Finite Group Databasebeta

← C13×#61902 #15748241

Subgroups — C13×#61902 #15748241

Order 3328.

1734 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3507C211yesmaximal, characteristic, complemented
2C13×#3480C211yesmaximal, characteristic, complemented
3C13×#3403C212yesmaximal, complemented
4C13×#3401C212yesmaximal, complemented
5C13×#3398C211yesmaximal, characteristic, complemented
6C13×#3397C211yesmaximal, characteristic, complemented
7C13×#3394C211yesmaximal, characteristic, complemented
8C13×#3393C211yesmaximal, characteristic, complemented
9C13×#3377C212yesmaximal, complemented
10C13×#3372C211yesmaximal, characteristic, complemented
11C13×#3371C212yesmaximal, complemented
12C13×#3366C211yesmaximal, characteristic, complemented
13C13×#3361C211yesmaximal, characteristic, complemented
14C13×#3360C211yesmaximal, characteristic, complemented
15C13×#3219C212yesmaximal, complemented
16C13×#3214C211yesmaximal, characteristic, complemented
17C13×#3212C212yesmaximal, complemented
18C13×#3210C211yesmaximal, characteristic, complemented
19C13×#3116C211yesmaximal, characteristic, complemented
20C13×#3111C212yesmaximal, complemented
21C13×#3106C211yesmaximal, characteristic, complemented
22C13×#3102C212yesmaximal, complemented
23C13×#2984C211yesmaximal, characteristic, complemented
24C13×#559C2211yescharacteristic
25C13×#559C2212yes—
26C13×#559C2212yes—
27C13×#557C2211yescharacteristic
28C13×#557C2212yes—
29C13×#556—22no—
30C13×#556C2211yescharacteristic
31C13×#556C2212yes—
32C13×#556C2211yescharacteristic
33C13×#556C2211yescharacteristic
34C13×#554C2211yescharacteristic
35C13×#554C2211yescharacteristic
36C13×#553—21no—
37C13×#553—22no—
38C13×#552—21no—
39C13×#552—21no—
40C13×#550C2211yescharacteristic
41C13×#548—21no—
42C13×#539—22no—
43C13×#536—21no—
44C13×#533C2211yescharacteristic
45C13×#532C2211yescharacteristic
46C13×#532C2212yes—
47C13×#532C2211yescharacteristic
48C13×#529—21no—
49C13×#529—22no—
50C13×#529C2212yes—
51C13×#529C2212yes—
52C13×#520—21no—
53C4×C13×#41—21no—
54C4×C13×#41C2212yes—
55C4×C13×#41C2211yescharacteristic
56C2×C4×Q8×C13C2211yescharacteristic
57C13×#497C2212yes—
58C13×#496C2212yes—
59C13×#496C2212yes—
60C13×#495C2212yes—
61C13×#495C2212yes—
62C13×#494C2211yescharacteristic
63C13×#492C2211yescharacteristic
64C13×#491C2212yes—
65C13×#490C2212yes—
66C13×#489C2212yes—
67C13×#488C2212yes—
68C13×#488C2212yes—
69C13×#487C2211yescharacteristic
70C13×#486C2211yescharacteristic
71C13×#485C2212yes—
72C13×#482C2211yescharacteristic
73C13×#482C2211yescharacteristic
74C13×#479C2212yes—
75C13×#479C2212yes—
76C13×#478C2212yes—
77C13×#478C2212yes—
78C13×#477C2211yescharacteristic
79C13×#477C2211yescharacteristic
80C13×#476C2211yescharacteristic
81C13×#476C2211yescharacteristic
82C13×#464C2212yes—
83C13×#464C2212yes—
84C13×#464C2212yes—
85C13×#464C2212yes—
86C13×#464C2212yes—
87C13×#464C2212yes—
88C13×#463C2212yes—
89C13×#463C2212yes—
90C13×#463C2212yes—
91C13×#463C2212yes—
92C13×#462C2211yescharacteristic
93C13×#462C2212yes—
94C13×#461C2211yescharacteristic
95C13×#461C2211yescharacteristic
96C13×#461C2211yescharacteristic
97C13×#461C2212yes—
98C13×#460C2211yescharacteristic
99C13×#460C2212yes—
100C13×#459C2211yescharacteristic
101C13×#459C2211yescharacteristic
102C13×#459C2211yescharacteristic
103C13×#459C2212yes—
104C13×#452C2212yes—
105C13×#452C2212yes—
106C13×#452C2212yes—
107C13×#449C2212yes—
108C13×#449C2211yescharacteristic
109C13×#449C2211yescharacteristic
110C13×#449C2212yes—
111C13×#446C2211yescharacteristic
112C13×#446C2212yes—
113C13×#446C2211yescharacteristic
114C13×#446C2212yes—
115C8×Q8×C13C2211yescharacteristic
116C8×Q8×C13C2211yescharacteristic
117C13×#442C2212yes—
118C13×#441C2212yes—
119C13×#441C2212yes—
120C13×#440C2212yes—
121C13×#440C2212yes—
122C13×#440C2212yes—
123C4×C13×Q16C2212yes—
124C4×C13×SD16C2212yes—
125C4×C13×SD16C2212yes—
126C4×C13×SD16C2211yescharacteristic
127C4×C13×SD16C2211yescharacteristic
128C4×C13×D8C2212yes—
129C4×C13×D8C2211yescharacteristic
130C4×C13×D8C2211yescharacteristic
131C13×#432C2212yes—
132C13×#432C2211yescharacteristic
133C13×#431C2212yes—
134C13×#431C2211yescharacteristic
135C2×C13×#41—21no—
136C2×C13×#41—21no—
137C2×C13×#41C2312yes—
138C2×C13×#41C2311yescharacteristic
139C22×Q8×C13D411yescharacteristic
140C2×C13×Q16C2312yes—
141C2×C13×Q16C2312yes—
142C2×C13×Q16C2312yes—
143C2×C13×SD16C2311yescharacteristic
144C2×C13×SD16C2311yescharacteristic
145C2×C13×SD16C2312yes—
146C2×C13×SD16C2312yes—
147C2×C13×SD16C2312yes—
148C2×C13×SD16C2312yes—
149C2×C13×SD16C2312yes—
150C2×C13×D8C2311yescharacteristic
151C2×C13×D8C2312yes—
152C2×C13×D8C2311yescharacteristic
153C2×C13×D8C2312yes—
154C13×C4⋊Q8—22no—
155C13×C4⋊Q8C2311yescharacteristic
156C13×C4⋊Q8C2312yes—
157C13×C4⋊Q8C2311yescharacteristic
158C13×C4⋊Q8C2311yescharacteristic
159C13×C4⋊Q8C2311yescharacteristic
160C13×#127C2311yescharacteristic
161C13×#127C2312yes—
162C13×#127C2311yescharacteristic
163C13×#126—22no—
164C13×#126—22no—
165C13×#126—22no—
166C13×#126—22no—
167C13×#126—22no—
168C13×#126—22no—
169C13×#126—22no—
170C13×#125—21no—
171C13×#125—22no—
172C13×#125—22no—
173C13×#125—22no—
174C13×#125—21no—
175C13×#125C2312yes—
176C13×#125C2312yes—
177C13×#124—21no—
178C13×#124—22no—
179C13×#124—22no—
180C13×#124—21no—
181C13×#124C2312yes—
182C13×#124C2312yes—
183C13×#124C2312yes—
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×C22⋊Q8—21no—
194C13×C22⋊Q8—22no—
195C13×C22⋊Q8—21no—
196C13×C22⋊Q8—21no—
197C13×C22⋊Q8—21no—
198C13×C22⋊Q8—21no—
199C13×C22⋊Q8—21no—
200C13×C22⋊Q8—22no—
201C13×C22⋊Q8—22no—
202C13×C22⋊Q8C2312yes—
203C13×#121—21no—
204C13×#121—21no—
205C13×#121—22no—
206C13×#121—22no—
207C13×#121—21no—
208C13×#121—21no—
209C13×#121—22no—
210C13×#121C2311yescharacteristic
211C13×#121C2311yescharacteristic
212C4×Q8×C13—21no—
213C4×Q8×C13—22no—
214C4×Q8×C13—21no—
215C4×Q8×C13D411yescharacteristic
216C4×Q8×C13D411yescharacteristic
217C4×Q8×C13D412yes—
218C4×Q8×C13C2311yescharacteristic
219C4×Q8×C13C2312yes—
220C4×Q8×C13C2312yes—
221C4×Q8×C13C2312yes—
222C4×Q8×C13C2312yes—
223C4×Q8×C13C2312yes—
224C4×Q8×C13C2311yescharacteristic
225C4×Q8×C13C2311yescharacteristic
226C4×Q8×C13C2311yescharacteristic
227C4×Q8×C13C2312yes—
228C4×D4×C13—21no—
229C4×D4×C13—22no—
230C4×D4×C13—22no—
231C4×D4×C13—21no—
232C4×D4×C13—22no—
233C4×D4×C13—22no—
234C4×D4×C13—21no—
235C4×D4×C13—22no—
236C4×D4×C13—22no—
237C4×D4×C13—22no—
238C4×D4×C13—21no—
239C4×D4×C13—22no—
240C4×D4×C13—21no—
241C4×D4×C13—21no—
242C4×D4×C13C2311yescharacteristic
243C4×D4×C13C2311yescharacteristic
244C4×D4×C13C2311yescharacteristic
245C4×D4×C13C2312yes—
246C4×D4×C13C2312yes—
247C4×D4×C13C2311yescharacteristic
248C4×D4×C13C2312yes—
249C4×D4×C13C2312yes—
250C13×#117—21no—
251C13×#117—21no—
252C13×#117—22no—
253C13×#117—21no—
254C13×#117—21no—
255C13×#117—22no—
256C13×#117—21no—
257C13×#117—22no—
258C13×#117—22no—
259C13×#117C2311yescharacteristic
260C2×C13×C4⋊C4—21no—
261C2×C13×C4⋊C4—21no—
262C2×C13×C4⋊C4D411yescharacteristic
263C2×C13×C4⋊C4D412yes—
264C2×C42×C13—22no—
265C2×C42×C13—21no—
266C2×C42×C13C2312yes—
267C2×C42×C13C2311yescharacteristic
268C13×#107C2311yescharacteristic
269C13×#107C2312yes—
270C13×#107C2311yescharacteristic
271C13×#106C2311yescharacteristic
272C13×#106C2311yescharacteristic
273C13×#106C2312yes—
274C13×C4⋊C8C2312yes—
275C13×C4⋊C8C2311yescharacteristic
276C13×C4⋊C8C2312yes—
277C13×C4⋊C8C2311yescharacteristic
278C13×C4⋊C8C2311yescharacteristic
279C13×C4⋊C8C2311yescharacteristic
280C13×C4⋊C8C2312yes—
281C13×C4⋊C8C2312yes—
282C13×#103C2312yes—
283C13×#103C2311yescharacteristic
284C13×#103C2311yescharacteristic
285C13×#103C2312yes—
286C13×#103C2312yes—
287C13×#103C2312yes—
288C13×#103C2312yes—
289C13×#103C2312yes—
290C13×#103C2312yes—
291C13×#102C2311yescharacteristic
292C13×#102C2311yescharacteristic
293C13×#102C2311yescharacteristic
294C13×#102C2311yescharacteristic
295C13×#102C2311yescharacteristic
296C13×#102C2312yes—
297C13×#102C2311yescharacteristic
298C13×#102C2312yes—
299C13×#102C2312yes—
300C13×#102C2312yes—
301C13×#102C2312yes—
302C13×C22⋊C8C2311yescharacteristic
303C13×C22⋊C8C2312yes—
304C13×C22⋊C8C2311yescharacteristic
305C13×#97C2312yes—
306C13×#97C2312yes—
307C13×#97C2312yes—
308C4×C8×C13C2311yescharacteristic
309C4×C8×C13C2311yescharacteristic
310C4×C8×C13C2312yes—
311C4×C8×C13C2312yes—
312#61902C1311yesmaximal, characteristic, direct product factor, Sylow
313C13×#41—41no—
314C13×#41—42no—
315C13×#41—42no—
316C13×#41—41no—
317C13×#41—44no—
318C13×#41—44no—
319C2×Q8×C13—21no—
320C2×Q8×C13—21no—
321C2×Q8×C13—42no—
322C2×Q8×C13C2×D411yescharacteristic
323C2×Q8×C13C2×D411yescharacteristic
324C2×Q8×C13C2×D412yes—
325C2×Q8×C13C2411yescharacteristic
326C2×Q8×C13C2412yes—
327C2×Q8×C13C2412yes—
328C2×D4×C13—21no—
329C2×D4×C13—22no—
330C2×D4×C13—21no—
331C2×D4×C13—21no—
332C2×D4×C13—22no—
333C2×D4×C13—21no—
334C2×D4×C13—21no—
335C2×D4×C13—22no—
336C2×D4×C13—21no—
337C2×D4×C13—21no—
338C2×D4×C13C2411yescharacteristic
339C2×D4×C13C2412yes—
340C2×D4×C13C2411yescharacteristic
341C2×D4×C13C2411yescharacteristic
342C22×C4×C13—22no—
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—21no—
350C22×C4×C13—22no—
351C22×C4×C13—22no—
352C22×C4×C13C2×D411yescharacteristic
353C22×C4×C13C2×D412yes—
354C22×C4×C13C2×D411yescharacteristic
355C22×C4×C13C2×D412yes—
356C22×C4×C13C2411yescharacteristic
357C13×Q16—42no—
358C13×Q16—42no—
359C13×Q16—42no—
360C13×SD16—42no—
361C13×SD16—42no—
362C13×SD16—42no—
363C13×SD16—42no—
364C13×SD16—42no—
365C13×SD16—41no—
366C13×SD16—41no—
367C13×D8—42no—
368C13×D8—41no—
369C13×D8—42no—
370C13×D8—41no—
371C2×C8×C13C2411yescharacteristic
372C2×C8×C13C2411yescharacteristic
373C2×C8×C13C2411yescharacteristic
374C2×C8×C13C2412yes—
375C2×C8×C13C2411yescharacteristic
376C2×C8×C13C2412yes—
377C13×C4⋊C4—21no—
378C13×C4⋊C4—22no—
379C13×C4⋊C4—22no—
380C13×C4⋊C4—21no—
381C13×C4⋊C4—22no—
382C13×C4⋊C4—22no—
383C13×C4⋊C4—21no—
384C13×C4⋊C4—21no—
385C13×C4⋊C4—22no—
386C13×C4⋊C4—22no—
387C13×C4⋊C4—21no—
388C13×C4⋊C4—22no—
389C13×C4⋊C4—22no—
390C13×C4⋊C4—21no—
391C13×C4⋊C4—22no—
392C13×C4⋊C4—21no—
393C13×C4⋊C4—21no—
394C13×C4⋊C4—22no—
395C13×C4⋊C4—22no—
396C13×C4⋊C4—22no—
397C13×C4⋊C4C2×D411yescharacteristic
398C13×C4⋊C4C2×D411yescharacteristic
399C13×C4⋊C4C2×D412yes—
400C13×C4⋊C4C2×D412yes—
401C13×C4⋊C4C2×D412yes—
402C13×C4⋊C4C2×D412yes—
403C13×C4⋊C4C2×D412yes—
404C13×C4⋊C4C2412yes—
405C13×C4⋊C4C2411yescharacteristic
406C13×C4⋊C4C2411yescharacteristic
407C13×C4⋊C4C2411yescharacteristic
408C13×C4⋊C4C2411yescharacteristic
409C13×C22⋊C4—22no—
410C13×C22⋊C4—21no—
411C13×C22⋊C4—21no—
412C13×C22⋊C4—21no—
413C13×C22⋊C4—22no—
414C13×C22⋊C4—22no—
415C13×C22⋊C4—22no—
416C13×C22⋊C4—22no—
417C13×C22⋊C4—22no—
418C13×C22⋊C4—22no—
419C13×C22⋊C4—21no—
420C13×C22⋊C4—21no—
421C13×C22⋊C4—22no—
422C13×C22⋊C4—22no—
423C13×C22⋊C4—22no—
424C13×C22⋊C4—22no—
425C13×C22⋊C4—22no—
426C13×C22⋊C4—22no—
427C13×C22⋊C4—21no—
428C13×C22⋊C4—21no—
429C13×C22⋊C4—22no—
430C13×C22⋊C4—22no—
431C42×C13—21no—
432C42×C13—22no—
433C42×C13—21no—
434C42×C13—22no—
435C42×C13—21no—
436C42×C13—22no—
437C42×C13—22no—
438C42×C13—22no—
439C42×C13C2×D412yes—
440C42×C13C2×D411yescharacteristic
441C42×C13C2×D412yes—
442C42×C13C2×D411yescharacteristic
443C42×C13C2411yescharacteristic
444C42×C13C2412yes—
445C42×C13C2412yes—
446C42×C13C2411yescharacteristic
447#3507C2×C1311yescharacteristic, complemented
448#3480C2×C1311yescharacteristic, complemented
449#3403C2×C1312yescomplemented
450#3401C2×C1312yescomplemented
451#3398C2×C1311yescharacteristic, complemented
452#3397C2×C1311yescharacteristic, complemented
453#3394C2×C1311yescharacteristic, complemented
454#3393C2×C1311yescharacteristic, complemented
455#3377C2×C1312yescomplemented
456#3372C2×C1311yescharacteristic, complemented
457#3371C2×C1312yescomplemented
458#3366C2×C1311yescharacteristic, complemented
459#3361C2×C1311yescharacteristic, complemented
460#3360C2×C1311yescharacteristic, complemented
461#3219C2×C1312yescomplemented
462#3214C2×C1311yescharacteristic, complemented
463#3212C2×C1312yescomplemented
464#3210C2×C1311yescharacteristic, complemented
465#3116C2×C1311yescharacteristic, complemented
466#3111C2×C1312yescomplemented
467#3106C2×C1311yescharacteristic, complemented
468#3102C2×C1312yescomplemented
469#2984C2×C1311yescharacteristic, complemented
470C23×C13—21no—
471C23×C13—21no—
472C23×C13—21no—
473C23×C13—22no—
474C23×C13C22×D411yescharacteristic
475Q8×C13—22no—
476Q8×C13—22no—
477Q8×C13—22no—
478Q8×C13—21no—
479Q8×C13—22no—
480Q8×C13—22no—
481Q8×C13—22no—
482Q8×C13—21no—
483Q8×C13—42no—
484Q8×C13—42no—
485Q8×C13—81no—
486D4×C13—21no—
487D4×C13—21no—
488D4×C13—21no—
489D4×C13—21no—
490D4×C13—22no—
491D4×C13—22no—
492D4×C13—21no—
493D4×C13—21no—
494D4×C13—42no—
495D4×C13—44no—
496D4×C13—42no—
497D4×C13—44no—
498D4×C13—42no—
499D4×C13—42no—
500D4×C13—42no—
501D4×C13—81no—
502D4×C13—82no—
503D4×C13—81no—
504C2×C4×C13—22no—
505C2×C4×C13—21no—
506C2×C4×C13—21no—
507C2×C4×C13—21no—
508C2×C4×C13—21no—
509C2×C4×C13—22no—
510C2×C4×C13—21no—
511C2×C4×C13—22no—
512C2×C4×C13—21no—
513C2×C4×C13—21no—
514C2×C4×C13—22no—
515C2×C4×C13—42no—
516C2×C4×C13—41no—
517C2×C4×C13—42no—
518C2×C4×C13—42no—
519C2×C4×C13—44no—
520C2×C4×C13—44no—
521C2×C4×C13—42no—
522C2×C4×C13—42no—
523C2×C4×C13—42no—
524C2×C4×C13—82no—
525C2×C4×C13—82no—
526C2×C4×C13—81no—
527C2×C4×C13—82no—
528C2×C4×C13C22×D412yes—
529C2×C4×C13C22×D411yescharacteristic
530C2×C4×C13C22×D411yescharacteristic
531C2×C4×C13C22×D411yescharacteristic
532C2×C4×C13C22×D412yes—
533C2×C4×C13C22×D412yes—
534C2×C4×C13C22×D412yes—
535C2×C4×C13C22×D411yescharacteristic
536C2×C4×C13C22×D411yescharacteristic
537C2×C4×C13C2511yescharacteristic
538C8×C13—22no—
539C8×C13—21no—
540C8×C13—22no—
541C8×C13—21no—
542C8×C13—21no—
543C8×C13—21no—
544#559C22×C1311yescharacteristic
545#559C22×C1312yes—
546#559C22×C1312yes—
547#557C22×C1311yescharacteristic
548#557C22×C1312yes—
549#556—22no—
550#556C22×C1311yescharacteristic
551#556C22×C1312yes—
552#556C22×C1311yescharacteristic
553#556C22×C1311yescharacteristic
554#554C22×C1311yescharacteristic
555#554C22×C1311yescharacteristic
556#553—21no—
557#553—22no—
558#552—21no—
559#552—21no—
560#550C22×C1311yescharacteristic
561#548—21no—
562#539—22no—
563#536—21no—
564#533C22×C1311yescharacteristic
565#532C22×C1311yescharacteristic
566#532C22×C1312yes—
567#532C22×C1311yescharacteristic
568#529—21no—
569#529—22no—
570#529C22×C1312yes—
571#529C22×C1312yes—
572#520—21no—
573C4×#41—21no—
574C4×#41C22×C1312yes—
575C4×#41C22×C1311yescharacteristic
576C2×C4×Q8C22×C1311yescharacteristic
577#497C22×C1312yes—
578#496C22×C1312yes—
579#496C22×C1312yes—
580#495C22×C1312yes—
581#495C22×C1312yes—
582#494C22×C1311yescharacteristic
583#492C22×C1311yescharacteristic
584#491C22×C1312yes—
585#490C22×C1312yes—
586#489C22×C1312yes—
587#488C22×C1312yes—
588#488C22×C1312yes—
589#487C22×C1311yescharacteristic
590#486C22×C1311yescharacteristic
591#485C22×C1312yes—
592#482C22×C1311yescharacteristic
593#482C22×C1311yescharacteristic
594#479C22×C1312yes—
595#479C22×C1312yes—
596#478C22×C1312yes—
597#478C22×C1312yes—
598#477C22×C1311yescharacteristic
599#477C22×C1311yescharacteristic
600#476C22×C1311yescharacteristic
601#476C22×C1311yescharacteristic
602#464C22×C1312yes—
603#464C22×C1312yes—
604#464C22×C1312yes—
605#464C22×C1312yes—
606#464C22×C1312yes—
607#464C22×C1312yes—
608#463C22×C1312yes—
609#463C22×C1312yes—
610#463C22×C1312yes—
611#463C22×C1312yes—
612#462C22×C1311yescharacteristic
613#462C22×C1312yes—
614#461C22×C1311yescharacteristic
615#461C22×C1311yescharacteristic
616#461C22×C1311yescharacteristic
617#461C22×C1312yes—
618#460C22×C1311yescharacteristic
619#460C22×C1312yes—
620#459C22×C1311yescharacteristic
621#459C22×C1311yescharacteristic
622#459C22×C1311yescharacteristic
623#459C22×C1312yes—
624#452C22×C1312yes—
625#452C22×C1312yes—
626#452C22×C1312yes—
627#449C22×C1312yes—
628#449C22×C1311yescharacteristic
629#449C22×C1311yescharacteristic
630#449C22×C1312yes—
631#446C22×C1311yescharacteristic
632#446C22×C1312yes—
633#446C22×C1311yescharacteristic
634#446C22×C1312yes—
635C8×Q8C22×C1311yescharacteristic
636C8×Q8C22×C1311yescharacteristic
637#442C22×C1312yes—
638#441C22×C1312yes—
639#441C22×C1312yes—
640#440C22×C1312yes—
641#440C22×C1312yes—
642#440C22×C1312yes—
643C4×Q16C22×C1312yes—
644C4×SD16C22×C1312yes—
645C4×SD16C22×C1312yes—
646C4×SD16C22×C1311yescharacteristic
647C4×SD16C22×C1311yescharacteristic
648C4×D8C22×C1312yes—
649C4×D8C22×C1311yescharacteristic
650C4×D8C22×C1311yescharacteristic
651#432C22×C1312yes—
652#432C22×C1311yescharacteristic
653#431C22×C1312yes—
654#431C22×C1311yescharacteristic
655C22×C13—21no—
656C22×C13—21no—
657C22×C13—21no—
658C22×C13—41no—
659C22×C13—41no—
660C22×C13—42no—
661C22×C13—41no—
662C22×C13—41no—
663C22×C13—42no—
664C22×C13—41no—
665C22×C13—41no—
666C22×C13—42no—
667C22×C13—41no—
668C22×C13—41no—
669C22×C13—41no—
670C22×C13C23×D411yescharacteristic
671C4×C13—22no—
672C4×C13—22no—
673C4×C13—21no—
674C4×C13—21no—
675C4×C13—21no—
676C4×C13—21no—
677C4×C13—22no—
678C4×C13—22no—
679C4×C13—41no—
680C4×C13—42no—
681C4×C13—41no—
682C4×C13—42no—
683C4×C13—42no—
684C4×C13—41no—
685C4×C13—41no—
686C4×C13—41no—
687C4×C13#57512yes—
688C4×C13#58511yescharacteristic
689C4×C13#58511yescharacteristic
690C2×#41—21no—
691C2×#41—21no—
692C2×#41C23×C1312yes—
693C2×#41C23×C1311yescharacteristic
694C22×Q8D4×C1311yescharacteristic
695C2×Q16C23×C1312yes—
696C2×Q16C23×C1312yes—
697C2×Q16C23×C1312yes—
698C2×SD16C23×C1311yescharacteristic
699C2×SD16C23×C1311yescharacteristic
700C2×SD16C23×C1312yes—
701C2×SD16C23×C1312yes—
702C2×SD16C23×C1312yes—
703C2×SD16C23×C1312yes—
704C2×SD16C23×C1312yes—
705C2×D8C23×C1311yescharacteristic
706C2×D8C23×C1312yes—
707C2×D8C23×C1311yescharacteristic
708C2×D8C23×C1312yes—
709C4⋊Q8—22no—
710C4⋊Q8C23×C1311yescharacteristic
711C4⋊Q8C23×C1312yes—
712C4⋊Q8C23×C1311yescharacteristic
713C4⋊Q8C23×C1311yescharacteristic
714C4⋊Q8C23×C1311yescharacteristic
715#127C23×C1311yescharacteristic
716#127C23×C1312yes—
717#127C23×C1311yescharacteristic
718#126—22no—
719#126—22no—
720#126—22no—
721#126—22no—
722#126—22no—
723#126—22no—
724#126—22no—
725#125—21no—
726#125—22no—
727#125—22no—
728#125—22no—
729#125—21no—
730#125C23×C1312yes—
731#125C23×C1312yes—
732#124—21no—
733#124—22no—
734#124—22no—
735#124—21no—
736#124C23×C1312yes—
737#124C23×C1312yes—
738#124C23×C1312yes—
739#124C23×C1312yes—
740#124C23×C1312yes—
741#123—22no—
742#123—22no—
743#123—22no—
744#123—22no—
745#123—22no—
746#123—22no—
747#123—22no—
748C22⋊Q8—21no—
749C22⋊Q8—22no—
750C22⋊Q8—21no—
751C22⋊Q8—21no—
752C22⋊Q8—21no—
753C22⋊Q8—21no—
754C22⋊Q8—21no—
755C22⋊Q8—22no—
756C22⋊Q8—22no—
757C22⋊Q8C23×C1312yes—
758#121—21no—
759#121—21no—
760#121—22no—
761#121—22no—
762#121—21no—
763#121—21no—
764#121—22no—
765#121C23×C1311yescharacteristic
766#121C23×C1311yescharacteristic
767C4×Q8—21no—
768C4×Q8—22no—
769C4×Q8—21no—
770C4×Q8D4×C1311yescharacteristic
771C4×Q8D4×C1311yescharacteristic
772C4×Q8D4×C1312yes—
773C4×Q8C23×C1312yes—
774C4×Q8C23×C1311yescharacteristic
775C4×Q8C23×C1311yescharacteristic
776C4×Q8C23×C1312yes—
777C4×Q8C23×C1312yes—
778C4×Q8C23×C1312yes—
779C4×Q8C23×C1312yes—
780C4×Q8C23×C1311yescharacteristic
781C4×Q8C23×C1311yescharacteristic
782C4×Q8C23×C1312yes—
783C4×D4—21no—
784C4×D4—22no—
785C4×D4—22no—
786C4×D4—21no—
787C4×D4—22no—
788C4×D4—22no—
789C4×D4—21no—
790C4×D4—22no—
791C4×D4—22no—
792C4×D4—22no—
793C4×D4—21no—
794C4×D4—22no—
795C4×D4—21no—
796C4×D4—21no—
797C4×D4C23×C1311yescharacteristic
798C4×D4C23×C1312yes—
799C4×D4C23×C1312yes—
800C4×D4C23×C1311yescharacteristic
801C4×D4C23×C1312yes—
802C4×D4C23×C1312yes—
803C4×D4C23×C1311yescharacteristic
804C4×D4C23×C1311yescharacteristic
805#117—21no—
806#117—21no—
807#117—22no—
808#117—21no—
809#117—21no—
810#117—22no—
811#117—21no—
812#117—22no—
813#117—22no—
814#117C23×C1311yescharacteristic
815C2×C4⋊C4—21no—
816C2×C4⋊C4—21no—
817C2×C4⋊C4D4×C1311yescharacteristic
818C2×C4⋊C4D4×C1312yes—
819C2×C42—22no—
820C2×C42—21no—
821C2×C42C23×C1312yes—
822C2×C42C23×C1311yescharacteristic
823#107C23×C1311yescharacteristic
824#107C23×C1312yes—
825#107C23×C1311yescharacteristic
826#106C23×C1311yescharacteristic
827#106C23×C1311yescharacteristic
828#106C23×C1312yes—
829C4⋊C8C23×C1312yes—
830C4⋊C8C23×C1311yescharacteristic
831C4⋊C8C23×C1312yes—
832C4⋊C8C23×C1311yescharacteristic
833C4⋊C8C23×C1311yescharacteristic
834C4⋊C8C23×C1311yescharacteristic
835C4⋊C8C23×C1312yes—
836C4⋊C8C23×C1312yes—
837#103C23×C1312yes—
838#103C23×C1311yescharacteristic
839#103C23×C1311yescharacteristic
840#103C23×C1312yes—
841#103C23×C1312yes—
842#103C23×C1312yes—
843#103C23×C1312yes—
844#103C23×C1312yes—
845#103C23×C1312yes—
846#102C23×C1311yescharacteristic
847#102C23×C1311yescharacteristic
848#102C23×C1311yescharacteristic
849#102C23×C1311yescharacteristic
850#102C23×C1311yescharacteristic
851#102C23×C1312yes—
852#102C23×C1311yescharacteristic
853#102C23×C1312yes—
854#102C23×C1312yes—
855#102C23×C1312yes—
856#102C23×C1312yes—
857C22⋊C8C23×C1311yescharacteristic
858C22⋊C8C23×C1312yes—
859C22⋊C8C23×C1311yescharacteristic
860#97C23×C1312yes—
861#97C23×C1312yes—
862#97C23×C1312yes—
863C4×C8C23×C1311yescharacteristic
864C4×C8C23×C1311yescharacteristic
865C4×C8C23×C1312yes—
866C4×C8C23×C1312yes—
867C2×C13—41no—
868C2×C13—81no—
869C2×C13—81no—
870C2×C13—81no—
871C2×C13—82no—
872C2×C13#348711yescharacteristic
873C2×C13C2×#57511yescharacteristic
874C2×C13#358411yescharacteristic
875#41—41no—
876#41—42no—
877#41—42no—
878#41—41no—
879#41—44no—
880#41—44no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—42no—
884C2×Q8C2×D4×C1311yescharacteristic
885C2×Q8C2×D4×C1311yescharacteristic
886C2×Q8C2×D4×C1312yes—
887C2×Q8C24×C1311yescharacteristic
888C2×Q8C24×C1312yes—
889C2×Q8C24×C1312yes—
890C2×D4—21no—
891C2×D4—22no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—22no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—22no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4C24×C1311yescharacteristic
901C2×D4C24×C1312yes—
902C2×D4C24×C1311yescharacteristic
903C2×D4C24×C1311yescharacteristic
904C22×C4—22no—
905C22×C4—21no—
906C22×C4—22no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—22no—
911C22×C4—21no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4C2×D4×C1311yescharacteristic
915C22×C4C2×D4×C1312yes—
916C22×C4C2×D4×C1311yescharacteristic
917C22×C4C2×D4×C1312yes—
918C22×C4C24×C1311yescharacteristic
919Q16—42no—
920Q16—42no—
921Q16—42no—
922SD16—42no—
923SD16—42no—
924SD16—42no—
925SD16—42no—
926SD16—42no—
927SD16—41no—
928SD16—41no—
929D8—42no—
930D8—41no—
931D8—42no—
932D8—41no—
933C2×C8C24×C1311yescharacteristic
934C2×C8C24×C1311yescharacteristic
935C2×C8C24×C1311yescharacteristic
936C2×C8C24×C1312yes—
937C2×C8C24×C1311yescharacteristic
938C2×C8C24×C1312yes—
939C4⋊C4—21no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—21no—
943C4⋊C4—22no—
944C4⋊C4—22no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—21no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—21no—
953C4⋊C4—22no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4C2×D4×C1311yescharacteristic
960C4⋊C4C2×D4×C1311yescharacteristic
961C4⋊C4C2×D4×C1312yes—
962C4⋊C4C2×D4×C1312yes—
963C4⋊C4C2×D4×C1312yes—
964C4⋊C4C2×D4×C1312yes—
965C4⋊C4C2×D4×C1312yes—
966C4⋊C4C24×C1312yes—
967C4⋊C4C24×C1311yescharacteristic
968C4⋊C4C24×C1311yescharacteristic
969C4⋊C4C24×C1311yescharacteristic
970C4⋊C4C24×C1311yescharacteristic
971C22⋊C4—22no—
972C22⋊C4—21no—
973C22⋊C4—21no—
974C22⋊C4—21no—
975C22⋊C4—22no—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—22no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—21no—
982C22⋊C4—21no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—21no—
990C22⋊C4—21no—
991C22⋊C4—22no—
992C22⋊C4—22no—
993C42—21no—
994C42—22no—
995C42—21no—
996C42—22no—
997C42—21no—
998C42—22no—
999C42—22no—
1000C42—22no—
1001C42C2×D4×C1312yes—
1002C42C2×D4×C1311yescharacteristic
1003C42C2×D4×C1312yes—
1004C42C2×D4×C1311yescharacteristic
1005C42C24×C1311yescharacteristic
1006C42C24×C1312yes—
1007C42C24×C1312yes—
1008C42C24×C1311yescharacteristic
1009C13#6190211yescharacteristic, direct product factor, Sylow
1010C23—21no—
1011C23—21no—
1012C23—22no—
1013C23—21no—
1014C23C22×D4×C1311yescharacteristic
1015Q8—22no—
1016Q8—22no—
1017Q8—22no—
1018Q8—21no—
1019Q8—22no—
1020Q8—22no—
1021Q8—22no—
1022Q8—21no—
1023Q8—42no—
1024Q8—42no—
1025Q8—81no—
1026D4—21no—
1027D4—21no—
1028D4—21no—
1029D4—21no—
1030D4—22no—
1031D4—22no—
1032D4—21no—
1033D4—21no—
1034D4—42no—
1035D4—44no—
1036D4—42no—
1037D4—42no—
1038D4—42no—
1039D4—44no—
1040D4—42no—
1041D4—81no—
1042D4—82no—
1043D4—81no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—22no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—42no—
1056C2×C4—41no—
1057C2×C4—42no—
1058C2×C4—44no—
1059C2×C4—42no—
1060C2×C4—44no—
1061C2×C4—42no—
1062C2×C4—42no—
1063C2×C4—42no—
1064C2×C4—82no—
1065C2×C4—82no—
1066C2×C4—81no—
1067C2×C4—82no—
1068C2×C4C22×D4×C1312yes—
1069C2×C4C22×D4×C1311yescharacteristic
1070C2×C4C22×D4×C1311yescharacteristic
1071C2×C4C22×D4×C1311yescharacteristic
1072C2×C4C22×D4×C1312yes—
1073C2×C4C22×D4×C1312yes—
1074C2×C4C22×D4×C1312yes—
1075C2×C4C22×D4×C1311yescharacteristic
1076C2×C4C22×D4×C1311yescharacteristic
1077C2×C4C25×C1311yescharacteristic
1078C8—22no—
1079C8—21no—
1080C8—22no—
1081C8—21no—
1082C8—21no—
1083C8—21no—
1084C22—21no—
1085C22—21no—
1086C22—21no—
1087C22—42no—
1088C22—41no—
1089C22—41no—
1090C22—41no—
1091C22—41no—
1092C22—41no—
1093C22—42no—
1094C22—41no—
1095C22—41no—
1096C22—42no—
1097C22—41no—
1098C22—41no—
1099C22C23×D4×C1311yescharacteristic
1100C4—21no—
1101C4—22no—
1102C4—22no—
1103C4—22no—
1104C4—22no—
1105C4—21no—
1106C4—21no—
1107C4—21no—
1108C4—41no—
1109C4—41no—
1110C4—41no—
1111C4—41no—
1112C4—42no—
1113C4—41no—
1114C4—42no—
1115C4—42no—
1116C4C13×#57512yes—
1117C4C13×#58511yescharacteristic
1118C4C13×#58511yescharacteristic
1119C2—41no—
1120C2—81no—
1121C2—81no—
1122C2—82no—
1123C2—81no—
1124C2C13×#348711yescharacteristic
1125C2C2×C13×#57511yescharacteristic
1126C2C13×#358411yescharacteristic
subgroupG/H
center, socleC22×C13C23×D4
commutator, Frattini, cosocleC2×C4C25×C13
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C4×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3507C2semidirect
2. C13×#3480C2semidirect
3. C13×#3403C2semidirect
4. C13×#3401C2semidirect
5. C13×#3398C2semidirect
6. C13×#3397C2semidirect
7. C13×#3394C2semidirect
8. C13×#3393C2semidirect
9. C13×#3377C2semidirect
10. C13×#3372C2semidirect
11. C13×#3371C2semidirect
12. C13×#3366C2semidirect
13. C13×#3361C2semidirect
14. C13×#3360C2semidirect
15. C13×#3219C2semidirect
16. C13×#3214C2semidirect
17. C13×#3212C2semidirect
18. C13×#3210C2semidirect
19. C13×#3116C2semidirect
20. C13×#3111C2semidirect
21. C13×#3106C2semidirect
22. C13×#3102C2semidirect
23. C13×#2984C2semidirect
312. #61902C13direct (N × H)
447. #3507C2×C13semidirect
448. #3480C2×C13semidirect
449. #3403C2×C13semidirect
450. #3401C2×C13semidirect
451. #3398C2×C13semidirect
452. #3397C2×C13semidirect
453. #3394C2×C13semidirect
454. #3393C2×C13semidirect
455. #3377C2×C13semidirect
456. #3372C2×C13semidirect
457. #3371C2×C13semidirect
458. #3366C2×C13semidirect
459. #3361C2×C13semidirect
460. #3360C2×C13semidirect
461. #3219C2×C13semidirect
462. #3214C2×C13semidirect
463. #3212C2×C13semidirect
464. #3210C2×C13semidirect
465. #3116C2×C13semidirect
466. #3111C2×C13semidirect
467. #3106C2×C13semidirect
468. #3102C2×C13semidirect
469. #2984C2×C13semidirect
1009. C13#61902direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35072
C13×#34802
C13×#34032
C13×#34012
C13×#33982
C13×#33972
C13×#33942
C13×#33932
C13×#33772
C13×#33722
C13×#33712
C13×#33662
C13×#33612
C13×#33602
C13×#32192
C13×#32142
C13×#32122
C13×#32102
C13×#31162
C13×#31112
C13×#31062
C13×#31022
C13×#29842
#6190213