescharacteristic
subgroupG/H
center, socleC22×C13C23×D4
commutator, Frattini, cosocleC2×C4C25×C13
prime radicalC13×#3543C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C13×#529 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3563C2semidirect
3. C13×#3371C2semidirect
4. C13×#3368C2semidirect
5. C13×#3317C2semidirect
6. C13×#3314C2semidirect
7. C13×#3310C2semidirect
8. C13×#3310C2semidirect
9. C13×#3296C2semidirect
10. C13×#3295C2semidirect
11. C13×#3241C2semidirect
12. C13×#3232C2semidirect
13. C13×#3222C2semidirect
14. C13×#3208C2semidirect
15. C13×#3181C2semidirect
16. C13×#3174C2semidirect
17. C13×#3136C2semidirect
18. C2×C13×#490C2semidirect
19. C13×#2968C2semidirect
24. C13×#557C22semidirect
25. C13×#554C22semidirect
27. C13×#552C22semidirect
28. C13×#552C22semidirect
37. C13×#544C22semidirect
39. C13×#541C22semidirect
46. C13×#533C22semidirect
50. C2×C13×#125C22semidirect
51. C13×#501C22semidirect
52. C13×#499C22semidirect
53. C13×#497C22semidirect
54. C13×#492C22semidirect
55. C13×#491C22semidirect
57. C13×#490C22semidirect
58. C13×#490C22semidirect
59. C13×#490C22semidirect
60. C13×#490C22semidirect
61. C13×#489C22semidirect
62. C13×#489C22semidirect
63. C13×#488C22semidirect
64. C13×#488C22semidirect
65. C13×#486C22semidirect
66. C13×#486C22semidirect
67. C13×#484C22semidirect
68. C13×#483C22semidirect
69. C13×#482C22semidirect
70. C13×#482C22semidirect
72. C13×#481C22semidirect
74. C13×#480C22semidirect
75. C13×#479C22semidirect
76. C13×#478C22semidirect
77. C13×#478C22semidirect
78. C13×#478C22semidirect
79. C13×#476C22semidirect
80. C13×#474C22semidirect
81. C13×#468C22semidirect
82. C13×#468C22semidirect
83. C13×#467C22semidirect
85. C13×#465C22semidirect
86. C13×#465C22semidirect
87. C13×#464C22semidirect
88. C13×#464C22semidirect
90. C13×#460C22semidirect
91. C13×#460C22semidirect
92. C13×#460C22semidirect
93. C13×#452C22semidirect
94. C13×#452C22semidirect
95. C13×#450C22semidirect
96. C13×#450C22semidirect
97. C13×#450C22semidirect
98. C13×#450C22semidirect
99. C13×#446C22semidirect
100. C13×#441C22semidirect
101. C13×#440C22semidirect
102. C13×#440C22semidirect
103. C13×#440C22semidirect
104. C4×C13×SD16C22semidirect
105. C4×C13×SD16C22semidirect
106. C13×#435C22semidirect
107. C13×#435C22semidirect
108. C8×D4×C13C22semidirect
109. C13×#433C22semidirect
110. C13×#431C22semidirect
111. C13×#418C22semidirect
112. C13×#417C22semidirect
113. C13×#416C22semidirect
114. C2×C13×#102C22semidirect
115. C2×C13×#102C22semidirect
116. C2×C13×#102C22semidirect
117. C13×#405C22semidirect
118. C2×C13×#97C22semidirect
280. #62596C13direct (N × H)
406. #3563C2×C13semidirect
408. #3371C2×C13semidirect
409. #3368C2×C13semidirect
410. #3317C2×C13semidirect
411. #3314C2×C13semidirect
412. #3310C2×C13semidirect
413. #3310C2×C13semidirect
414. #3296C2×C13semidirect
415. #3295C2×C13semidirect
416. #3241C2×C13semidirect
417. #3232C2×C13semidirect
418. #3222C2×C13semidirect
419. #3208C2×C13semidirect
420. #3181C2×C13semidirect
421. #3174C2×C13semidirect
422. #3136C2×C13semidirect
423. C2×#490C2×C13semidirect
424. #2968C2×C13semidirect
499. #557C22×C13semidirect
500. #554C22×C13semidirect
502. #552C22×C13semidirect
503. #552C22×C13semidirect
512. #544C22×C13semidirect
514. #541C22×C13semidirect
521. #533C22×C13semidirect
525. C2×#125C22×C13semidirect
526. #501C22×C13semidirect
527. #499C22×C13semidirect
528. #497C22×C13semidirect
529. #492C22×C13semidirect
530. #491C22×C13semidirect
532. #490C22×C13semidirect
533. #490C22×C13semidirect
534. #490C22×C13semidirect
535. #490C22×C13semidirect
536. #489C22×C13semidirect
537. #489C22×C13semidirect
538. #488C22×C13semidirect
539. #488C22×C13semidirect
540. #486C22×C13semidirect
541. #486C22×C13semidirect
542. #484C22×C13semidirect
543. #483C22×C13semidirect
544. #482C22×C13semidirect
545. #482C22×C13semidirect
547. #481C22×C13semidirect
549. #480C22×C13semidirect
550. #479C22×C13semidirect
551. #478C22×C13semidirect
552. #478C22×C13semidirect
553. #478C22×C13semidirect
554. #476C22×C13semidirect
555. #474C22×C13semidirect
556. #468C22×C13semidirect
557. #468C22×C13semidirect
558. #467C22×C13semidirect
560. #465C22×C13semidirect
561. #465C22×C13semidirect
562. #464C22×C13semidirect
563. #464C22×C13semidirect
565. #460C22×C13semidirect
566. #460C22×C13semidirect
567. #460C22×C13semidirect
568. #452C22×C13semidirect
569. #452C22×C13semidirect
570. #450C22×C13semidirect
571. #450C22×C13semidirect
572. #450C22×C13semidirect
573. #450C22×C13semidirect
574. #446C22×C13semidirect
575. #441C22×C13semidirect
576. #440C22×C13semidirect
577. #440C22×C13semidirect
578. #440C22×C13semidirect
579. C4×SD16C22×C13semidirect
580. C4×SD16C22×C13semidirect
581. #435C22×C13semidirect
582. #435C22×C13semidirect
583. C8×D4C22×C13semidirect
584. #433C22×C13semidirect
585. #431C22×C13semidirect
586. #418C22×C13semidirect
587. #417C22×C13semidirect
588. #416C22×C13semidirect
589. C2×#102C22×C13semidirect
590. C2×#102C22×C13semidirect
591. C2×#102C22×C13semidirect
592. #405C22×C13semidirect
593. C2×#97C22×C13semidirect
922. C13#62596direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35632
C13×#35432
C13×#33712
C13×#33682
C13×#33172
C13×#33142
C13×#33102
C13×#32962
C13×#32952
C13×#32412
C13×#32322
C13×#32222
C13×#32082
C13×#31812
C13×#31742
C13×#31362
C2×C13×#4902
C13×#29682
#6259613