Finite Group Databasebeta

← C13×#61928 #15748267

Subgroups — C13×#61928 #15748267

Order 3328.

1710 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3554C211yesmaximal, characteristic, complemented
2C13×#3507C211yesmaximal, characteristic, complemented
3C13×#3401C212yesmaximal, complemented
4C13×#3400C211yesmaximal, characteristic, complemented
5C13×#3399C211yesmaximal, characteristic, complemented
6C13×#3396C211yesmaximal, characteristic, complemented
7C13×#3394C212yesmaximal, complemented
8C13×#3392C211yesmaximal, characteristic, complemented
9C13×#3376C212yesmaximal, complemented
10C13×#3374C211yesmaximal, characteristic, complemented
11C13×#3373C211yesmaximal, characteristic, complemented
12C13×#3365C211yesmaximal, characteristic, complemented
13C13×#3360C212yesmaximal, complemented
14C13×#3359C211yesmaximal, characteristic, complemented
15C13×#3225C212yesmaximal, complemented
16C13×#3221C212yesmaximal, complemented
17C13×#3212C211yesmaximal, characteristic, complemented
18C13×#3207C211yesmaximal, characteristic, complemented
19C13×#3125C212yesmaximal, complemented
20C13×#3119C212yesmaximal, complemented
21C13×#3108C211yesmaximal, characteristic, complemented
22C13×#3103C211yesmaximal, characteristic, complemented
23C13×#2986C211yesmaximal, characteristic, complemented
24C13×#562—22no—
25C13×#559C2212yes—
26C13×#559C2211yescharacteristic
27C13×#559C2211yescharacteristic
28C13×#559C2211yescharacteristic
29C13×#557C2211yescharacteristic
30C13×#557C2211yescharacteristic
31C13×#557C2211yescharacteristic
32C13×#556—21no—
33C13×#556C2212yes—
34C13×#556C2212yes—
35C13×#554—21no—
36C13×#554C2212yes—
37C13×#552—22no—
38C13×#550C2211yescharacteristic
39D4×Q8×C13C2211yescharacteristic
40C13×#548—21no—
41C13×#547—21no—
42C13×#542—21no—
43C13×#542C2212yes—
44C13×#540C2212yes—
45C13×#539—22no—
46C13×#539—22no—
47C13×#536—21no—
48C13×#536C2212yes—
49C13×#533C2211yescharacteristic
50C13×#532C2211yescharacteristic
51C13×#532C2211yescharacteristic
52C13×#529—21no—
53C13×#529—21no—
54C13×#529C2211yescharacteristic
55C13×#520C2212yes—
56C2×C4×Q8×C13C2211yescharacteristic
57C13×#497C2212yes—
58C13×#496C2212yes—
59C13×#495C2212yes—
60C13×#495C2212yes—
61C13×#493C2211yescharacteristic
62C13×#492C2212yes—
63C13×#492C2211yescharacteristic
64C13×#491C2212yes—
65C13×#489C2212yes—
66C13×#488C2212yes—
67C13×#488C2212yes—
68C13×#487C2212yes—
69C13×#487C2211yescharacteristic
70C13×#486C2211yescharacteristic
71C13×#483C2211yescharacteristic
72C13×#481C2212yes—
73C13×#480C2211yescharacteristic
74C13×#479C2211yescharacteristic
75C13×#479C2212yes—
76C13×#479C2211yescharacteristic
77C13×#478C2212yes—
78C13×#476C2212yes—
79C13×#475C2211yescharacteristic
80C13×#475C2211yescharacteristic
81C13×#475C2212yes—
82C13×#464C2211yescharacteristic
83C13×#464C2211yescharacteristic
84C13×#464C2212yes—
85C13×#464C2212yes—
86C13×#463C2212yes—
87C13×#463C2212yes—
88C13×#463C2212yes—
89C13×#463C2212yes—
90C13×#463C2212yes—
91C13×#463C2212yes—
92C13×#462C2212yes—
93C13×#462C2211yescharacteristic
94C13×#461C2211yescharacteristic
95C13×#461C2212yes—
96C13×#461C2212yes—
97C13×#461C2212yes—
98C13×#460C2211yescharacteristic
99C13×#460C2211yescharacteristic
100C13×#460C2211yescharacteristic
101C13×#460C2212yes—
102C13×#459C2211yescharacteristic
103C13×#459C2212yes—
104C13×#452C2212yes—
105C13×#451C2211yescharacteristic
106C13×#449C2212yes—
107C13×#449C2212yes—
108C13×#449C2212yes—
109C13×#448C2212yes—
110C13×#448C2211yescharacteristic
111C13×#446C2211yescharacteristic
112C13×#446C2211yescharacteristic
113C13×#446C2212yes—
114C8×Q8×C13C2211yescharacteristic
115C8×Q8×C13C2212yes—
116C8×Q8×C13C2211yescharacteristic
117C13×#442C2212yes—
118C13×#442C2212yes—
119C13×#441C2212yes—
120C13×#440C2212yes—
121C4×C13×Q16C2211yescharacteristic
122C4×C13×Q16C2211yescharacteristic
123C4×C13×SD16C2212yes—
124C4×C13×SD16C2212yes—
125C4×C13×SD16C2211yescharacteristic
126C4×C13×SD16C2212yes—
127C4×C13×SD16C2212yes—
128C4×C13×SD16C2211yescharacteristic
129C4×C13×SD16C2212yes—
130C4×C13×D8C2212yes—
131C13×#433C2212yes—
132C13×#433C2212yes—
133C13×#431C2211yescharacteristic
134C13×#431C2211yescharacteristic
135C2×C13×#41—21no—
136C2×C13×#41—21no—
137C2×C13×#41C2312yes—
138C22×Q8×C13—21no—
139C22×Q8×C13C2311yescharacteristic
140C2×C13×Q16C2311yescharacteristic
141C2×C13×Q16C2311yescharacteristic
142C2×C13×Q16C2312yes—
143C2×C13×SD16C2312yes—
144C2×C13×SD16C2312yes—
145C2×C13×SD16C2311yescharacteristic
146C2×C13×SD16C2311yescharacteristic
147C2×C13×SD16C2312yes—
148C2×C13×SD16C2312yes—
149C2×C13×SD16C2312yes—
150C2×C13×SD16C2312yes—
151C2×C13×D8C2312yes—
152C2×C13×D8C2312yes—
153C2×C13×D8C2312yes—
154C13×C4⋊Q8—21no—
155C13×C4⋊Q8D411yescharacteristic
156C13×C4⋊Q8D411yescharacteristic
157C13×C4⋊Q8C2312yes—
158C13×C4⋊Q8C2311yescharacteristic
159C13×C4⋊Q8C2312yes—
160C13×C4⋊Q8C2311yescharacteristic
161C13×C4⋊Q8C2312yes—
162C13×#127C2311yescharacteristic
163C13×#127C2312yes—
164C13×#127C2311yescharacteristic
165C13×#126—22no—
166C13×#126—22no—
167C13×#126—22no—
168C13×#126—22no—
169C13×#126—22no—
170C13×#126—21no—
171C13×#125—21no—
172C13×#125—21no—
173C13×#125—22no—
174C13×#125—22no—
175C13×#125—22no—
176C13×#125D412yes—
177C13×#125C2312yes—
178C13×#125C2311yescharacteristic
179C13×#124—21no—
180C13×#124—21no—
181C13×#124—21no—
182C13×#124—22no—
183C13×#124—22no—
184C13×#124—21no—
185C13×#124C2312yes—
186C13×#124C2312yes—
187C13×#124C2312yes—
188C13×#124C2312yes—
189C13×#124C2311yescharacteristic
190C13×#123—21no—
191C13×#123—22no—
192C13×#123—22no—
193C13×#123—22no—
194C13×#123—22no—
195C13×#123—22no—
196C13×#123—22no—
197C13×#123—22no—
198C13×#123—22no—
199C13×#123—22no—
200C13×#123—22no—
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⋊Q8—22no—
208C13×C22⋊Q8—22no—
209C13×C22⋊Q8—22no—
210C13×C22⋊Q8—21no—
211C13×C22⋊Q8D411yescharacteristic
212C13×C22⋊Q8D411yescharacteristic
213C13×C22⋊Q8D412yes—
214C13×C22⋊Q8C2311yescharacteristic
215C13×#121—21no—
216C13×#121—21no—
217C13×#121—21no—
218C13×#121—22no—
219C13×#121—21no—
220C13×#121—22no—
221C13×#121—22no—
222C13×#121C2311yescharacteristic
223C13×#121C2312yes—
224C4×Q8×C13—21no—
225C4×Q8×C13—21no—
226C4×Q8×C13—21no—
227C4×Q8×C13—21no—
228C4×Q8×C13—21no—
229C4×Q8×C13C2311yescharacteristic
230C4×Q8×C13C2311yescharacteristic
231C4×Q8×C13C2311yescharacteristic
232C4×Q8×C13C2311yescharacteristic
233C4×Q8×C13C2312yes—
234C4×Q8×C13C2312yes—
235C4×Q8×C13C2312yes—
236C4×Q8×C13C2311yescharacteristic
237C4×Q8×C13C2311yescharacteristic
238C4×Q8×C13C2311yescharacteristic
239C4×Q8×C13C2312yes—
240C4×D4×C13—21no—
241C4×D4×C13—21no—
242C4×D4×C13—21no—
243C4×D4×C13—22no—
244C4×D4×C13—21no—
245C4×D4×C13—22no—
246C4×D4×C13—22no—
247C4×D4×C13—21no—
248C4×D4×C13—21no—
249C4×D4×C13—21no—
250C4×D4×C13C2312yes—
251C4×D4×C13C2312yes—
252C4×D4×C13C2311yescharacteristic
253C4×D4×C13C2312yes—
254C4×D4×C13C2312yes—
255C4×D4×C13C2312yes—
256C4×D4×C13C2312yes—
257C13×#117—22no—
258C13×#117—22no—
259C13×#117—22no—
260C13×#117—21no—
261C13×#117C2312yes—
262C2×C13×C4⋊C4—21no—
263C2×C13×C4⋊C4—22no—
264C2×C13×C4⋊C4—22no—
265C2×C13×C4⋊C4C2311yescharacteristic
266C2×C42×C13—21no—
267C2×C42×C13C2311yescharacteristic
268C13×#107C2311yescharacteristic
269C13×#107C2311yescharacteristic
270C13×#106C2312yes—
271C13×#106C2311yescharacteristic
272C13×#106C2312yes—
273C13×#106C2311yescharacteristic
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×#103C2312yes—
284C13×#103C2312yes—
285C13×#103C2312yes—
286C13×#103C2311yescharacteristic
287C13×#103C2311yescharacteristic
288C13×#103C2312yes—
289C13×#103C2311yescharacteristic
290C13×#103C2311yescharacteristic
291C13×#103C2311yescharacteristic
292C13×#103C2312yes—
293C13×#103C2312yes—
294C13×#102C2312yes—
295C13×#102C2312yes—
296C13×#102C2311yescharacteristic
297C13×#102C2312yes—
298C13×#102C2311yescharacteristic
299C13×#102C2312yes—
300C13×#102C2312yes—
301C13×#102C2312yes—
302C13×C22⋊C8C2311yescharacteristic
303C13×C22⋊C8C2312yes—
304C13×C22⋊C8C2311yescharacteristic
305C13×#97C2312yes—
306C13×#97C2312yes—
307C4×C8×C13C2312yes—
308C4×C8×C13C2311yescharacteristic
309C4×C8×C13C2311yescharacteristic
310C4×C8×C13C2312yes—
311C4×C8×C13C2312yes—
312#61928C1311yesmaximal, characteristic, direct product factor, Sylow
313C13×#41—42no—
314C13×#41—42no—
315C13×#41—82no—
316C13×#41—82no—
317C2×Q8×C13—21no—
318C2×Q8×C13—21no—
319C2×Q8×C13—22no—
320C2×Q8×C13—41no—
321C2×Q8×C13—41no—
322C2×Q8×C13—82no—
323C2×Q8×C13C2×D411yescharacteristic
324C2×Q8×C13C2×D411yescharacteristic
325C2×Q8×C13C2×D412yes—
326C2×Q8×C13C2411yescharacteristic
327C2×Q8×C13C2411yescharacteristic
328C2×Q8×C13C2412yes—
329C2×Q8×C13C2411yescharacteristic
330C2×D4×C13—22no—
331C2×D4×C13—21no—
332C2×D4×C13—22no—
333C2×D4×C13—21no—
334C2×D4×C13—21no—
335C2×D4×C13—21no—
336C2×D4×C13—22no—
337C2×D4×C13—21no—
338C2×D4×C13—22no—
339C2×D4×C13C2412yes—
340C2×D4×C13C2411yescharacteristic
341C2×D4×C13C2412yes—
342C22×C4×C13—21no—
343C22×C4×C13—21no—
344C22×C4×C13—22no—
345C22×C4×C13—21no—
346C22×C4×C13—22no—
347C22×C4×C13—22no—
348C22×C4×C13—22no—
349C22×C4×C13—22no—
350C22×C4×C13—22no—
351C22×C4×C13—22no—
352C22×C4×C13C2×D411yescharacteristic
353C22×C4×C13C2×D411yescharacteristic
354C22×C4×C13C2411yescharacteristic
355C13×Q16—41no—
356C13×Q16—42no—
357C13×Q16—41no—
358C13×SD16—41no—
359C13×SD16—42no—
360C13×SD16—41no—
361C13×SD16—42no—
362C13×SD16—42no—
363C13×SD16—42no—
364C13×SD16—42no—
365C13×SD16—42no—
366C13×D8—42no—
367C13×D8—42no—
368C13×D8—42no—
369C2×C8×C13C2412yes—
370C2×C8×C13C2411yescharacteristic
371C2×C8×C13C2411yescharacteristic
372C2×C8×C13C2411yescharacteristic
373C2×C8×C13C2412yes—
374C2×C8×C13C2411yescharacteristic
375C13×C4⋊C4—21no—
376C13×C4⋊C4—21no—
377C13×C4⋊C4—22no—
378C13×C4⋊C4—22no—
379C13×C4⋊C4—21no—
380C13×C4⋊C4—21no—
381C13×C4⋊C4—21no—
382C13×C4⋊C4—21no—
383C13×C4⋊C4—22no—
384C13×C4⋊C4—22no—
385C13×C4⋊C4—21no—
386C13×C4⋊C4—21no—
387C13×C4⋊C4—22no—
388C13×C4⋊C4—22no—
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—22no—
396C13×C4⋊C4—21no—
397C13×C4⋊C4C2×D412yes—
398C13×C4⋊C4C2×D412yes—
399C13×C4⋊C4C2×D412yes—
400C13×C4⋊C4C2×D412yes—
401C13×C4⋊C4C2×D411yescharacteristic
402C13×C4⋊C4C2×D411yescharacteristic
403C13×C4⋊C4C2×D412yes—
404C13×C4⋊C4C2×D412yes—
405C13×C4⋊C4C2×D412yes—
406C13×C4⋊C4C2411yescharacteristic
407C13×C4⋊C4C2411yescharacteristic
408C13×C4⋊C4C2411yescharacteristic
409C13×C4⋊C4C2412yes—
410C13×C4⋊C4C2411yescharacteristic
411C13×C22⋊C4—21no—
412C13×C22⋊C4—22no—
413C13×C22⋊C4—22no—
414C13×C22⋊C4—22no—
415C13×C22⋊C4—21no—
416C13×C22⋊C4—22no—
417C13×C22⋊C4—22no—
418C13×C22⋊C4—21no—
419C13×C22⋊C4—21no—
420C13×C22⋊C4—22no—
421C13×C22⋊C4—22no—
422C13×C22⋊C4—22no—
423C13×C22⋊C4—22no—
424C13×C22⋊C4—22no—
425C13×C22⋊C4—22no—
426C13×C22⋊C4—21no—
427C13×C22⋊C4—22no—
428C13×C22⋊C4—22no—
429C13×C22⋊C4—22no—
430C13×C22⋊C4—22no—
431C13×C22⋊C4C2×D412yes—
432C13×C22⋊C4C2×D412yes—
433C42×C13—21no—
434C42×C13—21no—
435C42×C13—21no—
436C42×C13—21no—
437C42×C13—22no—
438C42×C13—22no—
439C42×C13—21no—
440C42×C13—22no—
441C42×C13C2×D411yescharacteristic
442C42×C13C2×D411yescharacteristic
443C42×C13C2411yescharacteristic
444C42×C13C2411yescharacteristic
445C42×C13C2412yes—
446C42×C13C2412yes—
447#3554C2×C1311yescharacteristic, complemented
448#3507C2×C1311yescharacteristic, complemented
449#3401C2×C1312yescomplemented
450#3400C2×C1311yescharacteristic, complemented
451#3399C2×C1311yescharacteristic, complemented
452#3396C2×C1311yescharacteristic, complemented
453#3394C2×C1312yescomplemented
454#3392C2×C1311yescharacteristic, complemented
455#3376C2×C1312yescomplemented
456#3374C2×C1311yescharacteristic, complemented
457#3373C2×C1311yescharacteristic, complemented
458#3365C2×C1311yescharacteristic, complemented
459#3360C2×C1312yescomplemented
460#3359C2×C1311yescharacteristic, complemented
461#3225C2×C1312yescomplemented
462#3221C2×C1312yescomplemented
463#3212C2×C1311yescharacteristic, complemented
464#3207C2×C1311yescharacteristic, complemented
465#3125C2×C1312yescomplemented
466#3119C2×C1312yescomplemented
467#3108C2×C1311yescharacteristic, complemented
468#3103C2×C1311yescharacteristic, complemented
469#2986C2×C1311yescharacteristic, complemented
470C23×C13—22no—
471C23×C13—22no—
472C23×C13—21no—
473C23×C13C22×D411yescharacteristic
474Q8×C13—22no—
475Q8×C13—22no—
476Q8×C13—21no—
477Q8×C13—21no—
478Q8×C13—21no—
479Q8×C13—22no—
480Q8×C13—21no—
481Q8×C13—21no—
482Q8×C13—22no—
483Q8×C13—21no—
484Q8×C13—42no—
485Q8×C13—42no—
486Q8×C13—42no—
487Q8×C13—82no—
488D4×C13—21no—
489D4×C13—22no—
490D4×C13—22no—
491D4×C13—22no—
492D4×C13—22no—
493D4×C13—21no—
494D4×C13—44no—
495D4×C13—42no—
496D4×C13—42no—
497D4×C13—81no—
498D4×C13—81no—
499D4×C13—82no—
500D4×C13—82no—
501D4×C13—81no—
502D4×C13—82no—
503C2×C4×C13—22no—
504C2×C4×C13—21no—
505C2×C4×C13—21no—
506C2×C4×C13—21no—
507C2×C4×C13—21no—
508C2×C4×C13—21no—
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—41no—
516C2×C4×C13—44no—
517C2×C4×C13—42no—
518C2×C4×C13—42no—
519C2×C4×C13—82no—
520C2×C4×C13—82no—
521C2×C4×C13—82no—
522C2×C4×C13—82no—
523C2×C4×C13—82no—
524C2×C4×C13—82no—
525C2×C4×C13—81no—
526C2×C4×C13C22×D411yescharacteristic
527C2×C4×C13C22×D412yes—
528C2×C4×C13C22×D412yes—
529C2×C4×C13C22×D412yes—
530C2×C4×C13C22×D411yescharacteristic
531C2×C4×C13C22×D411yescharacteristic
532C2×C4×C13C22×D411yescharacteristic
533C2×C4×C13C22×D412yes—
534C2×C4×C13C22×D411yescharacteristic
535C2×C4×C13C2511yescharacteristic
536C8×C13—21no—
537C8×C13—21no—
538C8×C13—22no—
539C8×C13—22no—
540C8×C13—21no—
541C8×C13—21no—
542#562—22no—
543#559C22×C1311yescharacteristic
544#559C22×C1311yescharacteristic
545#559C22×C1312yes—
546#559C22×C1311yescharacteristic
547#557C22×C1311yescharacteristic
548#557C22×C1311yescharacteristic
549#557C22×C1311yescharacteristic
550#556—21no—
551#556C22×C1312yes—
552#556C22×C1312yes—
553#554—21no—
554#554C22×C1312yes—
555#552—22no—
556#550C22×C1311yescharacteristic
557D4×Q8C22×C1311yescharacteristic
558#548—21no—
559#547—21no—
560#542—21no—
561#542C22×C1312yes—
562#540C22×C1312yes—
563#539—22no—
564#539—22no—
565#536—21no—
566#536C22×C1312yes—
567#533C22×C1311yescharacteristic
568#532C22×C1311yescharacteristic
569#532C22×C1311yescharacteristic
570#529—21no—
571#529—21no—
572#529C22×C1311yescharacteristic
573#520C22×C1312yes—
574C2×C4×Q8C22×C1311yescharacteristic
575#497C22×C1312yes—
576#496C22×C1312yes—
577#495C22×C1312yes—
578#495C22×C1312yes—
579#493C22×C1311yescharacteristic
580#492C22×C1312yes—
581#492C22×C1311yescharacteristic
582#491C22×C1312yes—
583#489C22×C1312yes—
584#488C22×C1312yes—
585#488C22×C1312yes—
586#487C22×C1312yes—
587#487C22×C1311yescharacteristic
588#486C22×C1311yescharacteristic
589#483C22×C1311yescharacteristic
590#481C22×C1312yes—
591#480C22×C1311yescharacteristic
592#479C22×C1311yescharacteristic
593#479C22×C1312yes—
594#479C22×C1311yescharacteristic
595#478C22×C1312yes—
596#476C22×C1312yes—
597#475C22×C1311yescharacteristic
598#475C22×C1311yescharacteristic
599#475C22×C1312yes—
600#464C22×C1311yescharacteristic
601#464C22×C1311yescharacteristic
602#464C22×C1312yes—
603#464C22×C1312yes—
604#463C22×C1312yes—
605#463C22×C1312yes—
606#463C22×C1312yes—
607#463C22×C1312yes—
608#463C22×C1312yes—
609#463C22×C1312yes—
610#462C22×C1312yes—
611#462C22×C1311yescharacteristic
612#461C22×C1311yescharacteristic
613#461C22×C1312yes—
614#461C22×C1312yes—
615#461C22×C1312yes—
616#460C22×C1311yescharacteristic
617#460C22×C1311yescharacteristic
618#460C22×C1311yescharacteristic
619#460C22×C1312yes—
620#459C22×C1311yescharacteristic
621#459C22×C1312yes—
622#452C22×C1312yes—
623#451C22×C1311yescharacteristic
624#449C22×C1312yes—
625#449C22×C1312yes—
626#449C22×C1312yes—
627#448C22×C1312yes—
628#448C22×C1311yescharacteristic
629#446C22×C1311yescharacteristic
630#446C22×C1311yescharacteristic
631#446C22×C1312yes—
632C8×Q8C22×C1311yescharacteristic
633C8×Q8C22×C1312yes—
634C8×Q8C22×C1311yescharacteristic
635#442C22×C1312yes—
636#442C22×C1312yes—
637#441C22×C1312yes—
638#440C22×C1312yes—
639C4×Q16C22×C1311yescharacteristic
640C4×Q16C22×C1311yescharacteristic
641C4×SD16C22×C1312yes—
642C4×SD16C22×C1312yes—
643C4×SD16C22×C1311yescharacteristic
644C4×SD16C22×C1312yes—
645C4×SD16C22×C1312yes—
646C4×SD16C22×C1311yescharacteristic
647C4×SD16C22×C1312yes—
648C4×D8C22×C1312yes—
649#433C22×C1312yes—
650#433C22×C1312yes—
651#431C22×C1311yescharacteristic
652#431C22×C1311yescharacteristic
653C22×C13—21no—
654C22×C13—21no—
655C22×C13—21no—
656C22×C13—42no—
657C22×C13—42no—
658C22×C13—41no—
659C22×C13—42no—
660C22×C13—41no—
661C22×C13—42no—
662C22×C13—41no—
663C22×C13—42no—
664C22×C13—42no—
665C22×C13C23×D411yescharacteristic
666C4×C13—21no—
667C4×C13—21no—
668C4×C13—22no—
669C4×C13—22no—
670C4×C13—21no—
671C4×C13—21no—
672C4×C13—22no—
673C4×C13—22no—
674C4×C13—41no—
675C4×C13—41no—
676C4×C13—41no—
677C4×C13—42no—
678C4×C13—41no—
679C4×C13—41no—
680C4×C13—41no—
681C4×C13—41no—
682C4×C13—42no—
683C4×C13#57712yes—
684C4×C13#58511yescharacteristic
685C4×C13#58511yescharacteristic
686C2×#41—21no—
687C2×#41—21no—
688C2×#41C23×C1312yes—
689C22×Q8—21no—
690C22×Q8C23×C1311yescharacteristic
691C2×Q16C23×C1311yescharacteristic
692C2×Q16C23×C1311yescharacteristic
693C2×Q16C23×C1312yes—
694C2×SD16C23×C1312yes—
695C2×SD16C23×C1312yes—
696C2×SD16C23×C1311yescharacteristic
697C2×SD16C23×C1311yescharacteristic
698C2×SD16C23×C1312yes—
699C2×SD16C23×C1312yes—
700C2×SD16C23×C1312yes—
701C2×SD16C23×C1312yes—
702C2×D8C23×C1312yes—
703C2×D8C23×C1312yes—
704C2×D8C23×C1312yes—
705C4⋊Q8—21no—
706C4⋊Q8D4×C1311yescharacteristic
707C4⋊Q8D4×C1311yescharacteristic
708C4⋊Q8C23×C1311yescharacteristic
709C4⋊Q8C23×C1312yes—
710C4⋊Q8C23×C1312yes—
711C4⋊Q8C23×C1311yescharacteristic
712C4⋊Q8C23×C1312yes—
713#127C23×C1311yescharacteristic
714#127C23×C1311yescharacteristic
715#127C23×C1312yes—
716#126—22no—
717#126—22no—
718#126—22no—
719#126—22no—
720#126—22no—
721#126—21no—
722#125—21no—
723#125—21no—
724#125—22no—
725#125—22no—
726#125—22no—
727#125D4×C1312yes—
728#125C23×C1311yescharacteristic
729#125C23×C1312yes—
730#124—21no—
731#124—21no—
732#124—21no—
733#124—22no—
734#124—22no—
735#124—21no—
736#124C23×C1311yescharacteristic
737#124C23×C1312yes—
738#124C23×C1312yes—
739#124C23×C1312yes—
740#124C23×C1312yes—
741#123—21no—
742#123—22no—
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—
752C22⋊Q8—22no—
753C22⋊Q8—22no—
754C22⋊Q8—22no—
755C22⋊Q8—22no—
756C22⋊Q8—22no—
757C22⋊Q8—22no—
758C22⋊Q8—22no—
759C22⋊Q8—22no—
760C22⋊Q8—22no—
761C22⋊Q8—21no—
762C22⋊Q8D4×C1311yescharacteristic
763C22⋊Q8D4×C1311yescharacteristic
764C22⋊Q8D4×C1312yes—
765C22⋊Q8C23×C1311yescharacteristic
766#121—21no—
767#121—21no—
768#121—21no—
769#121—22no—
770#121—21no—
771#121—22no—
772#121—22no—
773#121C23×C1311yescharacteristic
774#121C23×C1312yes—
775C4×Q8—21no—
776C4×Q8—21no—
777C4×Q8—21no—
778C4×Q8—21no—
779C4×Q8—21no—
780C4×Q8C23×C1311yescharacteristic
781C4×Q8C23×C1311yescharacteristic
782C4×Q8C23×C1311yescharacteristic
783C4×Q8C23×C1311yescharacteristic
784C4×Q8C23×C1312yes—
785C4×Q8C23×C1312yes—
786C4×Q8C23×C1311yescharacteristic
787C4×Q8C23×C1312yes—
788C4×Q8C23×C1311yescharacteristic
789C4×Q8C23×C1311yescharacteristic
790C4×Q8C23×C1312yes—
791C4×D4—21no—
792C4×D4—21no—
793C4×D4—21no—
794C4×D4—22no—
795C4×D4—21no—
796C4×D4—22no—
797C4×D4—22no—
798C4×D4—21no—
799C4×D4—21no—
800C4×D4—21no—
801C4×D4C23×C1312yes—
802C4×D4C23×C1312yes—
803C4×D4C23×C1311yescharacteristic
804C4×D4C23×C1312yes—
805C4×D4C23×C1312yes—
806C4×D4C23×C1312yes—
807C4×D4C23×C1312yes—
808#117—22no—
809#117—22no—
810#117—22no—
811#117—21no—
812#117C23×C1312yes—
813C2×C4⋊C4—21no—
814C2×C4⋊C4—22no—
815C2×C4⋊C4—22no—
816C2×C4⋊C4C23×C1311yescharacteristic
817C2×C42—21no—
818C2×C42C23×C1311yescharacteristic
819#107C23×C1311yescharacteristic
820#107C23×C1311yescharacteristic
821#106C23×C1312yes—
822#106C23×C1311yescharacteristic
823#106C23×C1312yes—
824#106C23×C1311yescharacteristic
825C4⋊C8C23×C1311yescharacteristic
826C4⋊C8C23×C1311yescharacteristic
827C4⋊C8C23×C1311yescharacteristic
828C4⋊C8C23×C1311yescharacteristic
829C4⋊C8C23×C1312yes—
830C4⋊C8C23×C1312yes—
831C4⋊C8C23×C1312yes—
832C4⋊C8C23×C1312yes—
833#103C23×C1311yescharacteristic
834#103C23×C1312yes—
835#103C23×C1312yes—
836#103C23×C1312yes—
837#103C23×C1311yescharacteristic
838#103C23×C1311yescharacteristic
839#103C23×C1312yes—
840#103C23×C1311yescharacteristic
841#103C23×C1311yescharacteristic
842#103C23×C1311yescharacteristic
843#103C23×C1312yes—
844#103C23×C1312yes—
845#102C23×C1312yes—
846#102C23×C1312yes—
847#102C23×C1311yescharacteristic
848#102C23×C1312yes—
849#102C23×C1311yescharacteristic
850#102C23×C1312yes—
851#102C23×C1312yes—
852#102C23×C1312yes—
853C22⋊C8C23×C1311yescharacteristic
854C22⋊C8C23×C1312yes—
855C22⋊C8C23×C1311yescharacteristic
856#97C23×C1312yes—
857#97C23×C1312yes—
858C4×C8C23×C1312yes—
859C4×C8C23×C1311yescharacteristic
860C4×C8C23×C1311yescharacteristic
861C4×C8C23×C1312yes—
862C4×C8C23×C1312yes—
863C2×C13—41no—
864C2×C13—82no—
865C2×C13—82no—
866C2×C13—81no—
867C2×C13#348711yescharacteristic
868C2×C13C2×#57711yescharacteristic
869C2×C13#358411yescharacteristic
870#41—42no—
871#41—42no—
872#41—82no—
873#41—82no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—22no—
877C2×Q8—41no—
878C2×Q8—41no—
879C2×Q8—82no—
880C2×Q8C2×D4×C1311yescharacteristic
881C2×Q8C2×D4×C1311yescharacteristic
882C2×Q8C2×D4×C1312yes—
883C2×Q8C24×C1311yescharacteristic
884C2×Q8C24×C1311yescharacteristic
885C2×Q8C24×C1312yes—
886C2×Q8C24×C1311yescharacteristic
887C2×D4—22no—
888C2×D4—21no—
889C2×D4—22no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—22no—
894C2×D4—21no—
895C2×D4—22no—
896C2×D4C24×C1312yes—
897C2×D4C24×C1311yescharacteristic
898C2×D4C24×C1312yes—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—22no—
902C22×C4—21no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4C2×D4×C1311yescharacteristic
910C22×C4C2×D4×C1311yescharacteristic
911C22×C4C24×C1311yescharacteristic
912Q16—41no—
913Q16—42no—
914Q16—41no—
915SD16—41no—
916SD16—42no—
917SD16—41no—
918SD16—42no—
919SD16—42no—
920SD16—42no—
921SD16—42no—
922SD16—42no—
923D8—42no—
924D8—42no—
925D8—42no—
926C2×C8C24×C1312yes—
927C2×C8C24×C1311yescharacteristic
928C2×C8C24×C1311yescharacteristic
929C2×C8C24×C1311yescharacteristic
930C2×C8C24×C1312yes—
931C2×C8C24×C1311yescharacteristic
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—22no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—21no—
954C4⋊C4C2×D4×C1312yes—
955C4⋊C4C2×D4×C1312yes—
956C4⋊C4C2×D4×C1312yes—
957C4⋊C4C2×D4×C1312yes—
958C4⋊C4C2×D4×C1311yescharacteristic
959C4⋊C4C2×D4×C1311yescharacteristic
960C4⋊C4C2×D4×C1312yes—
961C4⋊C4C2×D4×C1312yes—
962C4⋊C4C2×D4×C1312yes—
963C4⋊C4C24×C1311yescharacteristic
964C4⋊C4C24×C1311yescharacteristic
965C4⋊C4C24×C1311yescharacteristic
966C4⋊C4C24×C1312yes—
967C4⋊C4C24×C1311yescharacteristic
968C22⋊C4—21no—
969C22⋊C4—22no—
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—21no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—21no—
976C22⋊C4—21no—
977C22⋊C4—22no—
978C22⋊C4—22no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—21no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4C2×D4×C1312yes—
989C22⋊C4C2×D4×C1312yes—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—22no—
995C42—22no—
996C42—21no—
997C42—22no—
998C42C2×D4×C1311yescharacteristic
999C42C2×D4×C1311yescharacteristic
1000C42C24×C1311yescharacteristic
1001C42C24×C1311yescharacteristic
1002C42C24×C1312yes—
1003C42C24×C1312yes—
1004C13#6192811yescharacteristic, direct product factor, Sylow
1005C23—22no—
1006C23—21no—
1007C23—22no—
1008C23C22×D4×C1311yescharacteristic
1009Q8—22no—
1010Q8—22no—
1011Q8—21no—
1012Q8—21no—
1013Q8—21no—
1014Q8—22no—
1015Q8—21no—
1016Q8—21no—
1017Q8—22no—
1018Q8—21no—
1019Q8—42no—
1020Q8—42no—
1021Q8—42no—
1022Q8—82no—
1023D4—21no—
1024D4—22no—
1025D4—22no—
1026D4—22no—
1027D4—22no—
1028D4—21no—
1029D4—44no—
1030D4—42no—
1031D4—42no—
1032D4—81no—
1033D4—81no—
1034D4—82no—
1035D4—82no—
1036D4—81no—
1037D4—82no—
1038C2×C4—22no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—22no—
1049C2×C4—21no—
1050C2×C4—41no—
1051C2×C4—44no—
1052C2×C4—42no—
1053C2×C4—42no—
1054C2×C4—82no—
1055C2×C4—82no—
1056C2×C4—82no—
1057C2×C4—82no—
1058C2×C4—82no—
1059C2×C4—82no—
1060C2×C4—81no—
1061C2×C4C22×D4×C1311yescharacteristic
1062C2×C4C22×D4×C1312yes—
1063C2×C4C22×D4×C1312yes—
1064C2×C4C22×D4×C1312yes—
1065C2×C4C22×D4×C1311yescharacteristic
1066C2×C4C22×D4×C1311yescharacteristic
1067C2×C4C22×D4×C1311yescharacteristic
1068C2×C4C22×D4×C1312yes—
1069C2×C4C22×D4×C1311yescharacteristic
1070C2×C4C25×C1311yescharacteristic
1071C8—21no—
1072C8—21no—
1073C8—22no—
1074C8—22no—
1075C8—21no—
1076C8—21no—
1077C22—21no—
1078C22—21no—
1079C22—21no—
1080C22—41no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—41no—
1086C22—42no—
1087C22—41no—
1088C22—42no—
1089C22C23×D4×C1311yescharacteristic
1090C4—21no—
1091C4—22no—
1092C4—22no—
1093C4—21no—
1094C4—21no—
1095C4—22no—
1096C4—22no—
1097C4—21no—
1098C4—41no—
1099C4—42no—
1100C4—41no—
1101C4—41no—
1102C4—41no—
1103C4—42no—
1104C4—41no—
1105C4—41no—
1106C4—41no—
1107C4C13×#57712yes—
1108C4C13×#58511yescharacteristic
1109C4C13×#58511yescharacteristic
1110C2—41no—
1111C2—81no—
1112C2—82no—
1113C2—82no—
1114C2C13×#348711yescharacteristic
1115C2C2×C13×#57711yescharacteristic
1116C2C13×#358411yescharacteristic
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×#3507C2semidirect
3. C13×#3401C2semidirect
4. C13×#3400C2semidirect
5. C13×#3399C2semidirect
6. C13×#3396C2semidirect
7. C13×#3394C2semidirect
8. C13×#3392C2semidirect
9. C13×#3376C2semidirect
10. C13×#3374C2semidirect
11. C13×#3373C2semidirect
12. C13×#3365C2semidirect
13. C13×#3360C2semidirect
14. C13×#3359C2semidirect
15. C13×#3225C2semidirect
16. C13×#3221C2semidirect
17. C13×#3212C2semidirect
18. C13×#3207C2semidirect
19. C13×#3125C2semidirect
20. C13×#3119C2semidirect
21. C13×#3108C2semidirect
22. C13×#3103C2semidirect
23. C13×#2986C2semidirect
312. #61928C13direct (N × H)
447. #3554C2×C13semidirect
448. #3507C2×C13semidirect
449. #3401C2×C13semidirect
450. #3400C2×C13semidirect
451. #3399C2×C13semidirect
452. #3396C2×C13semidirect
453. #3394C2×C13semidirect
454. #3392C2×C13semidirect
455. #3376C2×C13semidirect
456. #3374C2×C13semidirect
457. #3373C2×C13semidirect
458. #3365C2×C13semidirect
459. #3360C2×C13semidirect
460. #3359C2×C13semidirect
461. #3225C2×C13semidirect
462. #3221C2×C13semidirect
463. #3212C2×C13semidirect
464. #3207C2×C13semidirect
465. #3125C2×C13semidirect
466. #3119C2×C13semidirect
467. #3108C2×C13semidirect
468. #3103C2×C13semidirect
469. #2986C2×C13semidirect
1004. C13#61928direct (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×#35072
C13×#34012
C13×#34002
C13×#33992
C13×#33962
C13×#33942
C13×#33922
C13×#33762
C13×#33742
C13×#33732
C13×#33652
C13×#33602
C13×#33592
C13×#32252
C13×#32212
C13×#32122
C13×#32072
C13×#31252
C13×#31192
C13×#31082
C13×#31032
C13×#29862
#6192813