Finite Group Databasebeta

← C13×#18235 #15704574

Subgroups — C13×#18235 #15704574

Order 3328.

938 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3535C211yesmaximal, characteristic
2C13×#3092C211yesmaximal, characteristic, complemented
3C2×C13×#484C211yesmaximal, characteristic, complemented
4C13×#2623C211yesmaximal, characteristic, complemented
5C13×#1618C212yesmaximal, complemented
6C13×#1617C212yesmaximal, complemented
7C13×#1615C212yesmaximal, complemented
8C13×#1614C212yesmaximal, complemented
9C13×#1516C211yesmaximal, characteristic, complemented
10C13×#1511C211yesmaximal, characteristic, complemented
11C13×#1468C211yesmaximal, characteristic, complemented
12C13×#563—21no—
13C13×#562—21no—
14C13×#554—21no—
15C13×#552—21no—
16C13×#551—21no—
17C13×#551—21no—
18C13×#547—21no—
19C13×#546—21no—
20C13×#544C2211yescharacteristic
21C13×#543C2211yescharacteristic
22C13×#542—21no—
23C13×#539—21no—
24C13×#539—21no—
25C13×#539C2211yescharacteristic
26C13×#538C2211yescharacteristic
27C13×#536—21no—
28C13×#525C2211yescharacteristic
29C2×C13×#123C2211yescharacteristic
30C2×C13×C22⋊Q8C2211yescharacteristic
31C22×C13×C4⋊C4C2211yescharacteristic
32C13×#484—21no—
33C13×#484—21no—
34C13×#484C2212yes—
35C13×#484C2212yes—
36C13×#484C2212yes—
37C13×#483—21no—
38C13×#481C2212yes—
39C13×#480—21no—
40C13×#428—21no—
41C2×C13×#107—21no—
42C13×#417—21no—
43C2×C13×#103—21no—
44C13×#407C2211yescharacteristic
45C2×C13×C22⋊C8C2211yescharacteristic
46C13×#400C2212yes—
47C13×#399C2212yes—
48C13×#398—21no—
49C13×#397—21no—
50C13×#386—21no—
51C13×#385—21no—
52C13×#381C2211yescharacteristic
53C13×#328C2212yes—
54C13×#328C2212yes—
55C13×#328C2212yes—
56C13×#327C2212yes—
57C13×#324C2212yes—
58C13×#323C2212yes—
59C2×C13×#41—21no—
60C2×C13×#41D411yescharacteristic
61C22×Q8×C13D411yescharacteristic
62C22×D4×C13D411yescharacteristic
63C23×C4×C13—21no—
64C23×C4×C13C2311yescharacteristic
65C2×C13×M16—21no—
66C22×C8×C13—21no—
67C13×C4⋊Q8—21no—
68C13×C4⋊Q8—21no—
69C13×C4⋊Q8—21no—
70C13×#126—21no—
71C13×#126—21no—
72C13×#126—21no—
73C13×#126—21no—
74C13×#126—21no—
75C13×#126—21no—
76C13×#125—21no—
77C13×#125—21no—
78C13×#125—21no—
79C13×#125—21no—
80C13×#125—21no—
81C13×#124—21no—
82C13×#124—21no—
83C13×#124—21no—
84C13×#124—21no—
85C13×#123—21no—
86C13×#123—21no—
87C13×#123—21no—
88C13×#123—21no—
89C13×#123—21no—
90C13×#123—21no—
91C13×#123—21no—
92C13×#123—21no—
93C13×#123—21no—
94C13×#123—21no—
95C13×#123—21no—
96C13×#123—21no—
97C13×#123—21no—
98C13×#123—21no—
99C13×C22⋊Q8—21no—
100C13×C22⋊Q8—21no—
101C13×C22⋊Q8—21no—
102C13×C22⋊Q8—21no—
103C13×C22⋊Q8—21no—
104C13×C22⋊Q8—21no—
105C13×C22⋊Q8—21no—
106C13×C22⋊Q8—21no—
107C13×C22⋊Q8—21no—
108C13×C22⋊Q8—21no—
109C13×C22⋊Q8—21no—
110C13×C22⋊Q8—21no—
111C13×C22⋊Q8—21no—
112C13×C22⋊Q8—21no—
113C13×C22⋊Q8D411yescharacteristic
114C13×C22⋊Q8D411yescharacteristic
115C13×C22⋊Q8D411yescharacteristic
116C13×C22⋊Q8C2311yescharacteristic
117C13×C22⋊Q8C2311yescharacteristic
118C13×C22⋊Q8C2311yescharacteristic
119C13×#121—21no—
120C13×#121—21no—
121C13×#121—21no—
122C13×#121—21no—
123C13×#121D411yescharacteristic
124C13×#121C2311yescharacteristic
125C13×#120—21no—
126C13×#120—21no—
127C4×Q8×C13—21no—
128C4×D4×C13—21no—
129C4×D4×C13—21no—
130C4×D4×C13—21no—
131C4×D4×C13—21no—
132C4×D4×C13—21no—
133C4×D4×C13—21no—
134C4×D4×C13—21no—
135C13×#117—21no—
136C13×#117—21no—
137C13×#117—21no—
138C13×#117D411yescharacteristic
139C2×C13×C4⋊C4—21no—
140C2×C13×C4⋊C4—21no—
141C2×C13×C4⋊C4—21no—
142C2×C13×C4⋊C4—21no—
143C2×C13×C4⋊C4—21no—
144C2×C13×C4⋊C4—21no—
145C2×C13×C4⋊C4—21no—
146C2×C13×C4⋊C4—22no—
147C2×C13×C4⋊C4D411yescharacteristic
148C2×C13×C4⋊C4D411yescharacteristic
149C2×C13×C4⋊C4C2312yes—
150C2×C13×C4⋊C4C2311yescharacteristic
151C2×C13×C22⋊C4—21no—
152C2×C13×C22⋊C4—21no—
153C2×C13×C22⋊C4—21no—
154C2×C13×C22⋊C4—22no—
155C2×C13×C22⋊C4D411yescharacteristic
156C2×C13×C22⋊C4D411yescharacteristic
157C2×C13×C22⋊C4C2311yescharacteristic
158C13×#107—22no—
159C13×#107—22no—
160C13×#107—22no—
161C13×#106—22no—
162C13×#103—22no—
163C13×#103—22no—
164C13×#103—22no—
165C13×#102—22no—
166C13×C22⋊C8—21no—
167C13×C22⋊C8—21no—
168C13×C22⋊C8C2312yes—
169C13×C22⋊C8C2312yes—
170C13×#95—21no—
171C13×#95—22no—
172C13×#95—22no—
173C13×#95C2312yes—
174#18235C1311yesmaximal, characteristic, direct product factor, Sylow
175C24×C13C2×D411yescharacteristic
176C24×C13C2×D411yescharacteristic
177C13×#41—42no—
178C13×#41—82no—
179C2×Q8×C13—21no—
180C2×Q8×C13—21no—
181C2×Q8×C13—21no—
182C2×Q8×C13—42no—
183C2×Q8×C13C2×D411yescharacteristic
184C2×Q8×C13C2×D411yescharacteristic
185C2×Q8×C13C2×D411yescharacteristic
186C2×D4×C13—21no—
187C2×D4×C13—21no—
188C2×D4×C13—21no—
189C2×D4×C13—21no—
190C2×D4×C13—21no—
191C2×D4×C13—21no—
192C2×D4×C13—21no—
193C2×D4×C13—42no—
194C2×D4×C13C2×D411yescharacteristic
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—22no—
203C22×C4×C13—22no—
204C22×C4×C13—42no—
205C22×C4×C13—41no—
206C22×C4×C13—41no—
207C22×C4×C13—82no—
208C22×C4×C13C2×D411yescharacteristic
209C22×C4×C13C2×D411yescharacteristic
210C22×C4×C13C2×D411yescharacteristic
211C22×C4×C13C2×D411yescharacteristic
212C22×C4×C13C2×D411yescharacteristic
213C22×C4×C13C2×D411yescharacteristic
214C22×C4×C13C2×D411yescharacteristic
215C22×C4×C13C2×D411yescharacteristic
216C22×C4×C13C2411yescharacteristic
217C13×M16—42no—
218C2×C8×C13—22no—
219C2×C8×C13—22no—
220C2×C8×C13—42no—
221C13×C4⋊C4—21no—
222C13×C4⋊C4—21no—
223C13×C4⋊C4—21no—
224C13×C4⋊C4—21no—
225C13×C4⋊C4—21no—
226C13×C4⋊C4—21no—
227C13×C4⋊C4—21no—
228C13×C4⋊C4—21no—
229C13×C4⋊C4—21no—
230C13×C4⋊C4—21no—
231C13×C4⋊C4—21no—
232C13×C4⋊C4—21no—
233C13×C4⋊C4—21no—
234C13×C4⋊C4—21no—
235C13×C4⋊C4—21no—
236C13×C4⋊C4—21no—
237C13×C4⋊C4—21no—
238C13×C4⋊C4—21no—
239C13×C4⋊C4—21no—
240C13×C4⋊C4—21no—
241C13×C4⋊C4—21no—
242C13×C4⋊C4—21no—
243C13×C4⋊C4—21no—
244C13×C4⋊C4—22no—
245C13×C4⋊C4—22no—
246C13×C4⋊C4—41no—
247C13×C4⋊C4—41no—
248C13×C4⋊C4—82no—
249C13×C4⋊C4C2×D411yescharacteristic
250C13×C4⋊C4C2×D411yescharacteristic
251C13×C4⋊C4C2×D411yescharacteristic
252C13×C4⋊C4C2×D411yescharacteristic
253C13×C22⋊C4—21no—
254C13×C22⋊C4—21no—
255C13×C22⋊C4—21no—
256C13×C22⋊C4—21no—
257C13×C22⋊C4—21no—
258C13×C22⋊C4—21no—
259C13×C22⋊C4—21no—
260C13×C22⋊C4—21no—
261C13×C22⋊C4—21no—
262C13×C22⋊C4—21no—
263C13×C22⋊C4—21no—
264C13×C22⋊C4—21no—
265C13×C22⋊C4—21no—
266C13×C22⋊C4—21no—
267C13×C22⋊C4—21no—
268C13×C22⋊C4—21no—
269C13×C22⋊C4—21no—
270C13×C22⋊C4—21no—
271C13×C22⋊C4—21no—
272C13×C22⋊C4—21no—
273C13×C22⋊C4—21no—
274C13×C22⋊C4—21no—
275C13×C22⋊C4—21no—
276C13×C22⋊C4—42no—
277C13×C22⋊C4—82no—
278C42×C13—21no—
279C42×C13—21no—
280C42×C13—21no—
281C42×C13—21no—
282C42×C13—21no—
283#3535C2×C1311yescharacteristic
284#3092C2×C1311yescharacteristic, complemented
285C2×#484C2×C1311yescharacteristic, complemented
286#2623C2×C1311yescharacteristic, complemented
287#1618C2×C1312yescomplemented
288#1617C2×C1312yescomplemented
289#1615C2×C1312yescomplemented
290#1614C2×C1312yescomplemented
291#1516C2×C1311yescharacteristic, complemented
292#1511C2×C1311yescharacteristic, complemented
293#1468C2×C1311yescharacteristic, complemented
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—21no—
297C23×C13—21no—
298C23×C13—22no—
299C23×C13—41no—
300C23×C13—41no—
301C23×C13—41no—
302C23×C13#12011yescharacteristic
303C23×C13#12011yescharacteristic
304C23×C13C22×D411yescharacteristic
305Q8×C13—41no—
306Q8×C13—41no—
307Q8×C13—41no—
308Q8×C13—81no—
309Q8×C13—81no—
310Q8×C13—81no—
311D4×C13—41no—
312D4×C13—42no—
313D4×C13—42no—
314D4×C13—42no—
315D4×C13—81no—
316D4×C13—81no—
317D4×C13—81no—
318D4×C13—81no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—21no—
322C2×C4×C13—21no—
323C2×C4×C13—21no—
324C2×C4×C13—21no—
325C2×C4×C13—21no—
326C2×C4×C13—21no—
327C2×C4×C13—21no—
328C2×C4×C13—21no—
329C2×C4×C13—21no—
330C2×C4×C13—21no—
331C2×C4×C13—22no—
332C2×C4×C13—41no—
333C2×C4×C13—41no—
334C2×C4×C13—41no—
335C2×C4×C13—41no—
336C2×C4×C13—42no—
337C2×C4×C13—41no—
338C2×C4×C13—41no—
339C2×C4×C13—42no—
340C2×C4×C13—42no—
341C2×C4×C13—42no—
342C2×C4×C13—42no—
343C2×C4×C13—42no—
344C2×C4×C13—42no—
345C2×C4×C13—81no—
346C2×C4×C13—81no—
347C2×C4×C13—81no—
348C2×C4×C13—81no—
349C2×C4×C13—81no—
350C2×C4×C13—81no—
351C2×C4×C13—82no—
352C2×C4×C13—82no—
353C2×C4×C13#12011yescharacteristic
354C2×C4×C13#12011yescharacteristic
355C2×C4×C13C22×D411yescharacteristic
356C2×C4×C13C22×D411yescharacteristic
357C8×C13—42no—
358C8×C13—42no—
359#563—21no—
360#562—21no—
361#554—21no—
362#552—21no—
363#551—21no—
364#551—21no—
365#547—21no—
366#546—21no—
367#544C22×C1311yescharacteristic
368#543C22×C1311yescharacteristic
369#542—21no—
370#539—21no—
371#539—21no—
372#539C22×C1311yescharacteristic
373#538C22×C1311yescharacteristic
374#536—21no—
375#525C22×C1311yescharacteristic
376C2×#123C22×C1311yescharacteristic
377C2×C22⋊Q8C22×C1311yescharacteristic
378C22×C4⋊C4C22×C1311yescharacteristic
379#484—21no—
380#484—21no—
381#484C22×C1312yes—
382#484C22×C1312yes—
383#484C22×C1312yes—
384#483—21no—
385#481C22×C1312yes—
386#480—21no—
387#428—21no—
388C2×#107—21no—
389#417—21no—
390C2×#103—21no—
391#407C22×C1311yescharacteristic
392C2×C22⋊C8C22×C1311yescharacteristic
393#400C22×C1312yes—
394#399C22×C1312yes—
395#398—21no—
396#397—21no—
397#386—21no—
398#385—21no—
399#381C22×C1311yescharacteristic
400#328C22×C1312yes—
401#328C22×C1312yes—
402#328C22×C1312yes—
403#327C22×C1312yes—
404#324C22×C1312yes—
405#323C22×C1312yes—
406C22×C13—21no—
407C22×C13—21no—
408C22×C13—21no—
409C22×C13—21no—
410C22×C13—21no—
411C22×C13—21no—
412C22×C13—21no—
413C22×C13—44no—
414C22×C13—41no—
415C22×C13—41no—
416C22×C13—41no—
417C22×C13—41no—
418C22×C13—41no—
419C22×C13—41no—
420C22×C13—82no—
421C22×C13#45812yes—
422C22×C13C2×#12011yescharacteristic
423C22×C13#57812yes—
424C4×C13—21no—
425C4×C13—21no—
426C4×C13—21no—
427C4×C13—21no—
428C4×C13—41no—
429C4×C13—41no—
430C4×C13—41no—
431C4×C13—41no—
432C4×C13—41no—
433C4×C13—41no—
434C4×C13—41no—
435C4×C13—41no—
436C4×C13—41no—
437C4×C13—41no—
438C4×C13—82no—
439C4×C13—82no—
440C2×#41—21no—
441C2×#41D4×C1311yescharacteristic
442C22×Q8D4×C1311yescharacteristic
443C22×D4D4×C1311yescharacteristic
444C23×C4—21no—
445C23×C4C23×C1311yescharacteristic
446C2×M16—21no—
447C22×C8—21no—
448C4⋊Q8—21no—
449C4⋊Q8—21no—
450C4⋊Q8—21no—
451#126—21no—
452#126—21no—
453#126—21no—
454#126—21no—
455#126—21no—
456#126—21no—
457#125—21no—
458#125—21no—
459#125—21no—
460#125—21no—
461#125—21no—
462#124—21no—
463#124—21no—
464#124—21no—
465#124—21no—
466#123—21no—
467#123—21no—
468#123—21no—
469#123—21no—
470#123—21no—
471#123—21no—
472#123—21no—
473#123—21no—
474#123—21no—
475#123—21no—
476#123—21no—
477#123—21no—
478#123—21no—
479#123—21no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—21no—
483C22⋊Q8—21no—
484C22⋊Q8—21no—
485C22⋊Q8—21no—
486C22⋊Q8—21no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8D4×C1311yescharacteristic
495C22⋊Q8D4×C1311yescharacteristic
496C22⋊Q8D4×C1311yescharacteristic
497C22⋊Q8C23×C1311yescharacteristic
498C22⋊Q8C23×C1311yescharacteristic
499C22⋊Q8C23×C1311yescharacteristic
500#121—21no—
501#121—21no—
502#121—21no—
503#121—21no—
504#121D4×C1311yescharacteristic
505#121C23×C1311yescharacteristic
506#120—21no—
507#120—21no—
508C4×Q8—21no—
509C4×D4—21no—
510C4×D4—21no—
511C4×D4—21no—
512C4×D4—21no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516#117—21no—
517#117—21no—
518#117—21no—
519#117D4×C1311yescharacteristic
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4D4×C1311yescharacteristic
529C2×C4⋊C4D4×C1311yescharacteristic
530C2×C4⋊C4C23×C1312yes—
531C2×C4⋊C4C23×C1311yescharacteristic
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4D4×C1311yescharacteristic
537C2×C22⋊C4D4×C1311yescharacteristic
538C2×C22⋊C4C23×C1311yescharacteristic
539#107—22no—
540#107—22no—
541#107—22no—
542#106—22no—
543#103—22no—
544#103—22no—
545#103—22no—
546#102—22no—
547C22⋊C8—21no—
548C22⋊C8—21no—
549C22⋊C8C23×C1312yes—
550C22⋊C8C23×C1312yes—
551#95—21no—
552#95—22no—
553#95—22no—
554#95C23×C1312yes—
555C2×C13—22no—
556C2×C13—22no—
557C2×C13—41no—
558C2×C13—81no—
559C2×C13—81no—
560C2×C13#301111yescharacteristic
561C2×C13#302111yescharacteristic
562C2×C13C2×#45811yescharacteristic
563C24C2×D4×C1311yescharacteristic
564C24C2×D4×C1311yescharacteristic
565#41—42no—
566#41—82no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—42no—
571C2×Q8C2×D4×C1311yescharacteristic
572C2×Q8C2×D4×C1311yescharacteristic
573C2×Q8C2×D4×C1311yescharacteristic
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—42no—
582C2×D4C2×D4×C1311yescharacteristic
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—42no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—82no—
596C22×C4C2×D4×C1311yescharacteristic
597C22×C4C2×D4×C1311yescharacteristic
598C22×C4C2×D4×C1311yescharacteristic
599C22×C4C2×D4×C1311yescharacteristic
600C22×C4C2×D4×C1311yescharacteristic
601C22×C4C2×D4×C1311yescharacteristic
602C22×C4C2×D4×C1311yescharacteristic
603C22×C4C2×D4×C1311yescharacteristic
604C22×C4C24×C1311yescharacteristic
605M16—42no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—42no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4—82no—
637C4⋊C4C2×D4×C1311yescharacteristic
638C4⋊C4C2×D4×C1311yescharacteristic
639C4⋊C4C2×D4×C1311yescharacteristic
640C4⋊C4C2×D4×C1311yescharacteristic
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—42no—
665C22⋊C4—82no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C13#1823511yescharacteristic, direct product factor, Sylow
672C23—22no—
673C23—22no—
674C23—21no—
675C23—21no—
676C23—22no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23C13×#12011yescharacteristic
681C23C13×#12011yescharacteristic
682C23C22×D4×C1311yescharacteristic
683Q8—41no—
684Q8—41no—
685Q8—41no—
686Q8—81no—
687Q8—81no—
688Q8—81no—
689D4—41no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—82no—
730C2×C4—82no—
731C2×C4C13×#12011yescharacteristic
732C2×C4C13×#12011yescharacteristic
733C2×C4C22×D4×C1311yescharacteristic
734C2×C4C22×D4×C1311yescharacteristic
735C8—42no—
736C8—42no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—44no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—82no—
752C22C13×#45812yes—
753C22C2×C13×#12011yescharacteristic
754C22C13×#57812yes—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—82no—
770C4—82no—
771C2—22no—
772C2—22no—
773C2—41no—
774C2—81no—
775C2—81no—
776C2C13×#301111yescharacteristic
777C2C13×#302111yescharacteristic
778C2C2×C13×#45811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3535C2
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
2. C13×#3092C2semidirect
3. C2×C13×#484C2semidirect
4. C13×#2623C2semidirect
5. C13×#1618C2semidirect
6. C13×#1617C2semidirect
7. C13×#1615C2semidirect
8. C13×#1614C2semidirect
9. C13×#1516C2semidirect
10. C13×#1511C2semidirect
11. C13×#1468C2semidirect
174. #18235C13direct (N × H)
284. #3092C2×C13semidirect
285. C2×#484C2×C13semidirect
286. #2623C2×C13semidirect
287. #1618C2×C13semidirect
288. #1617C2×C13semidirect
289. #1615C2×C13semidirect
290. #1614C2×C13semidirect
291. #1516C2×C13semidirect
292. #1511C2×C13semidirect
293. #1468C2×C13semidirect
671. C13#18235direct (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×#30922
C2×C13×#4842
C13×#26232
C13×#16182
C13×#16172
C13×#16152
C13×#16142
C13×#15162
C13×#15112
C13×#14682
#1823513