Finite Group Databasebeta

← C13×#61857 #15748196

Subgroups — C13×#61857 #15748196

Order 3328.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1102 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3554C211yesmaximal, characteristic, complemented
2C13×#3503C211yesmaximal, characteristic, complemented
3C13×#3389C212yesmaximal, complemented
4C13×#3386C211yesmaximal, characteristic, complemented
5C13×#3386C211yesmaximal, characteristic, complemented
6C13×#3385C212yesmaximal, complemented
7C13×#3383C211yesmaximal, characteristic, complemented
8Q8×C13×D8C211yesmaximal, characteristic, complemented
9C13×#3375C212yesmaximal, complemented
10C13×#3373C211yesmaximal, characteristic, complemented
11C13×#3370C212yesmaximal, complemented
12C13×#3368C211yesmaximal, characteristic, complemented
13C13×#3365C211yesmaximal, characteristic, complemented
14C13×#3358C211yesmaximal, characteristic, complemented
15C13×#3243C212yesmaximal, complemented
16C13×#3241C212yesmaximal, complemented
17C13×#3239C211yesmaximal, characteristic, complemented
18C13×#3226C211yesmaximal, characteristic, complemented
19C13×#3124C212yesmaximal, complemented
20C13×#3119C212yesmaximal, complemented
21C13×#3115C211yesmaximal, characteristic, complemented
22C13×#3102C211yesmaximal, characteristic, complemented
23C13×#2985C211yesmaximal, characteristic, complemented
24C13×#562—22no—
25C13×#559C2211yescharacteristic
26C13×#559C2212yes—
27Q82×C13C2212yes—
28C13×#557C2211yescharacteristic
29C13×#557C2211yescharacteristic
30C13×#557C2211yescharacteristic
31C13×#554—22no—
32C13×#554C2212yes—
33C13×#554C2212yes—
34C13×#550C2211yescharacteristic
35D4×Q8×C13—21no—
36D4×Q8×C13—21no—
37D4×Q8×C13C2211yescharacteristic
38D4×Q8×C13C2211yescharacteristic
39D4×Q8×C13C2211yescharacteristic
40C13×#548—21no—
41C13×#547—21no—
42C13×#544—22no—
43C13×#544C2212yes—
44C13×#542—21no—
45C13×#542C2212yes—
46C13×#540C2212yes—
47C13×#539—22no—
48C13×#536—21no—
49C13×#533—21no—
50C13×#533C2211yescharacteristic
51C13×#532C2211yescharacteristic
52C2×C13×C4⋊Q8—21no—
53C2×C13×C4⋊Q8C2211yescharacteristic
54C13×#529C2211yescharacteristic
55C13×#520C2212yes—
56C4×C13×#41C2211yescharacteristic
57C13×#501C2212yes—
58C13×#501C2212yes—
59C13×#501C2212yes—
60C13×#500C2211yescharacteristic
61C13×#500C2212yes—
62C13×#500C2211yescharacteristic
63C13×#499C2212yes—
64C13×#490C2212yes—
65C13×#489C2212yes—
66C13×#489C2212yes—
67C13×#488C2212yes—
68C13×#486C2211yescharacteristic
69C13×#486C2212yes—
70C13×#486C2211yescharacteristic
71C13×#485C2211yescharacteristic
72C13×#484C2212yes—
73C13×#482C2211yescharacteristic
74C13×#482C2212yes—
75C13×#481C2212yes—
76C13×#480C2212yes—
77C13×#480C2212yes—
78C13×#479C2211yescharacteristic
79C13×#479C2212yes—
80C13×#479C2212yes—
81C13×#478C2211yescharacteristic
82C13×#478C2212yes—
83C13×#478C2212yes—
84C13×#478C2212yes—
85C13×#478C2212yes—
86C13×#477C2212yes—
87C13×#477C2212yes—
88C13×#476C2212yes—
89C13×#475C2211yescharacteristic
90C13×#475C2211yescharacteristic
91C13×#475C2211yescharacteristic
92C13×#474C2212yes—
93C13×#474C2211yescharacteristic
94C13×#474C2211yescharacteristic
95C13×#474C2212yes—
96C13×#474C2211yescharacteristic
97C13×#474C2212yes—
98C13×#474C2212yes—
99C13×#474C2212yes—
100C13×#464C2211yescharacteristic
101C13×#464C2212yes—
102C13×#463C2211yescharacteristic
103C13×#463C2212yes—
104C13×#460C2211yescharacteristic
105C13×#460C2212yes—
106C13×#459C2212yes—
107C13×#459C2211yescharacteristic
108C13×#452C2211yescharacteristic
109C13×#449C2211yescharacteristic
110C13×#449C2212yes—
111C13×#446C2211yescharacteristic
112C13×#446C2212yes—
113C13×#446C2211yescharacteristic
114C13×#446C2212yes—
115C8×Q8×C13C2211yescharacteristic
116C8×Q8×C13C2211yescharacteristic
117C13×#442C2212yes—
118C13×#442C2212yes—
119C13×#440C2212yes—
120C13×#440C2212yes—
121C13×#440C2212yes—
122C13×#440C2212yes—
123C4×C13×Q16C2211yescharacteristic
124C4×C13×Q16C2212yes—
125C4×C13×SD16C2211yescharacteristic
126C4×C13×SD16C2211yescharacteristic
127C4×C13×SD16C2212yes—
128C4×C13×D8C2211yescharacteristic
129C4×C13×D8C2212yes—
130C4×C13×D8C2212yes—
131C13×#433C2212yes—
132C13×#433C2212yes—
133C13×#432C2211yescharacteristic
134C13×#431C2211yescharacteristic
135C2×C13×#41—21no—
136C2×C13×#41—21no—
137C2×C13×#41C2311yescharacteristic
138C22×Q8×C13—21no—
139C22×Q8×C13—21no—
140C22×Q8×C13—21no—
141C22×Q8×C13—21no—
142C2×C13×Q16C2311yescharacteristic
143C2×C13×SD16C2311yescharacteristic
144C2×C13×SD16C2312yes—
145C2×C13×SD16C2311yescharacteristic
146C2×C13×D8C2311yescharacteristic
147C2×C13×D8C2312yes—
148C13×C4⋊Q8—21no—
149C13×C4⋊Q8—21no—
150C13×C4⋊Q8—21no—
151C13×C4⋊Q8—22no—
152C13×C4⋊Q8—22no—
153C13×C4⋊Q8—22no—
154C13×C4⋊Q8—22no—
155C13×C4⋊Q8—21no—
156C13×C4⋊Q8—21no—
157C13×C4⋊Q8D411yescharacteristic
158C13×C4⋊Q8D411yescharacteristic
159C13×C4⋊Q8C2312yes—
160C13×C4⋊Q8C2311yescharacteristic
161C13×C4⋊Q8C2311yescharacteristic
162C13×C4⋊Q8C2311yescharacteristic
163C13×C4⋊Q8C2312yes—
164C13×C4⋊Q8C2312yes—
165C13×C4⋊Q8C2312yes—
166C13×#127C2311yescharacteristic
167C13×#127C2312yes—
168C13×#126—22no—
169C13×#126—21no—
170C13×#125—22no—
171C13×#125—22no—
172C13×#125—22no—
173C13×#125—22no—
174C13×#125D412yes—
175C13×#125C2312yes—
176C13×#125C2312yes—
177C13×#125C2312yes—
178C13×#125C2311yescharacteristic
179C13×#124—21no—
180C13×#124—22no—
181C13×#124—22no—
182C13×#124—21no—
183C13×#124C2312yes—
184C13×#124C2311yescharacteristic
185C13×#123—21no—
186C13×#123—22no—
187C13×#123—22no—
188C13×#123—22no—
189C13×#123—22no—
190C13×#123—22no—
191C13×#123—22no—
192C13×C22⋊Q8—22no—
193C13×C22⋊Q8—22no—
194C13×C22⋊Q8—21no—
195C13×C22⋊Q8—21no—
196C13×C22⋊Q8—22no—
197C13×C22⋊Q8—22no—
198C13×C22⋊Q8—22no—
199C13×C22⋊Q8—22no—
200C13×C22⋊Q8—21no—
201C13×C22⋊Q8—22no—
202C13×C22⋊Q8—22no—
203C13×C22⋊Q8—22no—
204C13×C22⋊Q8—22no—
205C13×C22⋊Q8—22no—
206C13×C22⋊Q8—22no—
207C13×C22⋊Q8D411yescharacteristic
208C13×C22⋊Q8D411yescharacteristic
209C13×C22⋊Q8D412yes—
210C13×C22⋊Q8C2311yescharacteristic
211C13×#121—21no—
212C13×#121—22no—
213C13×#121—21no—
214C13×#121—22no—
215C13×#121—22no—
216C13×#121C2312yes—
217C13×#121C2311yescharacteristic
218C4×Q8×C13—22no—
219C4×Q8×C13—21no—
220C4×Q8×C13—21no—
221C4×Q8×C13—21no—
222C4×Q8×C13C2311yescharacteristic
223C4×Q8×C13C2311yescharacteristic
224C4×Q8×C13C2312yes—
225C4×Q8×C13C2312yes—
226C4×Q8×C13C2312yes—
227C4×Q8×C13C2311yescharacteristic
228C4×Q8×C13C2311yescharacteristic
229C4×Q8×C13C2311yescharacteristic
230C4×Q8×C13C2312yes—
231C4×D4×C13—21no—
232C4×D4×C13—21no—
233C4×D4×C13—21no—
234C4×D4×C13—22no—
235C4×D4×C13—21no—
236C4×D4×C13—22no—
237C4×D4×C13—22no—
238C4×D4×C13—21no—
239C4×D4×C13C2311yescharacteristic
240C4×D4×C13C2311yescharacteristic
241C4×D4×C13C2312yes—
242C4×D4×C13C2312yes—
243C4×D4×C13C2312yes—
244C4×D4×C13C2312yes—
245C4×D4×C13C2312yes—
246C4×D4×C13C2312yes—
247C4×D4×C13C2311yescharacteristic
248C13×#117—22no—
249C13×#117—21no—
250C13×#117—21no—
251C13×#117C2311yescharacteristic
252C13×#117C2312yes—
253C2×C13×C4⋊C4—21no—
254C2×C13×C4⋊C4—22no—
255C2×C13×C4⋊C4—22no—
256C2×C13×C4⋊C4—22no—
257C2×C13×C4⋊C4C2312yes—
258C2×C42×C13—21no—
259C2×C42×C13C2311yescharacteristic
260C13×#107C2312yes—
261C13×#107C2311yescharacteristic
262C13×#107C2312yes—
263C13×#107C2312yes—
264C13×#107C2311yescharacteristic
265C13×#107C2312yes—
266C13×#107C2312yes—
267C13×#107C2312yes—
268C13×#107C2312yes—
269C13×#106C2312yes—
270C13×#106C2311yescharacteristic
271C13×#106C2311yescharacteristic
272C13×#106C2312yes—
273C13×#106C2312yes—
274C13×C4⋊C8C2311yescharacteristic
275C13×C4⋊C8C2311yescharacteristic
276C13×C4⋊C8C2311yescharacteristic
277C13×C4⋊C8C2311yescharacteristic
278C13×C4⋊C8C2312yes—
279C13×C4⋊C8C2312yes—
280C13×C4⋊C8C2312yes—
281C13×C4⋊C8C2312yes—
282C13×#103C2311yescharacteristic
283C13×#103C2311yescharacteristic
284C13×#103C2311yescharacteristic
285C13×#103C2312yes—
286C13×#103C2312yes—
287C13×#103C2311yescharacteristic
288C13×#103C2312yes—
289C13×#102C2311yescharacteristic
290C13×#102C2312yes—
291C13×#102C2312yes—
292C13×#102C2311yescharacteristic
293C13×#102C2312yes—
294C13×#102C2311yescharacteristic
295C13×#102C2312yes—
296C13×#102C2311yescharacteristic
297C13×#102C2312yes—
298C13×#102C2312yes—
299C13×#102C2312yes—
300C13×#102C2312yes—
301C13×#102C2312yes—
302C13×C22⋊C8C2311yescharacteristic
303C13×C22⋊C8C2311yescharacteristic
304C13×C22⋊C8C2312yes—
305C13×#97C2312yes—
306C13×#97C2312yes—
307C13×#97C2312yes—
308C4×C8×C13C2311yescharacteristic
309C4×C8×C13C2311yescharacteristic
310C4×C8×C13C2312yes—
311C4×C8×C13C2312yes—
312#61857C1311yesmaximal, characteristic, direct product factor, Sylow
313C13×#41—22no—
314C13×#41—22no—
315C13×#41—82no—
316C13×#41—82no—
317C2×Q8×C13—21no—
318C2×Q8×C13—21no—
319C2×Q8×C13—21no—
320C2×Q8×C13—22no—
321C2×Q8×C13—22no—
322C2×Q8×C13—22no—
323C2×Q8×C13—22no—
324C2×Q8×C13—82no—
325C2×Q8×C13—82no—
326C2×Q8×C13—82no—
327C2×Q8×C13—82no—
328C2×Q8×C13C2×D411yescharacteristic
329C2×Q8×C13C2×D411yescharacteristic
330C2×Q8×C13C2×D412yes—
331C2×Q8×C13C2411yescharacteristic
332C2×Q8×C13C2411yescharacteristic
333C2×D4×C13—21no—
334C2×D4×C13—21no—
335C2×D4×C13—22no—
336C2×D4×C13—21no—
337C2×D4×C13—21no—
338C2×D4×C13—22no—
339C2×D4×C13—22no—
340C2×D4×C13C2411yescharacteristic
341C2×D4×C13C2412yes—
342C2×D4×C13C2411yescharacteristic
343C22×C4×C13—21no—
344C22×C4×C13—22no—
345C22×C4×C13—21no—
346C22×C4×C13—21no—
347C22×C4×C13—21no—
348C22×C4×C13—22no—
349C22×C4×C13—22no—
350C22×C4×C13—22no—
351C22×C4×C13—22no—
352C22×C4×C13—22no—
353C22×C4×C13—22no—
354C22×C4×C13C2×D411yescharacteristic
355C22×C4×C13C2×D411yescharacteristic
356C22×C4×C13C2411yescharacteristic
357C13×Q16—22no—
358C13×SD16—22no—
359C13×SD16—24no—
360C13×SD16—22no—
361C13×D8—22no—
362C13×D8—24no—
363C2×C8×C13C2411yescharacteristic
364C2×C8×C13C2411yescharacteristic
365C2×C8×C13C2411yescharacteristic
366C2×C8×C13C2411yescharacteristic
367C2×C8×C13C2412yes—
368C2×C8×C13C2412yes—
369C13×C4⋊C4—21no—
370C13×C4⋊C4—22no—
371C13×C4⋊C4—22no—
372C13×C4⋊C4—22no—
373C13×C4⋊C4—22no—
374C13×C4⋊C4—22no—
375C13×C4⋊C4—22no—
376C13×C4⋊C4—21no—
377C13×C4⋊C4—21no—
378C13×C4⋊C4—22no—
379C13×C4⋊C4—22no—
380C13×C4⋊C4—21no—
381C13×C4⋊C4—21no—
382C13×C4⋊C4—21no—
383C13×C4⋊C4—21no—
384C13×C4⋊C4—21no—
385C13×C4⋊C4—22no—
386C13×C4⋊C4—22no—
387C13×C4⋊C4—22no—
388C13×C4⋊C4—22no—
389C13×C4⋊C4—22no—
390C13×C4⋊C4—22no—
391C13×C4⋊C4—21no—
392C13×C4⋊C4C2×D412yes—
393C13×C4⋊C4C2×D412yes—
394C13×C4⋊C4C2×D412yes—
395C13×C4⋊C4C2×D412yes—
396C13×C4⋊C4C2×D411yescharacteristic
397C13×C4⋊C4C2×D412yes—
398C13×C4⋊C4C2×D411yescharacteristic
399C13×C4⋊C4C2×D412yes—
400C13×C4⋊C4C2×D412yes—
401C13×C4⋊C4C2411yescharacteristic
402C13×C4⋊C4C2412yes—
403C13×C4⋊C4C2412yes—
404C13×C4⋊C4C2411yescharacteristic
405C13×C4⋊C4C2411yescharacteristic
406C13×C4⋊C4C2411yescharacteristic
407C13×C4⋊C4C2412yes—
408C13×C22⋊C4—21no—
409C13×C22⋊C4—21no—
410C13×C22⋊C4—21no—
411C13×C22⋊C4—21no—
412C13×C22⋊C4—22no—
413C13×C22⋊C4—22no—
414C13×C22⋊C4—21no—
415C13×C22⋊C4—21no—
416C13×C22⋊C4—21no—
417C13×C22⋊C4—22no—
418C13×C22⋊C4—22no—
419C13×C22⋊C4—22no—
420C13×C22⋊C4—21no—
421C13×C22⋊C4—22no—
422C13×C22⋊C4—22no—
423C13×C22⋊C4—22no—
424C13×C22⋊C4—22no—
425C13×C22⋊C4C2×D412yes—
426C13×C22⋊C4C2×D412yes—
427C42×C13—21no—
428C42×C13—21no—
429C42×C13—21no—
430C42×C13—21no—
431C42×C13—22no—
432C42×C13—22no—
433C42×C13—22no—
434C42×C13C2×D411yescharacteristic
435C42×C13C2×D411yescharacteristic
436C42×C13C2411yescharacteristic
437C42×C13C2412yes—
438C42×C13C2412yes—
439C42×C13C2411yescharacteristic
440#3554C2×C1311yescharacteristic, complemented
441#3503C2×C1311yescharacteristic, complemented
442#3389C2×C1312yescomplemented
443#3386C2×C1311yescharacteristic, complemented
444#3386C2×C1311yescharacteristic, complemented
445#3385C2×C1312yescomplemented
446#3383C2×C1311yescharacteristic, complemented
447Q8×D8C2×C1311yescharacteristic, complemented
448#3375C2×C1312yescomplemented
449#3373C2×C1311yescharacteristic, complemented
450#3370C2×C1312yescomplemented
451#3368C2×C1311yescharacteristic, complemented
452#3365C2×C1311yescharacteristic, complemented
453#3358C2×C1311yescharacteristic, complemented
454#3243C2×C1312yescomplemented
455#3241C2×C1312yescomplemented
456#3239C2×C1311yescharacteristic, complemented
457#3226C2×C1311yescharacteristic, complemented
458#3124C2×C1312yescomplemented
459#3119C2×C1312yescomplemented
460#3115C2×C1311yescharacteristic, complemented
461#3102C2×C1311yescharacteristic, complemented
462#2985C2×C1311yescharacteristic, complemented
463C23×C13—21no—
464C23×C13—22no—
465C23×C13—21no—
466C23×C13C22×D411yescharacteristic
467Q8×C13—22no—
468Q8×C13—22no—
469Q8×C13—21no—
470Q8×C13—21no—
471Q8×C13—21no—
472Q8×C13—42no—
473Q8×C13—42no—
474Q8×C13—42no—
475Q8×C13—42no—
476Q8×C13—82no—
477Q8×C13—82no—
478Q8×C13—82no—
479Q8×C13—82no—
480Q8×C132−1+412yes—
481D4×C13—24no—
482D4×C13—21no—
483D4×C13—21no—
484D4×C13—22no—
485D4×C13—21no—
486D4×C13—22no—
487D4×C13—42no—
488D4×C13—81no—
489D4×C13—82no—
490D4×C13—82no—
491D4×C13—81no—
492D4×C13—82no—
493D4×C132−1+412yes—
494C2×C4×C13—24no—
495C2×C4×C13—21no—
496C2×C4×C13—22no—
497C2×C4×C13—21no—
498C2×C4×C13—21no—
499C2×C4×C13—21no—
500C2×C4×C13—21no—
501C2×C4×C13—21no—
502C2×C4×C13—21no—
503C2×C4×C13—22no—
504C2×C4×C13—22no—
505C2×C4×C13—22no—
506C2×C4×C13—21no—
507C2×C4×C13—41no—
508C2×C4×C13—42no—
509C2×C4×C13—42no—
510C2×C4×C13—42no—
511C2×C4×C13—82no—
512C2×C4×C13—82no—
513C2×C4×C13—82no—
514C2×C4×C13—82no—
515C2×C4×C13—82no—
516C2×C4×C13—82no—
517C2×C4×C13—82no—
518C2×C4×C13C22×D412yes—
519C2×C4×C13C22×D411yescharacteristic
520C2×C4×C13C22×D411yescharacteristic
521C2×C4×C13C22×D412yes—
522C2×C4×C13C22×D411yescharacteristic
523C2×C4×C13C22×D411yescharacteristic
524C2×C4×C13C22×D412yes—
525C2×C4×C13C22×D412yes—
526C2×C4×C13C22×D411yescharacteristic
527C2×C4×C13C2511yescharacteristic
528C8×C13—21no—
529C8×C13—22no—
530C8×C13—21no—
531C8×C13—22no—
532C8×C13—21no—
533C8×C13—21no—
534#562—22no—
535#559C22×C1311yescharacteristic
536#559C22×C1312yes—
537Q82C22×C1312yes—
538#557C22×C1311yescharacteristic
539#557C22×C1311yescharacteristic
540#557C22×C1311yescharacteristic
541#554—22no—
542#554C22×C1312yes—
543#554C22×C1312yes—
544#550C22×C1311yescharacteristic
545D4×Q8—21no—
546D4×Q8—21no—
547D4×Q8C22×C1311yescharacteristic
548D4×Q8C22×C1311yescharacteristic
549D4×Q8C22×C1311yescharacteristic
550#548—21no—
551#547—21no—
552#544—22no—
553#544C22×C1312yes—
554#542—21no—
555#542C22×C1312yes—
556#540C22×C1312yes—
557#539—22no—
558#536—21no—
559#533—21no—
560#533C22×C1311yescharacteristic
561#532C22×C1311yescharacteristic
562C2×C4⋊Q8—21no—
563C2×C4⋊Q8C22×C1311yescharacteristic
564#529C22×C1311yescharacteristic
565#520C22×C1312yes—
566C4×#41C22×C1311yescharacteristic
567#501C22×C1312yes—
568#501C22×C1312yes—
569#501C22×C1312yes—
570#500C22×C1311yescharacteristic
571#500C22×C1312yes—
572#500C22×C1311yescharacteristic
573#499C22×C1312yes—
574#490C22×C1312yes—
575#489C22×C1312yes—
576#489C22×C1312yes—
577#488C22×C1312yes—
578#486C22×C1311yescharacteristic
579#486C22×C1312yes—
580#486C22×C1311yescharacteristic
581#485C22×C1311yescharacteristic
582#484C22×C1312yes—
583#482C22×C1311yescharacteristic
584#482C22×C1312yes—
585#481C22×C1312yes—
586#480C22×C1312yes—
587#480C22×C1312yes—
588#479C22×C1311yescharacteristic
589#479C22×C1312yes—
590#479C22×C1312yes—
591#478C22×C1311yescharacteristic
592#478C22×C1312yes—
593#478C22×C1312yes—
594#478C22×C1312yes—
595#478C22×C1312yes—
596#477C22×C1312yes—
597#477C22×C1312yes—
598#476C22×C1312yes—
599#475C22×C1311yescharacteristic
600#475C22×C1311yescharacteristic
601#475C22×C1311yescharacteristic
602#474C22×C1312yes—
603#474C22×C1311yescharacteristic
604#474C22×C1311yescharacteristic
605#474C22×C1312yes—
606#474C22×C1311yescharacteristic
607#474C22×C1312yes—
608#474C22×C1312yes—
609#474C22×C1312yes—
610#464C22×C1311yescharacteristic
611#464C22×C1312yes—
612#463C22×C1311yescharacteristic
613#463C22×C1312yes—
614#460C22×C1311yescharacteristic
615#460C22×C1312yes—
616#459C22×C1312yes—
617#459C22×C1311yescharacteristic
618#452C22×C1311yescharacteristic
619#449C22×C1311yescharacteristic
620#449C22×C1312yes—
621#446C22×C1311yescharacteristic
622#446C22×C1312yes—
623#446C22×C1311yescharacteristic
624#446C22×C1312yes—
625C8×Q8C22×C1311yescharacteristic
626C8×Q8C22×C1311yescharacteristic
627#442C22×C1312yes—
628#442C22×C1312yes—
629#440C22×C1312yes—
630#440C22×C1312yes—
631#440C22×C1312yes—
632#440C22×C1312yes—
633C4×Q16C22×C1311yescharacteristic
634C4×Q16C22×C1312yes—
635C4×SD16C22×C1311yescharacteristic
636C4×SD16C22×C1311yescharacteristic
637C4×SD16C22×C1312yes—
638C4×D8C22×C1311yescharacteristic
639C4×D8C22×C1312yes—
640C4×D8C22×C1312yes—
641#433C22×C1312yes—
642#433C22×C1312yes—
643#432C22×C1311yescharacteristic
644#431C22×C1311yescharacteristic
645C22×C13—21no—
646C22×C13—21no—
647C22×C13—22no—
648C22×C13—21no—
649C22×C13—41no—
650C22×C13—41no—
651C22×C13—42no—
652C22×C13—41no—
653C22×C13—42no—
654C22×C13—41no—
655C22×C13—41no—
656C22×C13—42no—
657C22×C13C23×D411yescharacteristic
658C4×C13—21no—
659C4×C13—21no—
660C4×C13—22no—
661C4×C13—22no—
662C4×C13—21no—
663C4×C13—22no—
664C4×C13—21no—
665C4×C13—22no—
666C4×C13—22no—
667C4×C13—41no—
668C4×C13—41no—
669C4×C13—41no—
670C4×C13—41no—
671C4×C13—41no—
672C4×C13—42no—
673C4×C13—42no—
674C4×C13—42no—
675C4×C13#57612yes—
676C4×C13C2×2−1+411yescharacteristic
677C4×C13C2×2−1+411yescharacteristic
678C2×#41—21no—
679C2×#41—21no—
680C2×#41C23×C1311yescharacteristic
681C22×Q8—21no—
682C22×Q8—21no—
683C22×Q8—21no—
684C22×Q8—21no—
685C2×Q16C23×C1311yescharacteristic
686C2×SD16C23×C1311yescharacteristic
687C2×SD16C23×C1312yes—
688C2×SD16C23×C1311yescharacteristic
689C2×D8C23×C1311yescharacteristic
690C2×D8C23×C1312yes—
691C4⋊Q8—21no—
692C4⋊Q8—21no—
693C4⋊Q8—21no—
694C4⋊Q8—22no—
695C4⋊Q8—22no—
696C4⋊Q8—22no—
697C4⋊Q8—22no—
698C4⋊Q8—21no—
699C4⋊Q8—21no—
700C4⋊Q8D4×C1311yescharacteristic
701C4⋊Q8D4×C1311yescharacteristic
702C4⋊Q8C23×C1311yescharacteristic
703C4⋊Q8C23×C1311yescharacteristic
704C4⋊Q8C23×C1312yes—
705C4⋊Q8C23×C1311yescharacteristic
706C4⋊Q8C23×C1312yes—
707C4⋊Q8C23×C1312yes—
708C4⋊Q8C23×C1312yes—
709#127C23×C1311yescharacteristic
710#127C23×C1312yes—
711#126—22no—
712#126—21no—
713#125—22no—
714#125—22no—
715#125—22no—
716#125—22no—
717#125D4×C1312yes—
718#125C23×C1311yescharacteristic
719#125C23×C1312yes—
720#125C23×C1312yes—
721#125C23×C1312yes—
722#124—21no—
723#124—22no—
724#124—22no—
725#124—21no—
726#124C23×C1311yescharacteristic
727#124C23×C1312yes—
728#123—21no—
729#123—22no—
730#123—22no—
731#123—22no—
732#123—22no—
733#123—22no—
734#123—22no—
735C22⋊Q8—22no—
736C22⋊Q8—22no—
737C22⋊Q8—21no—
738C22⋊Q8—21no—
739C22⋊Q8—22no—
740C22⋊Q8—22no—
741C22⋊Q8—22no—
742C22⋊Q8—22no—
743C22⋊Q8—21no—
744C22⋊Q8—22no—
745C22⋊Q8—22no—
746C22⋊Q8—22no—
747C22⋊Q8—22no—
748C22⋊Q8—22no—
749C22⋊Q8—22no—
750C22⋊Q8D4×C1311yescharacteristic
751C22⋊Q8D4×C1311yescharacteristic
752C22⋊Q8D4×C1312yes—
753C22⋊Q8C23×C1311yescharacteristic
754#121—21no—
755#121—22no—
756#121—21no—
757#121—22no—
758#121—22no—
759#121C23×C1311yescharacteristic
760#121C23×C1312yes—
761C4×Q8—22no—
762C4×Q8—21no—
763C4×Q8—21no—
764C4×Q8—21no—
765C4×Q8C23×C1311yescharacteristic
766C4×Q8C23×C1311yescharacteristic
767C4×Q8C23×C1312yes—
768C4×Q8C23×C1312yes—
769C4×Q8C23×C1311yescharacteristic
770C4×Q8C23×C1312yes—
771C4×Q8C23×C1311yescharacteristic
772C4×Q8C23×C1311yescharacteristic
773C4×Q8C23×C1312yes—
774C4×D4—21no—
775C4×D4—21no—
776C4×D4—21no—
777C4×D4—22no—
778C4×D4—21no—
779C4×D4—22no—
780C4×D4—22no—
781C4×D4—21no—
782C4×D4C23×C1311yescharacteristic
783C4×D4C23×C1311yescharacteristic
784C4×D4C23×C1312yes—
785C4×D4C23×C1312yes—
786C4×D4C23×C1311yescharacteristic
787C4×D4C23×C1312yes—
788C4×D4C23×C1312yes—
789C4×D4C23×C1312yes—
790C4×D4C23×C1312yes—
791#117—22no—
792#117—21no—
793#117—21no—
794#117C23×C1311yescharacteristic
795#117C23×C1312yes—
796C2×C4⋊C4—21no—
797C2×C4⋊C4—22no—
798C2×C4⋊C4—22no—
799C2×C4⋊C4—22no—
800C2×C4⋊C4C23×C1312yes—
801C2×C42—21no—
802C2×C42C23×C1311yescharacteristic
803#107C23×C1312yes—
804#107C23×C1311yescharacteristic
805#107C23×C1312yes—
806#107C23×C1312yes—
807#107C23×C1311yescharacteristic
808#107C23×C1312yes—
809#107C23×C1312yes—
810#107C23×C1312yes—
811#107C23×C1312yes—
812#106C23×C1312yes—
813#106C23×C1311yescharacteristic
814#106C23×C1311yescharacteristic
815#106C23×C1312yes—
816#106C23×C1312yes—
817C4⋊C8C23×C1311yescharacteristic
818C4⋊C8C23×C1311yescharacteristic
819C4⋊C8C23×C1311yescharacteristic
820C4⋊C8C23×C1311yescharacteristic
821C4⋊C8C23×C1312yes—
822C4⋊C8C23×C1312yes—
823C4⋊C8C23×C1312yes—
824C4⋊C8C23×C1312yes—
825#103C23×C1311yescharacteristic
826#103C23×C1311yescharacteristic
827#103C23×C1311yescharacteristic
828#103C23×C1312yes—
829#103C23×C1312yes—
830#103C23×C1311yescharacteristic
831#103C23×C1312yes—
832#102C23×C1311yescharacteristic
833#102C23×C1312yes—
834#102C23×C1312yes—
835#102C23×C1311yescharacteristic
836#102C23×C1312yes—
837#102C23×C1311yescharacteristic
838#102C23×C1312yes—
839#102C23×C1311yescharacteristic
840#102C23×C1312yes—
841#102C23×C1312yes—
842#102C23×C1312yes—
843#102C23×C1312yes—
844#102C23×C1312yes—
845C22⋊C8C23×C1311yescharacteristic
846C22⋊C8C23×C1311yescharacteristic
847C22⋊C8C23×C1312yes—
848#97C23×C1312yes—
849#97C23×C1312yes—
850#97C23×C1312yes—
851C4×C8C23×C1311yescharacteristic
852C4×C8C23×C1311yescharacteristic
853C4×C8C23×C1312yes—
854C4×C8C23×C1312yes—
855C2×C13—41no—
856C2×C13—42no—
857C2×C13—82no—
858C2×C13—81no—
859C2×C13#348611yescharacteristic
860C2×C13C2×#57611yescharacteristic
861C2×C13#358611yescharacteristic
862#41—22no—
863#41—22no—
864#41—82no—
865#41—82no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—22no—
870C2×Q8—22no—
871C2×Q8—22no—
872C2×Q8—22no—
873C2×Q8—82no—
874C2×Q8—82no—
875C2×Q8—82no—
876C2×Q8—82no—
877C2×Q8C2×D4×C1311yescharacteristic
878C2×Q8C2×D4×C1311yescharacteristic
879C2×Q8C2×D4×C1312yes—
880C2×Q8C24×C1311yescharacteristic
881C2×Q8C24×C1311yescharacteristic
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—22no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—22no—
888C2×D4—22no—
889C2×D4C24×C1311yescharacteristic
890C2×D4C24×C1312yes—
891C2×D4C24×C1311yescharacteristic
892C22×C4—21no—
893C22×C4—22no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—22no—
903C22×C4C2×D4×C1311yescharacteristic
904C22×C4C2×D4×C1311yescharacteristic
905C22×C4C24×C1311yescharacteristic
906Q16—22no—
907SD16—22no—
908SD16—24no—
909SD16—22no—
910D8—22no—
911D8—24no—
912C2×C8C24×C1311yescharacteristic
913C2×C8C24×C1311yescharacteristic
914C2×C8C24×C1311yescharacteristic
915C2×C8C24×C1311yescharacteristic
916C2×C8C24×C1312yes—
917C2×C8C24×C1312yes—
918C4⋊C4—21no—
919C4⋊C4—22no—
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—22no—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—21no—
941C4⋊C4C2×D4×C1312yes—
942C4⋊C4C2×D4×C1312yes—
943C4⋊C4C2×D4×C1312yes—
944C4⋊C4C2×D4×C1312yes—
945C4⋊C4C2×D4×C1311yescharacteristic
946C4⋊C4C2×D4×C1312yes—
947C4⋊C4C2×D4×C1311yescharacteristic
948C4⋊C4C2×D4×C1312yes—
949C4⋊C4C2×D4×C1312yes—
950C4⋊C4C24×C1311yescharacteristic
951C4⋊C4C24×C1312yes—
952C4⋊C4C24×C1312yes—
953C4⋊C4C24×C1311yescharacteristic
954C4⋊C4C24×C1311yescharacteristic
955C4⋊C4C24×C1311yescharacteristic
956C4⋊C4C24×C1312yes—
957C22⋊C4—21no—
958C22⋊C4—21no—
959C22⋊C4—21no—
960C22⋊C4—21no—
961C22⋊C4—22no—
962C22⋊C4—22no—
963C22⋊C4—21no—
964C22⋊C4—21no—
965C22⋊C4—21no—
966C22⋊C4—22no—
967C22⋊C4—22no—
968C22⋊C4—22no—
969C22⋊C4—21no—
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4C2×D4×C1312yes—
975C22⋊C4C2×D4×C1312yes—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—22no—
981C42—22no—
982C42—22no—
983C42C2×D4×C1311yescharacteristic
984C42C2×D4×C1311yescharacteristic
985C42C24×C1311yescharacteristic
986C42C24×C1312yes—
987C42C24×C1312yes—
988C42C24×C1311yescharacteristic
989C13#6185711yescharacteristic, direct product factor, Sylow
990C23—21no—
991C23—21no—
992C23—22no—
993C23C22×D4×C1311yescharacteristic
994Q8—22no—
995Q8—22no—
996Q8—21no—
997Q8—21no—
998Q8—21no—
999Q8—42no—
1000Q8—42no—
1001Q8—42no—
1002Q8—42no—
1003Q8—82no—
1004Q8—82no—
1005Q8—82no—
1006Q8—82no—
1007Q8C13×2−1+412yes—
1008D4—24no—
1009D4—21no—
1010D4—21no—
1011D4—22no—
1012D4—21no—
1013D4—22no—
1014D4—42no—
1015D4—81no—
1016D4—82no—
1017D4—82no—
1018D4—81no—
1019D4—82no—
1020D4C13×2−1+412yes—
1021C2×C4—24no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—21no—
1034C2×C4—41no—
1035C2×C4—42no—
1036C2×C4—42no—
1037C2×C4—42no—
1038C2×C4—82no—
1039C2×C4—82no—
1040C2×C4—82no—
1041C2×C4—82no—
1042C2×C4—82no—
1043C2×C4—82no—
1044C2×C4—82no—
1045C2×C4C22×D4×C1312yes—
1046C2×C4C22×D4×C1311yescharacteristic
1047C2×C4C22×D4×C1311yescharacteristic
1048C2×C4C22×D4×C1312yes—
1049C2×C4C22×D4×C1311yescharacteristic
1050C2×C4C22×D4×C1311yescharacteristic
1051C2×C4C22×D4×C1312yes—
1052C2×C4C22×D4×C1312yes—
1053C2×C4C22×D4×C1311yescharacteristic
1054C2×C4C25×C1311yescharacteristic
1055C8—21no—
1056C8—22no—
1057C8—21no—
1058C8—22no—
1059C8—21no—
1060C8—21no—
1061C22—21no—
1062C22—21no—
1063C22—21no—
1064C22—22no—
1065C22—41no—
1066C22—41no—
1067C22—41no—
1068C22—42no—
1069C22—42no—
1070C22—41no—
1071C22—41no—
1072C22—42no—
1073C22C23×D4×C1311yescharacteristic
1074C4—21no—
1075C4—22no—
1076C4—22no—
1077C4—21no—
1078C4—21no—
1079C4—22no—
1080C4—22no—
1081C4—21no—
1082C4—22no—
1083C4—41no—
1084C4—41no—
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—41no—
1089C4—41no—
1090C4—41no—
1091C4C13×#57612yes—
1092C4C2×C13×2−1+411yescharacteristic
1093C4C2×C13×2−1+411yescharacteristic
1094C2—41no—
1095C2—42no—
1096C2—81no—
1097C2—82no—
1098C2C13×#348611yescharacteristic
1099C2C2×C13×#57611yescharacteristic
1100C2C13×#358611yescharacteristic
subgroupG/H
center, socleC22×C13C23×D4
commutator, Frattini, cosocleC2×C4C25×C13
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C13×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3554C2semidirect
2. C13×#3503C2semidirect
3. C13×#3389C2semidirect
4. C13×#3386C2semidirect
5. C13×#3386C2semidirect
6. C13×#3385C2semidirect
7. C13×#3383C2semidirect
8. Q8×C13×D8C2semidirect
9. C13×#3375C2semidirect
10. C13×#3373C2semidirect
11. C13×#3370C2semidirect
12. C13×#3368C2semidirect
13. C13×#3365C2semidirect
14. C13×#3358C2semidirect
15. C13×#3243C2semidirect
16. C13×#3241C2semidirect
17. C13×#3239C2semidirect
18. C13×#3226C2semidirect
19. C13×#3124C2semidirect
20. C13×#3119C2semidirect
21. C13×#3115C2semidirect
22. C13×#3102C2semidirect
23. C13×#2985C2semidirect
312. #61857C13direct (N × H)
440. #3554C2×C13semidirect
441. #3503C2×C13semidirect
442. #3389C2×C13semidirect
443. #3386C2×C13semidirect
444. #3386C2×C13semidirect
445. #3385C2×C13semidirect
446. #3383C2×C13semidirect
447. Q8×D8C2×C13semidirect
448. #3375C2×C13semidirect
449. #3373C2×C13semidirect
450. #3370C2×C13semidirect
451. #3368C2×C13semidirect
452. #3365C2×C13semidirect
453. #3358C2×C13semidirect
454. #3243C2×C13semidirect
455. #3241C2×C13semidirect
456. #3239C2×C13semidirect
457. #3226C2×C13semidirect
458. #3124C2×C13semidirect
459. #3119C2×C13semidirect
460. #3115C2×C13semidirect
461. #3102C2×C13semidirect
462. #2985C2×C13semidirect
989. C13#61857direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35542
C13×#35032
C13×#33892
C13×#33862
C13×#33852
C13×#33832
Q8×C13×D82
C13×#33752
C13×#33732
C13×#33702
C13×#33682
C13×#33652
C13×#33582
C13×#32432
C13×#32412
C13×#32392
C13×#32262
C13×#31242
C13×#31192
C13×#31152
C13×#31022
C13×#29852
#6185713