Finite Group Databasebeta

← C13×#18253 #15704592

Subgroups — C13×#18253 #15704592

Order 3328.

1196 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3535C211yesmaximal, characteristic, complemented
2C13×#3007C211yesmaximal, characteristic, complemented
3C13×#3002C211yesmaximal, characteristic, complemented
4C13×#2430C211yesmaximal, characteristic, complemented
5C13×#1606C211yesmaximal, characteristic, complemented
6C13×#1605C211yesmaximal, characteristic, complemented
7C13×#1603C211yesmaximal, characteristic, complemented
8C13×#1602C211yesmaximal, characteristic, complemented
9C13×#1600C211yesmaximal, characteristic, complemented
10C13×#1599C211yesmaximal, characteristic, complemented
11C13×#1597C211yesmaximal, characteristic, complemented
12C13×#1596C211yesmaximal, characteristic, complemented
13C13×#1504C211yesmaximal, characteristic, complemented
14C2×C13×#328C211yesmaximal, characteristic, complemented
15C13×#1468C211yesmaximal, characteristic, complemented
16C22×C13×#41C2211yescharacteristic
17C2×C13×#137—21no—
18C2×C13×#135—21no—
19C13×#563—21no—
20C13×#562—21no—
21C13×#554—21no—
22C13×#552—21no—
23C13×#551—21no—
24C13×#551—21no—
25C13×#547—21no—
26C13×#546—21no—
27C13×#544C2211yescharacteristic
28C13×#543C2211yescharacteristic
29C13×#542—21no—
30C13×#539—21no—
31C13×#539—21no—
32C13×#539C2211yescharacteristic
33C13×#538C2211yescharacteristic
34C13×#536—21no—
35C13×#525C2211yescharacteristic
36C2×C13×#123C2211yescharacteristic
37C2×C13×C22⋊Q8C2211yescharacteristic
38C2×C13×#121—21no—
39C13×#452—21no—
40C13×#452—21no—
41C13×#452—21no—
42C13×#451C2211yescharacteristic
43C13×#451C2211yescharacteristic
44C13×#451C2211yescharacteristic
45C13×#450C2211yescharacteristic
46C13×#450C2211yescharacteristic
47C13×#450C2211yescharacteristic
48C13×#449—21no—
49C13×#448C2211yescharacteristic
50C13×#447C2211yescharacteristic
51C13×#417—21no—
52C13×#416—21no—
53C13×#407C2211yescharacteristic
54C2×C13×C22⋊C8C2211yescharacteristic
55C13×#395C2211yescharacteristic
56C13×#394C2211yescharacteristic
57C13×#393C2211yescharacteristic
58C13×#392C2211yescharacteristic
59C13×#386—21no—
60C13×#386—21no—
61C13×#385—21no—
62C2×C13×#95C2211yescharacteristic
63C13×#328C2211yescharacteristic
64C13×#328C2211yescharacteristic
65C13×#328C2211yescharacteristic
66C13×#328C2211yescharacteristic
67C13×#328C2211yescharacteristic
68C13×#328C2211yescharacteristic
69C13×#327C2211yescharacteristic
70C13×#327C2211yescharacteristic
71C13×#324C2211yescharacteristic
72C13×#324C2211yescharacteristic
73C13×#323C2211yescharacteristic
74C13×#323C2211yescharacteristic
75C2×C13×#41—21no—
76C2×C13×#41—21no—
77C2×C13×#41—21no—
78C2×C13×#41—21no—
79C2×C13×#41—21no—
80C2×C13×#41—44no—
81C2×C13×#41D411yescharacteristic, complemented
82C22×Q8×C13D411yescharacteristic, complemented
83C22×Q8×C13C2311yescharacteristic
84C22×D4×C13—21no—
85C22×D4×C13—21no—
86C22×D4×C13D411yescharacteristic
87C22×D4×C13C2311yescharacteristic
88C23×C4×C13—21no—
89C23×C4×C13—21no—
90C23×C4×C13C2311yescharacteristic
91C13×#137—44no—
92C13×#135—44no—
93C2×C13×Q16—21no—
94C2×C13×Q16—21no—
95C2×C13×Q16—21no—
96C2×C13×SD16—21no—
97C2×C13×SD16—21no—
98C2×C13×SD16—21no—
99C2×C13×SD16—21no—
100C2×C13×D8—21no—
101C2×C13×M16—21no—
102C22×C8×C13—21no—
103C13×C4⋊Q8—21no—
104C13×C4⋊Q8—21no—
105C13×C4⋊Q8—21no—
106C13×#126—21no—
107C13×#126—21no—
108C13×#126—21no—
109C13×#126—21no—
110C13×#126—21no—
111C13×#126—21no—
112C13×#125—21no—
113C13×#125—21no—
114C13×#125—21no—
115C13×#125—21no—
116C13×#125—21no—
117C13×#124—21no—
118C13×#124—21no—
119C13×#124—21no—
120C13×#124—21no—
121C13×#123—21no—
122C13×#123—21no—
123C13×#123—21no—
124C13×#123—21no—
125C13×#123—21no—
126C13×#123—21no—
127C13×#123—21no—
128C13×#123—21no—
129C13×#123—21no—
130C13×#123—21no—
131C13×#123—21no—
132C13×#123—21no—
133C13×#123—21no—
134C13×#123—21no—
135C13×C22⋊Q8—21no—
136C13×C22⋊Q8—21no—
137C13×C22⋊Q8—21no—
138C13×C22⋊Q8—21no—
139C13×C22⋊Q8—21no—
140C13×C22⋊Q8—21no—
141C13×C22⋊Q8—21no—
142C13×C22⋊Q8—21no—
143C13×C22⋊Q8—21no—
144C13×C22⋊Q8—21no—
145C13×C22⋊Q8—21no—
146C13×C22⋊Q8—21no—
147C13×C22⋊Q8—21no—
148C13×C22⋊Q8—21no—
149C13×C22⋊Q8D411yescharacteristic, complemented
150C13×C22⋊Q8D411yescharacteristic, complemented
151C13×C22⋊Q8D411yescharacteristic, complemented
152C13×C22⋊Q8C2311yescharacteristic
153C13×C22⋊Q8C2311yescharacteristic
154C13×C22⋊Q8C2311yescharacteristic
155C13×#121—21no—
156C13×#121—21no—
157C13×#121—21no—
158C13×#121—21no—
159C13×#121—44no—
160C13×#121D411yescharacteristic, complemented
161C13×#121C2311yescharacteristic
162C13×#120—21no—
163C13×#120—21no—
164C4×Q8×C13—21no—
165C4×D4×C13—21no—
166C4×D4×C13—21no—
167C4×D4×C13—21no—
168C4×D4×C13—21no—
169C4×D4×C13—21no—
170C4×D4×C13—21no—
171C4×D4×C13—21no—
172C13×#117—21no—
173C13×#117—21no—
174C13×#117—21no—
175C13×#117D411yescharacteristic, complemented
176C2×C13×C4⋊C4—21no—
177C2×C13×C4⋊C4—21no—
178C2×C13×C4⋊C4—21no—
179C2×C13×C4⋊C4D411yescharacteristic
180C2×C13×C4⋊C4D411yescharacteristic, complemented
181C2×C13×C4⋊C4C2311yescharacteristic
182C2×C13×C22⋊C4—21no—
183C2×C13×C22⋊C4—21no—
184C2×C13×C22⋊C4—21no—
185C2×C13×C22⋊C4—21no—
186C2×C13×C22⋊C4—21no—
187C2×C13×C22⋊C4—21no—
188C2×C13×C22⋊C4D411yescharacteristic
189C2×C13×C22⋊C4D411yescharacteristic
190C2×C13×C22⋊C4C2311yescharacteristic
191C13×#103—21no—
192C13×#103—21no—
193C13×#103—21no—
194C13×#103—21no—
195C13×#102—21no—
196C13×#102—21no—
197C13×#102—21no—
198C13×#102—21no—
199C13×C22⋊C8—21no—
200C13×C22⋊C8—21no—
201C13×C22⋊C8C2311yescharacteristic
202C13×C22⋊C8C2311yescharacteristic
203C13×C22⋊C8C2311yescharacteristic
204C13×C22⋊C8C2311yescharacteristic
205C13×#95—21no—
206C13×#95—21no—
207C13×#95—21no—
208C13×#95C2311yescharacteristic
209C13×#95C2311yescharacteristic
210#18253C1311yesmaximal, characteristic, direct product factor, Sylow
211C24×C13—21no—
212C24×C13C2×D411yescharacteristic
213C24×C13C2×D411yescharacteristic
214C13×#41—24no—
215C13×#41—24no—
216C13×#41—42no—
217C13×#41—42no—
218C13×#41—42no—
219C13×#41—42no—
220C13×#41—42no—
221C13×#41—42no—
222C13×#41—42no—
223C13×#41—82no—
224C2×Q8×C13—21no—
225C2×Q8×C13—21no—
226C2×Q8×C13—21no—
227C2×Q8×C13—21no—
228C2×Q8×C13—21no—
229C2×Q8×C13—42no—
230C2×Q8×C13—42no—
231C2×Q8×C13C2×D411yescharacteristic
232C2×Q8×C13C2×D411yescharacteristic
233C2×Q8×C13C2×D411yescharacteristic
234C2×D4×C13—24no—
235C2×D4×C13—21no—
236C2×D4×C13—21no—
237C2×D4×C13—21no—
238C2×D4×C13—21no—
239C2×D4×C13—21no—
240C2×D4×C13—21no—
241C2×D4×C13—21no—
242C2×D4×C13—21no—
243C2×D4×C13—21no—
244C2×D4×C13—42no—
245C2×D4×C13—42no—
246C2×D4×C13—42no—
247C2×D4×C13—41no—
248C2×D4×C13—41no—
249C2×D4×C13—42no—
250C2×D4×C13—42no—
251C2×D4×C13—81no—
252C2×D4×C13C2×D411yescharacteristic
253C22×C4×C13—21no—
254C22×C4×C13—21no—
255C22×C4×C13—21no—
256C22×C4×C13—21no—
257C22×C4×C13—21no—
258C22×C4×C13—21no—
259C22×C4×C13—21no—
260C22×C4×C13—21no—
261C22×C4×C13—21no—
262C22×C4×C13—21no—
263C22×C4×C13—42no—
264C22×C4×C13—42no—
265C22×C4×C13—42no—
266C22×C4×C13—42no—
267C22×C4×C13—41no—
268C22×C4×C13—41no—
269C22×C4×C13—42no—
270C22×C4×C13—81no—
271C22×C4×C13C2×D411yescharacteristic
272C22×C4×C13C2×D411yescharacteristic
273C22×C4×C13C2×D411yescharacteristic
274C22×C4×C13C2×D411yescharacteristic
275C22×C4×C13C2×D411yescharacteristic
276C22×C4×C13C2×D411yescharacteristic
277C22×C4×C13C2×D411yescharacteristic
278C22×C4×C13C2×D411yescharacteristic
279C22×C4×C13C2411yescharacteristic
280C13×Q16—42no—
281C13×Q16—42no—
282C13×Q16—42no—
283C13×SD16—42no—
284C13×SD16—42no—
285C13×SD16—42no—
286C13×SD16—42no—
287C13×D8—42no—
288C13×M16—42no—
289C2×C8×C13—21no—
290C2×C8×C13—21no—
291C2×C8×C13—21no—
292C2×C8×C13—21no—
293C2×C8×C13—42no—
294C13×C4⋊C4—21no—
295C13×C4⋊C4—21no—
296C13×C4⋊C4—21no—
297C13×C4⋊C4—21no—
298C13×C4⋊C4—21no—
299C13×C4⋊C4—21no—
300C13×C4⋊C4—21no—
301C13×C4⋊C4—21no—
302C13×C4⋊C4—21no—
303C13×C4⋊C4—21no—
304C13×C4⋊C4—21no—
305C13×C4⋊C4—21no—
306C13×C4⋊C4—21no—
307C13×C4⋊C4—21no—
308C13×C4⋊C4—21no—
309C13×C4⋊C4—21no—
310C13×C4⋊C4—21no—
311C13×C4⋊C4—21no—
312C13×C4⋊C4—21no—
313C13×C4⋊C4—21no—
314C13×C4⋊C4—21no—
315C13×C4⋊C4—21no—
316C13×C4⋊C4—21no—
317C13×C4⋊C4—42no—
318C13×C4⋊C4C2×D411yescharacteristic
319C13×C4⋊C4C2×D411yescharacteristic
320C13×C4⋊C4C2×D411yescharacteristic
321C13×C4⋊C4C2×D411yescharacteristic
322C13×C22⋊C4—21no—
323C13×C22⋊C4—21no—
324C13×C22⋊C4—21no—
325C13×C22⋊C4—21no—
326C13×C22⋊C4—21no—
327C13×C22⋊C4—21no—
328C13×C22⋊C4—21no—
329C13×C22⋊C4—21no—
330C13×C22⋊C4—21no—
331C13×C22⋊C4—21no—
332C13×C22⋊C4—21no—
333C13×C22⋊C4—21no—
334C13×C22⋊C4—21no—
335C13×C22⋊C4—21no—
336C13×C22⋊C4—21no—
337C13×C22⋊C4—21no—
338C13×C22⋊C4—21no—
339C13×C22⋊C4—21no—
340C13×C22⋊C4—21no—
341C13×C22⋊C4—21no—
342C13×C22⋊C4—21no—
343C13×C22⋊C4—21no—
344C13×C22⋊C4—21no—
345C13×C22⋊C4—42no—
346C13×C22⋊C4—42no—
347C13×C22⋊C4—42no—
348C13×C22⋊C4—81no—
349C42×C13—21no—
350C42×C13—21no—
351C42×C13—21no—
352C42×C13—21no—
353C42×C13—21no—
354#3535C2×C1311yescharacteristic, complemented
355#3007C2×C1311yescharacteristic, complemented
356#3002C2×C1311yescharacteristic, complemented
357#2430C2×C1311yescharacteristic, complemented
358#1606C2×C1311yescharacteristic, complemented
359#1605C2×C1311yescharacteristic, complemented
360#1603C2×C1311yescharacteristic, complemented
361#1602C2×C1311yescharacteristic, complemented
362#1600C2×C1311yescharacteristic, complemented
363#1599C2×C1311yescharacteristic, complemented
364#1597C2×C1311yescharacteristic, complemented
365#1596C2×C1311yescharacteristic, complemented
366#1504C2×C1311yescharacteristic, complemented
367C2×#328C2×C1311yescharacteristic, complemented
368#1468C2×C1311yescharacteristic, complemented
369C23×C13—21no—
370C23×C13—21no—
371C23×C13—22no—
372C23×C13—22no—
373C23×C13—21no—
374C23×C13—21no—
375C23×C13—21no—
376C23×C13—21no—
377C23×C13—41no—
378C23×C13—41no—
379C23×C13—41no—
380C23×C13—41no—
381C23×C13—41no—
382C23×C13—41no—
383C23×C13—41no—
384C23×C13—41no—
385C23×C13—41no—
386C23×C13#12011yescharacteristic
387C23×C13#12011yescharacteristic
388C23×C13C22×D411yescharacteristic
389Q8×C13—22no—
390Q8×C13—22no—
391Q8×C13—41no—
392Q8×C13—41no—
393Q8×C13—41no—
394Q8×C13—41no—
395Q8×C13—41no—
396Q8×C13—81no—
397Q8×C13—81no—
398Q8×C13—81no—
399D4×C13—22no—
400D4×C13—22no—
401D4×C13—41no—
402D4×C13—41no—
403D4×C13—41no—
404D4×C13—44no—
405D4×C13—41no—
406D4×C13—41no—
407D4×C13—44no—
408D4×C13—42no—
409D4×C13—42no—
410D4×C13—81no—
411D4×C13—81no—
412D4×C13—81no—
413D4×C13—81no—
414D4×C13—84no—
415C2×C4×C13—22no—
416C2×C4×C13—22no—
417C2×C4×C13—22no—
418C2×C4×C13—22no—
419C2×C4×C13—21no—
420C2×C4×C13—21no—
421C2×C4×C13—21no—
422C2×C4×C13—21no—
423C2×C4×C13—21no—
424C2×C4×C13—21no—
425C2×C4×C13—21no—
426C2×C4×C13—21no—
427C2×C4×C13—21no—
428C2×C4×C13—21no—
429C2×C4×C13—21no—
430C2×C4×C13—21no—
431C2×C4×C13—41no—
432C2×C4×C13—41no—
433C2×C4×C13—41no—
434C2×C4×C13—41no—
435C2×C4×C13—44no—
436C2×C4×C13—44no—
437C2×C4×C13—41no—
438C2×C4×C13—41no—
439C2×C4×C13—41no—
440C2×C4×C13—41no—
441C2×C4×C13—42no—
442C2×C4×C13—41no—
443C2×C4×C13—41no—
444C2×C4×C13—41no—
445C2×C4×C13—41no—
446C2×C4×C13—41no—
447C2×C4×C13—81no—
448C2×C4×C13—81no—
449C2×C4×C13—81no—
450C2×C4×C13—81no—
451C2×C4×C13—81no—
452C2×C4×C13—81no—
453C2×C4×C13—84no—
454C2×C4×C13#12011yescharacteristic
455C2×C4×C13#12011yescharacteristic
456C2×C4×C13C22×D411yescharacteristic
457C2×C4×C13C22×D411yescharacteristic
458C8×C13—41no—
459C8×C13—41no—
460C8×C13—41no—
461C8×C13—41no—
462C22×#41C22×C1311yescharacteristic
463C2×#137—21no—
464C2×#135—21no—
465#563—21no—
466#562—21no—
467#554—21no—
468#552—21no—
469#551—21no—
470#551—21no—
471#547—21no—
472#546—21no—
473#544C22×C1311yescharacteristic
474#543C22×C1311yescharacteristic
475#542—21no—
476#539—21no—
477#539—21no—
478#539C22×C1311yescharacteristic
479#538C22×C1311yescharacteristic
480#536—21no—
481#525C22×C1311yescharacteristic
482C2×#123C22×C1311yescharacteristic
483C2×C22⋊Q8C22×C1311yescharacteristic
484C2×#121—21no—
485#452—21no—
486#452—21no—
487#452—21no—
488#451C22×C1311yescharacteristic
489#451C22×C1311yescharacteristic
490#451C22×C1311yescharacteristic
491#450C22×C1311yescharacteristic
492#450C22×C1311yescharacteristic
493#450C22×C1311yescharacteristic
494#449—21no—
495#448C22×C1311yescharacteristic
496#447C22×C1311yescharacteristic
497#417—21no—
498#416—21no—
499#407C22×C1311yescharacteristic
500C2×C22⋊C8C22×C1311yescharacteristic
501#395C22×C1311yescharacteristic
502#394C22×C1311yescharacteristic
503#393C22×C1311yescharacteristic
504#392C22×C1311yescharacteristic
505#386—21no—
506#386—21no—
507#385—21no—
508C2×#95C22×C1311yescharacteristic
509#328C22×C1311yescharacteristic
510#328C22×C1311yescharacteristic
511#328C22×C1311yescharacteristic
512#328C22×C1311yescharacteristic
513#328C22×C1311yescharacteristic
514#328C22×C1311yescharacteristic
515#327C22×C1311yescharacteristic
516#327C22×C1311yescharacteristic
517#324C22×C1311yescharacteristic
518#324C22×C1311yescharacteristic
519#323C22×C1311yescharacteristic
520#323C22×C1311yescharacteristic
521C22×C13—21no—
522C22×C13—21no—
523C22×C13—21no—
524C22×C13—21no—
525C22×C13—21no—
526C22×C13—21no—
527C22×C13—21no—
528C22×C13—42no—
529C22×C13—42no—
530C22×C13—42no—
531C22×C13—42no—
532C22×C13—41no—
533C22×C13—41no—
534C22×C13—41no—
535C22×C13—41no—
536C22×C13—42no—
537C22×C13—41no—
538C22×C13—41no—
539C22×C13—81no—
540C22×C13—81no—
541C22×C13—81no—
542C22×C13—81no—
543C22×C13—81no—
544C22×C13—81no—
545C22×C13B(4,𝔽2)12yes—
546C22×C13C2×#12011yescharacteristic
547C22×C13#57711yescharacteristic
548C22×C13#57811yescharacteristic
549C4×C13—21no—
550C4×C13—21no—
551C4×C13—21no—
552C4×C13—21no—
553C4×C13—42no—
554C4×C13—41no—
555C4×C13—41no—
556C4×C13—41no—
557C4×C13—41no—
558C4×C13—41no—
559C4×C13—41no—
560C4×C13—42no—
561C4×C13—41no—
562C4×C13—41no—
563C4×C13—41no—
564C4×C13—41no—
565C4×C13—81no—
566C2×#41—21no—
567C2×#41—21no—
568C2×#41—21no—
569C2×#41—21no—
570C2×#41—21no—
571C2×#41—44no—
572C2×#41D4×C1311yescharacteristic, complemented
573C22×Q8D4×C1311yescharacteristic, complemented
574C22×Q8C23×C1311yescharacteristic
575C22×D4—21no—
576C22×D4—21no—
577C22×D4D4×C1311yescharacteristic
578C22×D4C23×C1311yescharacteristic
579C23×C4—21no—
580C23×C4—21no—
581C23×C4C23×C1311yescharacteristic
582#137—44no—
583#135—44no—
584C2×Q16—21no—
585C2×Q16—21no—
586C2×Q16—21no—
587C2×SD16—21no—
588C2×SD16—21no—
589C2×SD16—21no—
590C2×SD16—21no—
591C2×D8—21no—
592C2×M16—21no—
593C22×C8—21no—
594C4⋊Q8—21no—
595C4⋊Q8—21no—
596C4⋊Q8—21no—
597#126—21no—
598#126—21no—
599#126—21no—
600#126—21no—
601#126—21no—
602#126—21no—
603#125—21no—
604#125—21no—
605#125—21no—
606#125—21no—
607#125—21no—
608#124—21no—
609#124—21no—
610#124—21no—
611#124—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616#123—21no—
617#123—21no—
618#123—21no—
619#123—21no—
620#123—21no—
621#123—21no—
622#123—21no—
623#123—21no—
624#123—21no—
625#123—21no—
626C22⋊Q8—21no—
627C22⋊Q8—21no—
628C22⋊Q8—21no—
629C22⋊Q8—21no—
630C22⋊Q8—21no—
631C22⋊Q8—21no—
632C22⋊Q8—21no—
633C22⋊Q8—21no—
634C22⋊Q8—21no—
635C22⋊Q8—21no—
636C22⋊Q8—21no—
637C22⋊Q8—21no—
638C22⋊Q8—21no—
639C22⋊Q8—21no—
640C22⋊Q8D4×C1311yescharacteristic, complemented
641C22⋊Q8D4×C1311yescharacteristic, complemented
642C22⋊Q8D4×C1311yescharacteristic, complemented
643C22⋊Q8C23×C1311yescharacteristic
644C22⋊Q8C23×C1311yescharacteristic
645C22⋊Q8C23×C1311yescharacteristic
646#121—21no—
647#121—21no—
648#121—21no—
649#121—21no—
650#121—44no—
651#121D4×C1311yescharacteristic, complemented
652#121C23×C1311yescharacteristic
653#120—21no—
654#120—21no—
655C4×Q8—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—21no—
660C4×D4—21no—
661C4×D4—21no—
662C4×D4—21no—
663#117—21no—
664#117—21no—
665#117—21no—
666#117D4×C1311yescharacteristic, complemented
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4D4×C1311yescharacteristic
671C2×C4⋊C4D4×C1311yescharacteristic, complemented
672C2×C4⋊C4C23×C1311yescharacteristic
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4D4×C1311yescharacteristic
680C2×C22⋊C4D4×C1311yescharacteristic
681C2×C22⋊C4C23×C1311yescharacteristic
682#103—21no—
683#103—21no—
684#103—21no—
685#103—21no—
686#102—21no—
687#102—21no—
688#102—21no—
689#102—21no—
690C22⋊C8—21no—
691C22⋊C8—21no—
692C22⋊C8C23×C1311yescharacteristic
693C22⋊C8C23×C1311yescharacteristic
694C22⋊C8C23×C1311yescharacteristic
695C22⋊C8C23×C1311yescharacteristic
696#95—21no—
697#95—21no—
698#95—21no—
699#95C23×C1311yescharacteristic
700#95C23×C1311yescharacteristic
701C2×C13—21no—
702C2×C13—21no—
703C2×C13—22no—
704C2×C13—41no—
705C2×C13—81no—
706C2×C13—81no—
707C2×C13—82no—
708C2×C13#301311yescharacteristic
709C2×C13#301811yescharacteristic
710C2×C13C2×B(4,𝔽2)11yescharacteristic
711C24—21no—
712C24C2×D4×C1311yescharacteristic
713C24C2×D4×C1311yescharacteristic
714#41—24no—
715#41—24no—
716#41—42no—
717#41—42no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—82no—
724C2×Q8—21no—
725C2×Q8—21no—
726C2×Q8—21no—
727C2×Q8—21no—
728C2×Q8—21no—
729C2×Q8—42no—
730C2×Q8—42no—
731C2×Q8C2×D4×C1311yescharacteristic
732C2×Q8C2×D4×C1311yescharacteristic
733C2×Q8C2×D4×C1311yescharacteristic
734C2×D4—24no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—41no—
748C2×D4—41no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—81no—
752C2×D4C2×D4×C1311yescharacteristic
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—41no—
768C22×C4—41no—
769C22×C4—42no—
770C22×C4—81no—
771C22×C4C2×D4×C1311yescharacteristic
772C22×C4C2×D4×C1311yescharacteristic
773C22×C4C2×D4×C1311yescharacteristic
774C22×C4C2×D4×C1311yescharacteristic
775C22×C4C2×D4×C1311yescharacteristic
776C22×C4C2×D4×C1311yescharacteristic
777C22×C4C2×D4×C1311yescharacteristic
778C22×C4C2×D4×C1311yescharacteristic
779C22×C4C24×C1311yescharacteristic
780Q16—42no—
781Q16—42no—
782Q16—42no—
783SD16—42no—
784SD16—42no—
785SD16—42no—
786SD16—42no—
787D8—42no—
788M16—42no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—42no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—42no—
818C4⋊C4C2×D4×C1311yescharacteristic
819C4⋊C4C2×D4×C1311yescharacteristic
820C4⋊C4C2×D4×C1311yescharacteristic
821C4⋊C4C2×D4×C1311yescharacteristic
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—21no—
835C22⋊C4—21no—
836C22⋊C4—21no—
837C22⋊C4—21no—
838C22⋊C4—21no—
839C22⋊C4—21no—
840C22⋊C4—21no—
841C22⋊C4—21no—
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—42no—
846C22⋊C4—42no—
847C22⋊C4—42no—
848C22⋊C4—81no—
849C42—21no—
850C42—21no—
851C42—21no—
852C42—21no—
853C42—21no—
854C13#1825311yescharacteristic, direct product factor, Sylow
855C23—22no—
856C23—21no—
857C23—21no—
858C23—22no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23C13×#12011yescharacteristic
873C23C13×#12011yescharacteristic
874C23C22×D4×C1311yescharacteristic
875Q8—22no—
876Q8—22no—
877Q8—41no—
878Q8—41no—
879Q8—41no—
880Q8—41no—
881Q8—41no—
882Q8—81no—
883Q8—81no—
884Q8—81no—
885D4—22no—
886D4—22no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—44no—
891D4—44no—
892D4—42no—
893D4—42no—
894D4—41no—
895D4—41no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—84no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—44no—
922C2×C4—44no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—42no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4—81no—
939C2×C4—84no—
940C2×C4C13×#12011yescharacteristic
941C2×C4C13×#12011yescharacteristic
942C2×C4C22×D4×C1311yescharacteristic
943C2×C4C22×D4×C1311yescharacteristic
944C8—41no—
945C8—41no—
946C8—41no—
947C8—41no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22C13×B(4,𝔽2)12yes—
973C22C2×C13×#12011yescharacteristic
974C22C13×#57711yescharacteristic
975C22C13×#57811yescharacteristic
976C4—21no—
977C4—21no—
978C4—21no—
979C4—21no—
980C4—42no—
981C4—41no—
982C4—41no—
983C4—41no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—42no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—81no—
993C2—21no—
994C2—21no—
995C2—22no—
996C2—41no—
997C2—82no—
998C2—81no—
999C2—81no—
1000C2C13×#301311yescharacteristic
1001C2C13×#301811yescharacteristic
1002C2C2×C13×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3535C2semidirect
2. C13×#3007C2semidirect
3. C13×#3002C2semidirect
4. C13×#2430C2semidirect
5. C13×#1606C2semidirect
6. C13×#1605C2semidirect
7. C13×#1603C2semidirect
8. C13×#1602C2semidirect
9. C13×#1600C2semidirect
10. C13×#1599C2semidirect
11. C13×#1597C2semidirect
12. C13×#1596C2semidirect
13. C13×#1504C2semidirect
14. C2×C13×#328C2semidirect
15. C13×#1468C2semidirect
81. C2×C13×#41D4semidirect
82. C22×Q8×C13D4semidirect
149. C13×C22⋊Q8D4semidirect
150. C13×C22⋊Q8D4semidirect
151. C13×C22⋊Q8D4semidirect
160. C13×#121D4semidirect
175. C13×#117D4semidirect
180. C2×C13×C4⋊C4D4semidirect
210. #18253C13direct (N × H)
354. #3535C2×C13semidirect
355. #3007C2×C13semidirect
356. #3002C2×C13semidirect
357. #2430C2×C13semidirect
358. #1606C2×C13semidirect
359. #1605C2×C13semidirect
360. #1603C2×C13semidirect
361. #1602C2×C13semidirect
362. #1600C2×C13semidirect
363. #1599C2×C13semidirect
364. #1597C2×C13semidirect
365. #1596C2×C13semidirect
366. #1504C2×C13semidirect
367. C2×#328C2×C13semidirect
368. #1468C2×C13semidirect
572. C2×#41D4×C13semidirect
573. C22×Q8D4×C13semidirect
640. C22⋊Q8D4×C13semidirect
641. C22⋊Q8D4×C13semidirect
642. C22⋊Q8D4×C13semidirect
651. #121D4×C13semidirect
666. #117D4×C13semidirect
671. C2×C4⋊C4D4×C13semidirect
854. C13#18253direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35352
C13×#30072
C13×#30022
C13×#24302
C13×#16062
C13×#16052
C13×#16032
C13×#16022
C13×#16002
C13×#15992
C13×#15972
C13×#15962
C13×#15042
C2×C13×#3282
C13×#14682
#1825313