Finite Group Databasebeta

← C13×#62562 #15748901

Subgroups — C13×#62562 #15748901

Order 3328.

1716 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3554C211yesmaximal, characteristic, complemented
2C13×#3547C211yesmaximal, characteristic, complemented
3C13×#3373C211yesmaximal, characteristic, complemented
4C13×#3372C211yesmaximal, characteristic, complemented
5C13×#3361C211yesmaximal, characteristic, complemented
6C13×#3359C211yesmaximal, characteristic, complemented
7C13×#3332C211yesmaximal, characteristic, complemented
8C13×#3329C211yesmaximal, characteristic, complemented
9C13×#3321C212yesmaximal, complemented
10C13×#3307C212yesmaximal, complemented
11C13×#3305C211yesmaximal, characteristic, complemented
12C13×#3303C212yesmaximal, complemented
13C13×#3301C212yesmaximal, complemented
14C13×#3298C211yesmaximal, characteristic, complemented
15C13×#3244C212yesmaximal, complemented
16C13×#3237C211yesmaximal, characteristic, complemented
17C13×#3221C212yesmaximal, complemented
18C13×#3214C211yesmaximal, characteristic, complemented
19C13×#3179C212yesmaximal, complemented
20C13×#3167C211yesmaximal, characteristic, complemented
21C13×#3137C212yesmaximal, complemented
22C13×#3131C211yesmaximal, characteristic, complemented
23C13×#2966C211yesmaximal, characteristic, complemented
24C13×#562—22no—
25C13×#562—22no—
26C13×#559—21no—
27C13×#559C2211yescharacteristic
28C13×#557C2211yescharacteristic
29C13×#555C2212yes—
30C13×#555C2211yescharacteristic
31C13×#554—21no—
32C13×#554C2211yescharacteristic
33C13×#553C2212yes—
34C13×#552—21no—
35C13×#550C2211yescharacteristic
36D4×Q8×C13C2211yescharacteristic
37D4×Q8×C13C2211yescharacteristic
38C13×#548—21no—
39C13×#548C2212yes—
40C13×#547C2212yes—
41C13×#547C2211yescharacteristic
42C13×#544C2212yes—
43C13×#542—22no—
44C13×#542—21no—
45C13×#542C2212yes—
46C13×#540—21no—
47C13×#540C2212yes—
48C13×#539—22no—
49C13×#537—21no—
50C13×#536—21no—
51C13×#536C2212yes—
52C13×#533C2211yescharacteristic
53C13×#533C2211yescharacteristic
54C13×#532C2211yescharacteristic
55C13×#532C2211yescharacteristic
56C13×#529C2211yescharacteristic
57C13×#501C2212yes—
58C13×#498C2211yescharacteristic
59C13×#496C2212yes—
60C13×#492C2211yescharacteristic
61C13×#491C2212yes—
62C13×#491C2212yes—
63C13×#489C2212yes—
64C13×#489C2212yes—
65C13×#488C2212yes—
66C13×#488C2212yes—
67C13×#488C2212yes—
68C13×#487C2211yescharacteristic
69C13×#487C2212yes—
70C13×#487C2211yescharacteristic
71C13×#487C2211yescharacteristic
72C13×#486C2211yescharacteristic
73C13×#486C2211yescharacteristic
74C13×#486C2211yescharacteristic
75C13×#485C2212yes—
76C13×#485C2212yes—
77C13×#485C2212yes—
78C13×#483C2212yes—
79C13×#482C2212yes—
80C13×#481C2212yes—
81C13×#479C2212yes—
82C13×#478C2212yes—
83C13×#477C2211yescharacteristic
84C13×#477C2211yescharacteristic
85C13×#476C2212yes—
86C13×#475C2211yescharacteristic
87C13×#475C2212yes—
88C13×#475C2211yescharacteristic
89C13×#469C2212yes—
90C13×#468C2212yes—
91C13×#466C2212yes—
92C13×#465C2212yes—
93C13×#465C2211yescharacteristic
94C13×#465C2211yescharacteristic
95C13×#465C2211yescharacteristic
96C13×#465C2211yescharacteristic
97C13×#463C2212yes—
98C13×#463C2212yes—
99C13×#461C2211yescharacteristic
100C13×#461C2212yes—
101C13×#461C2212yes—
102C13×#461C2211yescharacteristic
103C13×#459C2211yescharacteristic
104C13×#459C2211yescharacteristic
105C13×#449C2212yes—
106C13×#449C2212yes—
107C13×#449C2212yes—
108C13×#449C2212yes—
109C13×#448C2212yes—
110C13×#448C2212yes—
111C13×#446C2211yescharacteristic
112C8×Q8×C13C2211yescharacteristic
113C13×#442C2212yes—
114C13×#440C2212yes—
115C4×C13×SD16C2211yescharacteristic
116C4×C13×SD16C2212yes—
117C4×C13×SD16C2211yescharacteristic
118C4×C13×SD16C2211yescharacteristic
119C4×C13×SD16C2211yescharacteristic
120C4×C13×D8C2212yes—
121C13×#436C2211yescharacteristic
122C13×#435C2212yes—
123C8×D4×C13C2211yescharacteristic
124C8×D4×C13C2212yes—
125C13×#433C2212yes—
126C13×#432C2211yescharacteristic
127C13×#419C2212yes—
128C13×#417C2212yes—
129C13×#416C2212yes—
130C13×#416C2212yes—
131C13×#416C2212yes—
132C2×C13×#103C2212yes—
133C13×#405C2212yes—
134C2×C4×C8×C13C2211yescharacteristic
135C2×C13×#41—21no—
136C2×C13×#41—21no—
137C2×C13×#41C2312yes—
138C2×C13×#41C2312yes—
139C22×Q8×C13—21no—
140C22×Q8×C13C2312yes—
141C2×C13×SD16C2311yescharacteristic
142C2×C13×SD16C2311yescharacteristic
143C2×C13×SD16C2312yes—
144C2×C13×SD16C2311yescharacteristic
145C2×C13×SD16C2311yescharacteristic
146C2×C13×SD16C2312yes—
147C2×C13×D8C2312yes—
148C2×C13×D8C2312yes—
149C2×C13×M16C2312yes—
150C22×C8×C13C2311yescharacteristic
151C22×C8×C13C2311yescharacteristic
152C22×C8×C13C2312yes—
153C13×C4⋊Q8—22no—
154C13×C4⋊Q8—21no—
155C13×C4⋊Q8C2311yescharacteristic
156C13×C4⋊Q8C2312yes—
157C13×C4⋊Q8C2311yescharacteristic
158C13×C4⋊Q8C2311yescharacteristic
159C13×C4⋊Q8C2312yes—
160C13×C4⋊Q8C2311yescharacteristic
161C13×C4⋊Q8C2311yescharacteristic
162C13×C4⋊Q8C2311yescharacteristic
163C13×#127—21no—
164C13×#127C2311yescharacteristic
165C13×#127C2311yescharacteristic
166C13×#126—22no—
167C13×#126—22no—
168C13×#126D412yes—
169C13×#125—22no—
170C13×#125—21no—
171C13×#125—22no—
172C13×#125—21no—
173C13×#125D411yescharacteristic
174C13×#125C2312yes—
175C13×#125C2312yes—
176C13×#124—21no—
177C13×#124—22no—
178C13×#124—22no—
179C13×#124—22no—
180C13×#124—22no—
181C13×#124—22no—
182C13×#124—21no—
183C13×#124D411yescharacteristic
184C13×#124C2312yes—
185C13×#124C2312yes—
186C13×#123—22no—
187C13×#123—22no—
188C13×#123—22no—
189C13×#123—22no—
190C13×#123—22no—
191C13×#123—22no—
192C13×#123—22no—
193C13×#123—22no—
194C13×#123—22no—
195C13×#123—22no—
196C13×#123D412yes—
197C13×C22⋊Q8—21no—
198C13×C22⋊Q8—21no—
199C13×C22⋊Q8—21no—
200C13×C22⋊Q8—21no—
201C13×C22⋊Q8—21no—
202C13×C22⋊Q8—22no—
203C13×C22⋊Q8—22no—
204C13×C22⋊Q8—21no—
205C13×C22⋊Q8—22no—
206C13×C22⋊Q8—22no—
207C13×C22⋊Q8—22no—
208C13×C22⋊Q8—22no—
209C13×C22⋊Q8—22no—
210C13×C22⋊Q8—22no—
211C13×C22⋊Q8—22no—
212C13×C22⋊Q8D411yescharacteristic
213C13×C22⋊Q8C2311yescharacteristic
214C13×C22⋊Q8C2311yescharacteristic
215C13×C22⋊Q8C2312yes—
216C13×#121—21no—
217C13×#121—22no—
218C13×#121—22no—
219C13×#121—22no—
220C13×#121—22no—
221C13×#121—21no—
222C13×#121—21no—
223C13×#121—21no—
224C13×#121—22no—
225C13×#121—22no—
226C13×#121—22no—
227C13×#121D411yescharacteristic
228C13×#121C2312yes—
229C13×#121C2312yes—
230C13×#121C2311yescharacteristic
231C13×#121C2311yescharacteristic
232C13×#121C2312yes—
233C4×Q8×C13—21no—
234C4×Q8×C13—21no—
235C4×Q8×C13—21no—
236C4×Q8×C13—21no—
237C4×Q8×C13C2311yescharacteristic
238C4×Q8×C13C2311yescharacteristic
239C4×Q8×C13C2312yes—
240C4×Q8×C13C2311yescharacteristic
241C4×D4×C13—21no—
242C4×D4×C13—21no—
243C4×D4×C13—21no—
244C4×D4×C13—22no—
245C4×D4×C13—22no—
246C4×D4×C13—21no—
247C4×D4×C13—21no—
248C4×D4×C13—21no—
249C4×D4×C13C2312yes—
250C4×D4×C13C2312yes—
251C4×D4×C13C2311yescharacteristic
252C4×D4×C13C2311yescharacteristic
253C4×D4×C13C2312yes—
254C4×D4×C13C2312yes—
255C4×D4×C13C2311yescharacteristic
256C13×#117—21no—
257C13×#117—21no—
258C13×#117—22no—
259C13×#117C2312yes—
260C13×#117C2312yes—
261C13×#117C2312yes—
262C2×C13×C4⋊C4—21no—
263C2×C13×C4⋊C4—22no—
264C2×C13×C4⋊C4C2312yes—
265C2×C42×C13C2311yescharacteristic
266C13×#107C2312yes—
267C13×#107C2312yes—
268C13×#106C2311yescharacteristic
269C13×#106C2311yescharacteristic
270C13×#106C2311yescharacteristic
271C13×#106C2311yescharacteristic
272C13×#106C2312yes—
273C13×#106C2312yes—
274C13×C4⋊C8C2311yescharacteristic
275C13×C4⋊C8C2311yescharacteristic
276C13×C4⋊C8C2312yes—
277C13×C4⋊C8C2312yes—
278C13×#103C2311yescharacteristic
279C13×#103C2312yes—
280C13×#103C2312yes—
281C13×#103C2312yes—
282C13×#103C2311yescharacteristic
283C13×#103C2312yes—
284C13×#103C2312yes—
285C13×#103C2312yes—
286C13×#103C2312yes—
287C13×#103C2311yescharacteristic
288C13×#103C2312yes—
289C13×#103C2311yescharacteristic
290C13×#103C2312yes—
291C13×#103C2312yes—
292C13×#102C2312yes—
293C13×#102C2312yes—
294C13×#102C2312yes—
295C13×#102C2312yes—
296C13×#102C2312yes—
297C13×#102C2312yes—
298C13×#102C2311yescharacteristic
299C13×#102C2311yescharacteristic
300C13×#102C2311yescharacteristic
301C13×#102C2311yescharacteristic
302C13×C22⋊C8C2312yes—
303C13×C22⋊C8C2312yes—
304C13×C22⋊C8C2312yes—
305C13×#97C2312yes—
306C13×#97C2312yes—
307C4×C8×C13C2311yescharacteristic
308C4×C8×C13C2311yescharacteristic
309C4×C8×C13C2311yescharacteristic
310C4×C8×C13C2311yescharacteristic
311C4×C8×C13C2312yes—
312#62562C1311yesmaximal, characteristic, direct product factor, Sylow
313C13×#41—42no—
314C13×#41—42no—
315C13×#41—42no—
316C13×#41—42no—
317C13×#41—82no—
318C13×#41—82no—
319C2×Q8×C13—21no—
320C2×Q8×C13—21no—
321C2×Q8×C13—21no—
322C2×Q8×C13—22no—
323C2×Q8×C13—22no—
324C2×Q8×C13—21no—
325C2×Q8×C13—42no—
326C2×Q8×C13—42no—
327C2×Q8×C13—82no—
328C2×Q8×C13C2×D411yescharacteristic
329C2×Q8×C13C2411yescharacteristic
330C2×Q8×C13C2412yes—
331C2×Q8×C13C2411yescharacteristic
332C2×D4×C13—22no—
333C2×D4×C13—22no—
334C2×D4×C13—22no—
335C2×D4×C13—21no—
336C2×D4×C13—22no—
337C2×D4×C13—21no—
338C2×D4×C13—22no—
339C2×D4×C13—21no—
340C2×D4×C13—21no—
341C2×D4×C13—21no—
342C2×D4×C13—21no—
343C2×D4×C13C2×D411yescharacteristic
344C2×D4×C13C2×D412yes—
345C2×D4×C13C2412yes—
346C2×D4×C13C2411yescharacteristic
347C2×D4×C13C2411yescharacteristic
348C22×C4×C13—22no—
349C22×C4×C13—22no—
350C22×C4×C13—21no—
351C22×C4×C13—21no—
352C22×C4×C13—22no—
353C22×C4×C13—22no—
354C22×C4×C13—22no—
355C22×C4×C13—22no—
356C22×C4×C13—22no—
357C22×C4×C13C2×D411yescharacteristic
358C22×C4×C13C2×D411yescharacteristic
359C22×C4×C13C2411yescharacteristic
360C22×C4×C13C2412yes—
361C13×SD16—42no—
362C13×SD16—41no—
363C13×SD16—41no—
364C13×SD16—41no—
365C13×SD16—41no—
366C13×SD16—42no—
367C13×D8—42no—
368C13×D8—42no—
369C13×M16—42no—
370C2×C8×C13—42no—
371C2×C8×C13—41no—
372C2×C8×C13—41no—
373C2×C8×C13C2411yescharacteristic
374C2×C8×C13C2411yescharacteristic
375C2×C8×C13C2411yescharacteristic
376C2×C8×C13C2411yescharacteristic
377C2×C8×C13C2412yes—
378C2×C8×C13C2412yes—
379C13×C4⋊C4—21no—
380C13×C4⋊C4—21no—
381C13×C4⋊C4—22no—
382C13×C4⋊C4—22no—
383C13×C4⋊C4—22no—
384C13×C4⋊C4—22no—
385C13×C4⋊C4—22no—
386C13×C4⋊C4—21no—
387C13×C4⋊C4—21no—
388C13×C4⋊C4—21no—
389C13×C4⋊C4—21no—
390C13×C4⋊C4—21no—
391C13×C4⋊C4—21no—
392C13×C4⋊C4—22no—
393C13×C4⋊C4—22no—
394C13×C4⋊C4—22no—
395C13×C4⋊C4—21no—
396C13×C4⋊C4—21no—
397C13×C4⋊C4—22no—
398C13×C4⋊C4—21no—
399C13×C4⋊C4—22no—
400C13×C4⋊C4—21no—
401C13×C4⋊C4C2×D412yes—
402C13×C4⋊C4C2×D411yescharacteristic
403C13×C4⋊C4C2×D411yescharacteristic
404C13×C4⋊C4C2×D412yes—
405C13×C4⋊C4C2×D412yes—
406C13×C4⋊C4C2×D412yes—
407C13×C4⋊C4C2411yescharacteristic
408C13×C4⋊C4C2412yes—
409C13×C4⋊C4C2411yescharacteristic
410C13×C4⋊C4C2412yes—
411C13×C4⋊C4C2411yescharacteristic
412C13×C4⋊C4C2411yescharacteristic
413C13×C22⋊C4—21no—
414C13×C22⋊C4—21no—
415C13×C22⋊C4—22no—
416C13×C22⋊C4—22no—
417C13×C22⋊C4—22no—
418C13×C22⋊C4—21no—
419C13×C22⋊C4—22no—
420C13×C22⋊C4—22no—
421C13×C22⋊C4—21no—
422C13×C22⋊C4—22no—
423C13×C22⋊C4—22no—
424C13×C22⋊C4—22no—
425C13×C22⋊C4—22no—
426C13×C22⋊C4—22no—
427C13×C22⋊C4—22no—
428C13×C22⋊C4—21no—
429C13×C22⋊C4—22no—
430C13×C22⋊C4—21no—
431C13×C22⋊C4—22no—
432C13×C22⋊C4C2×D412yes—
433C13×C22⋊C4C2×D412yes—
434C13×C22⋊C4C2×D412yes—
435C13×C22⋊C4C2×D412yes—
436C13×C22⋊C4C2×D412yes—
437C42×C13—22no—
438C42×C13—22no—
439C42×C13—21no—
440C42×C13—21no—
441C42×C13—22no—
442C42×C13C2×D411yescharacteristic
443C42×C13C2×D411yescharacteristic
444C42×C13C2411yescharacteristic
445C42×C13C2411yescharacteristic
446C42×C13C2412yes—
447#3554C2×C1311yescharacteristic, complemented
448#3547C2×C1311yescharacteristic, complemented
449#3373C2×C1311yescharacteristic, complemented
450#3372C2×C1311yescharacteristic, complemented
451#3361C2×C1311yescharacteristic, complemented
452#3359C2×C1311yescharacteristic, complemented
453#3332C2×C1311yescharacteristic, complemented
454#3329C2×C1311yescharacteristic, complemented
455#3321C2×C1312yescomplemented
456#3307C2×C1312yescomplemented
457#3305C2×C1311yescharacteristic, complemented
458#3303C2×C1312yescomplemented
459#3301C2×C1312yescomplemented
460#3298C2×C1311yescharacteristic, complemented
461#3244C2×C1312yescomplemented
462#3237C2×C1311yescharacteristic, complemented
463#3221C2×C1312yescomplemented
464#3214C2×C1311yescharacteristic, complemented
465#3179C2×C1312yescomplemented
466#3167C2×C1311yescharacteristic, complemented
467#3137C2×C1312yescomplemented
468#3131C2×C1311yescharacteristic, complemented
469#2966C2×C1311yescharacteristic, complemented
470C23×C13—21no—
471C23×C13—22no—
472C23×C13—21no—
473C23×C13C22×D411yescharacteristic
474C23×C13C22×D412yes—
475Q8×C13—22no—
476Q8×C13—21no—
477Q8×C13—21no—
478Q8×C13—22no—
479Q8×C13—22no—
480Q8×C13—21no—
481Q8×C13—21no—
482Q8×C13—42no—
483Q8×C13—81no—
484Q8×C13—81no—
485Q8×C13—82no—
486Q8×C13—82no—
487Q8×C13—81no—
488D4×C13—22no—
489D4×C13—21no—
490D4×C13—21no—
491D4×C13—22no—
492D4×C13—22no—
493D4×C13—21no—
494D4×C13—21no—
495D4×C13—42no—
496D4×C13—42no—
497D4×C13—81no—
498D4×C13—81no—
499D4×C13—81no—
500D4×C13—82no—
501D4×C13—82no—
502D4×C13—82no—
503D4×C13—82no—
504D4×C13—81no—
505D4×C13—81no—
506D4×C13—82no—
507C2×C4×C13—22no—
508C2×C4×C13—22no—
509C2×C4×C13—21no—
510C2×C4×C13—21no—
511C2×C4×C13—22no—
512C2×C4×C13—21no—
513C2×C4×C13—22no—
514C2×C4×C13—21no—
515C2×C4×C13—21no—
516C2×C4×C13—21no—
517C2×C4×C13—22no—
518C2×C4×C13—22no—
519C2×C4×C13—21no—
520C2×C4×C13—21no—
521C2×C4×C13—41no—
522C2×C4×C13—42no—
523C2×C4×C13—42no—
524C2×C4×C13—82no—
525C2×C4×C13—82no—
526C2×C4×C13—82no—
527C2×C4×C13—82no—
528C2×C4×C13—82no—
529C2×C4×C13—82no—
530C2×C4×C13—82no—
531C2×C4×C13C22×D411yescharacteristic
532C2×C4×C13C22×D412yes—
533C2×C4×C13C22×D412yes—
534C2×C4×C13C22×D411yescharacteristic
535C2×C4×C13C22×D411yescharacteristic
536C2×C4×C13C22×D411yescharacteristic
537C2×C4×C13C22×D412yes—
538C2×C4×C13C22×D411yescharacteristic
539C2×C4×C13C2511yescharacteristic
540C8×C13—21no—
541C8×C13—21no—
542C8×C13—22no—
543C8×C13—21no—
544C8×C13—21no—
545C8×C13—22no—
546#562—22no—
547#562—22no—
548#559—21no—
549#559C22×C1311yescharacteristic
550#557C22×C1311yescharacteristic
551#555C22×C1311yescharacteristic
552#555C22×C1312yes—
553#554—21no—
554#554C22×C1311yescharacteristic
555#553C22×C1312yes—
556#552—21no—
557#550C22×C1311yescharacteristic
558D4×Q8C22×C1311yescharacteristic
559D4×Q8C22×C1311yescharacteristic
560#548—21no—
561#548C22×C1312yes—
562#547C22×C1312yes—
563#547C22×C1311yescharacteristic
564#544C22×C1312yes—
565#542—22no—
566#542—21no—
567#542C22×C1312yes—
568#540—21no—
569#540C22×C1312yes—
570#539—22no—
571#537—21no—
572#536—21no—
573#536C22×C1312yes—
574#533C22×C1311yescharacteristic
575#533C22×C1311yescharacteristic
576#532C22×C1311yescharacteristic
577#532C22×C1311yescharacteristic
578#529C22×C1311yescharacteristic
579#501C22×C1312yes—
580#498C22×C1311yescharacteristic
581#496C22×C1312yes—
582#492C22×C1311yescharacteristic
583#491C22×C1312yes—
584#491C22×C1312yes—
585#489C22×C1312yes—
586#489C22×C1312yes—
587#488C22×C1312yes—
588#488C22×C1312yes—
589#488C22×C1312yes—
590#487C22×C1311yescharacteristic
591#487C22×C1311yescharacteristic
592#487C22×C1312yes—
593#487C22×C1311yescharacteristic
594#486C22×C1311yescharacteristic
595#486C22×C1311yescharacteristic
596#486C22×C1311yescharacteristic
597#485C22×C1312yes—
598#485C22×C1312yes—
599#485C22×C1312yes—
600#483C22×C1312yes—
601#482C22×C1312yes—
602#481C22×C1312yes—
603#479C22×C1312yes—
604#478C22×C1312yes—
605#477C22×C1311yescharacteristic
606#477C22×C1311yescharacteristic
607#476C22×C1312yes—
608#475C22×C1311yescharacteristic
609#475C22×C1312yes—
610#475C22×C1311yescharacteristic
611#469C22×C1312yes—
612#468C22×C1312yes—
613#466C22×C1312yes—
614#465C22×C1311yescharacteristic
615#465C22×C1311yescharacteristic
616#465C22×C1311yescharacteristic
617#465C22×C1311yescharacteristic
618#465C22×C1312yes—
619#463C22×C1312yes—
620#463C22×C1312yes—
621#461C22×C1311yescharacteristic
622#461C22×C1312yes—
623#461C22×C1311yescharacteristic
624#461C22×C1312yes—
625#459C22×C1311yescharacteristic
626#459C22×C1311yescharacteristic
627#449C22×C1312yes—
628#449C22×C1312yes—
629#449C22×C1312yes—
630#449C22×C1312yes—
631#448C22×C1312yes—
632#448C22×C1312yes—
633#446C22×C1311yescharacteristic
634C8×Q8C22×C1311yescharacteristic
635#442C22×C1312yes—
636#440C22×C1312yes—
637C4×SD16C22×C1311yescharacteristic
638C4×SD16C22×C1311yescharacteristic
639C4×SD16C22×C1311yescharacteristic
640C4×SD16C22×C1312yes—
641C4×SD16C22×C1311yescharacteristic
642C4×D8C22×C1312yes—
643#436C22×C1311yescharacteristic
644#435C22×C1312yes—
645C8×D4C22×C1311yescharacteristic
646C8×D4C22×C1312yes—
647#433C22×C1312yes—
648#432C22×C1311yescharacteristic
649#419C22×C1312yes—
650#417C22×C1312yes—
651#416C22×C1312yes—
652#416C22×C1312yes—
653#416C22×C1312yes—
654C2×#103C22×C1312yes—
655#405C22×C1312yes—
656C2×C4×C8C22×C1311yescharacteristic
657C22×C13—21no—
658C22×C13—22no—
659C22×C13—22no—
660C22×C13—21no—
661C22×C13—21no—
662C22×C13—22no—
663C22×C13—41no—
664C22×C13—42no—
665C22×C13—41no—
666C22×C13—42no—
667C22×C13—41no—
668C22×C13—41no—
669C22×C13—41no—
670C22×C13—41no—
671C22×C13—42no—
672C22×C13C23×D411yescharacteristic
673C4×C13—21no—
674C4×C13—21no—
675C4×C13—22no—
676C4×C13—21no—
677C4×C13—22no—
678C4×C13—21no—
679C4×C13—22no—
680C4×C13—41no—
681C4×C13—42no—
682C4×C13—41no—
683C4×C13—41no—
684C4×C13—42no—
685C4×C13—41no—
686C4×C13—41no—
687C4×C13—41no—
688C4×C13—42no—
689C4×C13#57712yes—
690C4×C13#58511yescharacteristic
691C4×C13#58511yescharacteristic
692C2×#41—21no—
693C2×#41—21no—
694C2×#41C23×C1312yes—
695C2×#41C23×C1312yes—
696C22×Q8—21no—
697C22×Q8C23×C1312yes—
698C2×SD16C23×C1311yescharacteristic
699C2×SD16C23×C1311yescharacteristic
700C2×SD16C23×C1312yes—
701C2×SD16C23×C1311yescharacteristic
702C2×SD16C23×C1311yescharacteristic
703C2×SD16C23×C1312yes—
704C2×D8C23×C1312yes—
705C2×D8C23×C1312yes—
706C2×M16C23×C1312yes—
707C22×C8C23×C1311yescharacteristic
708C22×C8C23×C1311yescharacteristic
709C22×C8C23×C1312yes—
710C4⋊Q8—22no—
711C4⋊Q8—21no—
712C4⋊Q8C23×C1311yescharacteristic
713C4⋊Q8C23×C1311yescharacteristic
714C4⋊Q8C23×C1312yes—
715C4⋊Q8C23×C1311yescharacteristic
716C4⋊Q8C23×C1311yescharacteristic
717C4⋊Q8C23×C1311yescharacteristic
718C4⋊Q8C23×C1311yescharacteristic
719C4⋊Q8C23×C1312yes—
720#127—21no—
721#127C23×C1311yescharacteristic
722#127C23×C1311yescharacteristic
723#126—22no—
724#126—22no—
725#126D4×C1312yes—
726#125—22no—
727#125—21no—
728#125—22no—
729#125—21no—
730#125D4×C1311yescharacteristic
731#125C23×C1312yes—
732#125C23×C1312yes—
733#124—21no—
734#124—22no—
735#124—22no—
736#124—22no—
737#124—22no—
738#124—22no—
739#124—21no—
740#124D4×C1311yescharacteristic
741#124C23×C1312yes—
742#124C23×C1312yes—
743#123—22no—
744#123—22no—
745#123—22no—
746#123—22no—
747#123—22no—
748#123—22no—
749#123—22no—
750#123—22no—
751#123—22no—
752#123—22no—
753#123D4×C1312yes—
754C22⋊Q8—21no—
755C22⋊Q8—21no—
756C22⋊Q8—21no—
757C22⋊Q8—21no—
758C22⋊Q8—21no—
759C22⋊Q8—22no—
760C22⋊Q8—22no—
761C22⋊Q8—21no—
762C22⋊Q8—22no—
763C22⋊Q8—22no—
764C22⋊Q8—22no—
765C22⋊Q8—22no—
766C22⋊Q8—22no—
767C22⋊Q8—22no—
768C22⋊Q8—22no—
769C22⋊Q8D4×C1311yescharacteristic
770C22⋊Q8C23×C1311yescharacteristic
771C22⋊Q8C23×C1311yescharacteristic
772C22⋊Q8C23×C1312yes—
773#121—21no—
774#121—22no—
775#121—22no—
776#121—22no—
777#121—22no—
778#121—21no—
779#121—21no—
780#121—21no—
781#121—22no—
782#121—22no—
783#121—22no—
784#121D4×C1311yescharacteristic
785#121C23×C1311yescharacteristic
786#121C23×C1311yescharacteristic
787#121C23×C1312yes—
788#121C23×C1312yes—
789#121C23×C1312yes—
790C4×Q8—21no—
791C4×Q8—21no—
792C4×Q8—21no—
793C4×Q8—21no—
794C4×Q8C23×C1311yescharacteristic
795C4×Q8C23×C1311yescharacteristic
796C4×Q8C23×C1312yes—
797C4×Q8C23×C1311yescharacteristic
798C4×D4—21no—
799C4×D4—21no—
800C4×D4—21no—
801C4×D4—22no—
802C4×D4—22no—
803C4×D4—21no—
804C4×D4—21no—
805C4×D4—21no—
806C4×D4C23×C1311yescharacteristic
807C4×D4C23×C1311yescharacteristic
808C4×D4C23×C1312yes—
809C4×D4C23×C1312yes—
810C4×D4C23×C1312yes—
811C4×D4C23×C1312yes—
812C4×D4C23×C1311yescharacteristic
813#117—21no—
814#117—21no—
815#117—22no—
816#117C23×C1312yes—
817#117C23×C1312yes—
818#117C23×C1312yes—
819C2×C4⋊C4—21no—
820C2×C4⋊C4—22no—
821C2×C4⋊C4C23×C1312yes—
822C2×C42C23×C1311yescharacteristic
823#107C23×C1312yes—
824#107C23×C1312yes—
825#106C23×C1311yescharacteristic
826#106C23×C1311yescharacteristic
827#106C23×C1311yescharacteristic
828#106C23×C1311yescharacteristic
829#106C23×C1312yes—
830#106C23×C1312yes—
831C4⋊C8C23×C1311yescharacteristic
832C4⋊C8C23×C1311yescharacteristic
833C4⋊C8C23×C1312yes—
834C4⋊C8C23×C1312yes—
835#103C23×C1311yescharacteristic
836#103C23×C1312yes—
837#103C23×C1312yes—
838#103C23×C1312yes—
839#103C23×C1311yescharacteristic
840#103C23×C1312yes—
841#103C23×C1312yes—
842#103C23×C1312yes—
843#103C23×C1312yes—
844#103C23×C1311yescharacteristic
845#103C23×C1312yes—
846#103C23×C1311yescharacteristic
847#103C23×C1312yes—
848#103C23×C1312yes—
849#102C23×C1312yes—
850#102C23×C1312yes—
851#102C23×C1312yes—
852#102C23×C1312yes—
853#102C23×C1312yes—
854#102C23×C1312yes—
855#102C23×C1311yescharacteristic
856#102C23×C1311yescharacteristic
857#102C23×C1311yescharacteristic
858#102C23×C1311yescharacteristic
859C22⋊C8C23×C1312yes—
860C22⋊C8C23×C1312yes—
861C22⋊C8C23×C1312yes—
862#97C23×C1312yes—
863#97C23×C1312yes—
864C4×C8C23×C1311yescharacteristic
865C4×C8C23×C1311yescharacteristic
866C4×C8C23×C1311yescharacteristic
867C4×C8C23×C1311yescharacteristic
868C4×C8C23×C1312yes—
869C2×C13—41no—
870C2×C13—42no—
871C2×C13—81no—
872C2×C13—82no—
873C2×C13—81no—
874C2×C13#350011yescharacteristic
875C2×C13C2×#57711yescharacteristic
876C2×C13#358411yescharacteristic
877#41—42no—
878#41—42no—
879#41—42no—
880#41—42no—
881#41—82no—
882#41—82no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—22no—
887C2×Q8—22no—
888C2×Q8—21no—
889C2×Q8—42no—
890C2×Q8—42no—
891C2×Q8—82no—
892C2×Q8C2×D4×C1311yescharacteristic
893C2×Q8C24×C1311yescharacteristic
894C2×Q8C24×C1312yes—
895C2×Q8C24×C1311yescharacteristic
896C2×D4—22no—
897C2×D4—22no—
898C2×D4—22no—
899C2×D4—21no—
900C2×D4—22no—
901C2×D4—21no—
902C2×D4—22no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4C2×D4×C1311yescharacteristic
908C2×D4C2×D4×C1312yes—
909C2×D4C24×C1312yes—
910C2×D4C24×C1311yescharacteristic
911C2×D4C24×C1311yescharacteristic
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—22no—
921C22×C4C2×D4×C1311yescharacteristic
922C22×C4C2×D4×C1311yescharacteristic
923C22×C4C24×C1311yescharacteristic
924C22×C4C24×C1312yes—
925SD16—42no—
926SD16—41no—
927SD16—41no—
928SD16—41no—
929SD16—41no—
930SD16—42no—
931D8—42no—
932D8—42no—
933M16—42no—
934C2×C8—42no—
935C2×C8—41no—
936C2×C8—41no—
937C2×C8C24×C1311yescharacteristic
938C2×C8C24×C1311yescharacteristic
939C2×C8C24×C1311yescharacteristic
940C2×C8C24×C1311yescharacteristic
941C2×C8C24×C1312yes—
942C2×C8C24×C1312yes—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—22no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—22no—
962C4⋊C4—21no—
963C4⋊C4—22no—
964C4⋊C4—21no—
965C4⋊C4C2×D4×C1312yes—
966C4⋊C4C2×D4×C1311yescharacteristic
967C4⋊C4C2×D4×C1311yescharacteristic
968C4⋊C4C2×D4×C1312yes—
969C4⋊C4C2×D4×C1312yes—
970C4⋊C4C2×D4×C1312yes—
971C4⋊C4C24×C1311yescharacteristic
972C4⋊C4C24×C1312yes—
973C4⋊C4C24×C1311yescharacteristic
974C4⋊C4C24×C1312yes—
975C4⋊C4C24×C1311yescharacteristic
976C4⋊C4C24×C1311yescharacteristic
977C22⋊C4—21no—
978C22⋊C4—21no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—21no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—21no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—22no—
992C22⋊C4—21no—
993C22⋊C4—22no—
994C22⋊C4—21no—
995C22⋊C4—22no—
996C22⋊C4C2×D4×C1312yes—
997C22⋊C4C2×D4×C1312yes—
998C22⋊C4C2×D4×C1312yes—
999C22⋊C4C2×D4×C1312yes—
1000C22⋊C4C2×D4×C1312yes—
1001C42—22no—
1002C42—22no—
1003C42—21no—
1004C42—21no—
1005C42—22no—
1006C42C2×D4×C1311yescharacteristic
1007C42C2×D4×C1311yescharacteristic
1008C42C24×C1311yescharacteristic
1009C42C24×C1311yescharacteristic
1010C42C24×C1312yes—
1011C13#6256211yescharacteristic, direct product factor, Sylow
1012C23—21no—
1013C23—21no—
1014C23—22no—
1015C23C22×D4×C1311yescharacteristic
1016C23C22×D4×C1312yes—
1017Q8—22no—
1018Q8—21no—
1019Q8—21no—
1020Q8—22no—
1021Q8—22no—
1022Q8—21no—
1023Q8—21no—
1024Q8—42no—
1025Q8—82no—
1026Q8—82no—
1027Q8—81no—
1028Q8—81no—
1029Q8—81no—
1030D4—22no—
1031D4—21no—
1032D4—21no—
1033D4—22no—
1034D4—22no—
1035D4—21no—
1036D4—21no—
1037D4—42no—
1038D4—42no—
1039D4—81no—
1040D4—81no—
1041D4—81no—
1042D4—82no—
1043D4—82no—
1044D4—82no—
1045D4—82no—
1046D4—81no—
1047D4—81no—
1048D4—82no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—21no—
1055C2×C4—22no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—41no—
1064C2×C4—42no—
1065C2×C4—42no—
1066C2×C4—82no—
1067C2×C4—82no—
1068C2×C4—82no—
1069C2×C4—82no—
1070C2×C4—82no—
1071C2×C4—82no—
1072C2×C4—82no—
1073C2×C4C22×D4×C1311yescharacteristic
1074C2×C4C22×D4×C1312yes—
1075C2×C4C22×D4×C1312yes—
1076C2×C4C22×D4×C1311yescharacteristic
1077C2×C4C22×D4×C1311yescharacteristic
1078C2×C4C22×D4×C1311yescharacteristic
1079C2×C4C22×D4×C1312yes—
1080C2×C4C22×D4×C1311yescharacteristic
1081C2×C4C25×C1311yescharacteristic
1082C8—21no—
1083C8—21no—
1084C8—22no—
1085C8—21no—
1086C8—21no—
1087C8—22no—
1088C22—21no—
1089C22—22no—
1090C22—21no—
1091C22—22no—
1092C22—22no—
1093C22—21no—
1094C22—41no—
1095C22—41no—
1096C22—42no—
1097C22—41no—
1098C22—42no—
1099C22—41no—
1100C22—42no—
1101C22—41no—
1102C22—41no—
1103C22C23×D4×C1311yescharacteristic
1104C4—21no—
1105C4—22no—
1106C4—21no—
1107C4—21no—
1108C4—22no—
1109C4—21no—
1110C4—22no—
1111C4—41no—
1112C4—41no—
1113C4—42no—
1114C4—41no—
1115C4—42no—
1116C4—41no—
1117C4—41no—
1118C4—42no—
1119C4—41no—
1120C4C13×#57712yes—
1121C4C13×#58511yescharacteristic
1122C4C13×#58511yescharacteristic
1123C2—41no—
1124C2—42no—
1125C2—81no—
1126C2—81no—
1127C2—82no—
1128C2C13×#350011yescharacteristic
1129C2C2×C13×#57711yescharacteristic
1130C2C13×#358411yescharacteristic
subgroupG/H
center, socleC22×C13C23×D4
commutator, Frattini, cosocleC2×C4C25×C13
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×#3554C2semidirect
2. C13×#3547C2semidirect
3. C13×#3373C2semidirect
4. C13×#3372C2semidirect
5. C13×#3361C2semidirect
6. C13×#3359C2semidirect
7. C13×#3332C2semidirect
8. C13×#3329C2semidirect
9. C13×#3321C2semidirect
10. C13×#3307C2semidirect
11. C13×#3305C2semidirect
12. C13×#3303C2semidirect
13. C13×#3301C2semidirect
14. C13×#3298C2semidirect
15. C13×#3244C2semidirect
16. C13×#3237C2semidirect
17. C13×#3221C2semidirect
18. C13×#3214C2semidirect
19. C13×#3179C2semidirect
20. C13×#3167C2semidirect
21. C13×#3137C2semidirect
22. C13×#3131C2semidirect
23. C13×#2966C2semidirect
312. #62562C13direct (N × H)
447. #3554C2×C13semidirect
448. #3547C2×C13semidirect
449. #3373C2×C13semidirect
450. #3372C2×C13semidirect
451. #3361C2×C13semidirect
452. #3359C2×C13semidirect
453. #3332C2×C13semidirect
454. #3329C2×C13semidirect
455. #3321C2×C13semidirect
456. #3307C2×C13semidirect
457. #3305C2×C13semidirect
458. #3303C2×C13semidirect
459. #3301C2×C13semidirect
460. #3298C2×C13semidirect
461. #3244C2×C13semidirect
462. #3237C2×C13semidirect
463. #3221C2×C13semidirect
464. #3214C2×C13semidirect
465. #3179C2×C13semidirect
466. #3167C2×C13semidirect
467. #3137C2×C13semidirect
468. #3131C2×C13semidirect
469. #2966C2×C13semidirect
1011. C13#62562direct (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×#35472
C13×#33732
C13×#33722
C13×#33612
C13×#33592
C13×#33322
C13×#33292
C13×#33212
C13×#33072
C13×#33052
C13×#33032
C13×#33012
C13×#32982
C13×#32442
C13×#32372
C13×#32212
C13×#32142
C13×#31792
C13×#31672
C13×#31372
C13×#31312
C13×#29662
#6256213