Finite Group Databasebeta

← C13×#18465 #15704804

Subgroups — C13×#18465 #15704804

Order 3328.

870 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3564C211yesmaximal, characteristic
2C13×#3218C211yesmaximal, characteristic, complemented
3C13×#3209C211yesmaximal, characteristic, complemented
4C13×#2821C211yesmaximal, characteristic, complemented
5C13×#1606C212yesmaximal
6C13×#1605C212yesmaximal, complemented
7C13×#1603C212yesmaximal, complemented
8C13×#1602C212yesmaximal, complemented
9C13×#1521C211yesmaximal, characteristic, complemented
10C13×#1515C211yesmaximal, characteristic, complemented
11C13×#1473C211yesmaximal, characteristic, complemented
12C13×#563—21no—
13C13×#563—21no—
14C13×#556—21no—
15C13×#554—21no—
16C13×#552—21no—
17C13×#552—21no—
18C13×#551—21no—
19C13×#551—21no—
20C13×#544C2211yescharacteristic
21C13×#543C2211yescharacteristic
22C13×#542—21no—
23C13×#541—21no—
24C13×#541—21no—
25C13×#539—21no—
26C13×#539C2211yescharacteristic
27C13×#538C2211yescharacteristic
28C13×#533C2211yescharacteristic
29C2×C13×C4⋊Q8C2211yescharacteristic
30C13×#529C2211yescharacteristic
31C2×C13×#126C2211yescharacteristic
32C13×#497—21no—
33C13×#494—21no—
34C13×#491—21no—
35C13×#487—21no—
36C13×#462—21no—
37C13×#462—21no—
38C13×#462—21no—
39C13×#461—21no—
40C13×#451C2212yes—
41C13×#451C2212yes—
42C13×#451C2212yes—
43C13×#448C2212yes—
44C13×#432C2211yescharacteristic
45C13×#431C2211yescharacteristic
46C13×#400—21no—
47C13×#399—21no—
48C13×#398—21no—
49C13×#397—21no—
50C13×#395C2212yes—
51C13×#393C2212yes—
52C13×#383C2211yescharacteristic
53C13×#328C2212yes—
54C13×#328C2212yes—
55C13×#328C2212yes—
56C13×#327C2212yes—
57C13×#324C2212yes—
58C13×#323C2212yes—
59C22×Q8×C13C2312yes—
60C2×C13×Q16—22no—
61C2×C13×Q16—22no—
62C2×C13×Q16—22no—
63C2×C13×SD16—22no—
64C13×C4⋊Q8—21no—
65C13×C4⋊Q8—21no—
66C13×C4⋊Q8—21no—
67C13×C4⋊Q8—21no—
68C13×C4⋊Q8—21no—
69C13×C4⋊Q8—21no—
70C13×C4⋊Q8—21no—
71C13×C4⋊Q8D411yescharacteristic
72C13×C4⋊Q8D411yescharacteristic
73C13×#126—21no—
74C13×#126—21no—
75C13×#126—21no—
76C13×#126—21no—
77C13×#126—21no—
78C13×#126—21no—
79C13×#126—21no—
80C13×#126—21no—
81C13×#126—21no—
82C13×#126—21no—
83C13×#126—21no—
84C13×#126—21no—
85C13×#126—21no—
86C13×#125—21no—
87C13×#125—21no—
88C13×#125—21no—
89C13×#125—21no—
90C13×#125—21no—
91C13×#125—21no—
92C13×#125—21no—
93C13×#125—21no—
94C13×#125—21no—
95C13×#125D411yescharacteristic
96C13×#124—21no—
97C13×#124—21no—
98C13×#124—21no—
99C13×#124D411yescharacteristic
100C13×#123—21no—
101C13×#123—21no—
102C13×#123—21no—
103C13×#123—21no—
104C13×#123—21no—
105C13×#123—21no—
106C13×#123—21no—
107C13×#123—21no—
108C13×C22⋊Q8—21no—
109C13×C22⋊Q8—21no—
110C13×C22⋊Q8—21no—
111C13×C22⋊Q8—21no—
112C13×C22⋊Q8—21no—
113C13×C22⋊Q8—21no—
114C13×C22⋊Q8—21no—
115C13×C22⋊Q8—21no—
116C13×C22⋊Q8—21no—
117C13×C22⋊Q8—21no—
118C13×C22⋊Q8—21no—
119C13×C22⋊Q8—21no—
120C13×C22⋊Q8—21no—
121C13×C22⋊Q8—21no—
122C13×C22⋊Q8C2311yescharacteristic
123C13×C22⋊Q8C2311yescharacteristic
124C13×C22⋊Q8C2311yescharacteristic
125C13×#121—21no—
126C13×#121C2311yescharacteristic
127C13×#120—21no—
128C4×Q8×C13—21no—
129C4×Q8×C13—21no—
130C4×Q8×C13—21no—
131C4×Q8×C13D411yescharacteristic
132C4×Q8×C13D411yescharacteristic
133C4×Q8×C13D411yescharacteristic
134C4×D4×C13—21no—
135C4×D4×C13—21no—
136C4×D4×C13—21no—
137C4×D4×C13—21no—
138C4×D4×C13—21no—
139C4×D4×C13D411yescharacteristic
140C13×#117—21no—
141C13×#117—21no—
142C13×#117—21no—
143C13×#117—21no—
144C13×#117—21no—
145C13×#117—21no—
146C2×C13×C4⋊C4—21no—
147C2×C13×C4⋊C4—21no—
148C2×C13×C4⋊C4—21no—
149C2×C13×C4⋊C4—22no—
150C2×C13×C4⋊C4D411yescharacteristic
151C2×C13×C4⋊C4D411yescharacteristic
152C2×C13×C4⋊C4C2311yescharacteristic
153C2×C13×C22⋊C4—21no—
154C2×C13×C22⋊C4—22no—
155C2×C13×C22⋊C4D411yescharacteristic
156C2×C13×C22⋊C4D411yescharacteristic
157C2×C13×C22⋊C4C2311yescharacteristic
158C2×C42×C13C2311yescharacteristic
159C13×C4⋊C8—21no—
160C13×C4⋊C8—21no—
161C13×#103—22no—
162C13×#103—22no—
163C13×#103—22no—
164C13×#103—22no—
165C13×C22⋊C8C2312yes—
166C13×C22⋊C8C2312yes—
167C13×#97—21no—
168C4×C8×C13—21no—
169C13×#95—21no—
170C13×#95—21no—
171C13×#95—22no—
172C13×#95—22no—
173C13×#95C2312yes—
174#18465C1311yesmaximal, characteristic, direct product factor, Sylow
175C24×C13C2×D411yescharacteristic
176C2×Q8×C13—21no—
177C2×Q8×C13—21no—
178C2×Q8×C13—21no—
179C2×Q8×C13—22no—
180C2×Q8×C13—22no—
181C2×Q8×C13—82no—
182C2×Q8×C13C2×D411yescharacteristic
183C2×Q8×C13C2×D411yescharacteristic
184C2×Q8×C13C2×D411yescharacteristic
185C2×D4×C13—21no—
186C2×D4×C13—21no—
187C2×D4×C13—21no—
188C2×D4×C13C2×D411yescharacteristic
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—22no—
195C22×C4×C13—22no—
196C22×C4×C13C2×D411yescharacteristic
197C22×C4×C13C2×D411yescharacteristic
198C22×C4×C13C2×D411yescharacteristic
199C22×C4×C13C2×D411yescharacteristic
200C22×C4×C13C2×D411yescharacteristic
201C22×C4×C13C2411yescharacteristic
202C13×Q16—82no—
203C13×Q16—82no—
204C13×Q16—82no—
205C13×SD16—82no—
206C2×C8×C13—22no—
207C2×C8×C13—22no—
208C13×C4⋊C4—21no—
209C13×C4⋊C4—21no—
210C13×C4⋊C4—21no—
211C13×C4⋊C4—21no—
212C13×C4⋊C4—21no—
213C13×C4⋊C4—21no—
214C13×C4⋊C4—21no—
215C13×C4⋊C4—21no—
216C13×C4⋊C4—21no—
217C13×C4⋊C4—21no—
218C13×C4⋊C4—21no—
219C13×C4⋊C4—21no—
220C13×C4⋊C4—21no—
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—41no—
238C13×C4⋊C4—41no—
239C13×C4⋊C4—41no—
240C13×C4⋊C4—41no—
241C13×C4⋊C4—82no—
242C13×C4⋊C4C2×D411yescharacteristic
243C13×C4⋊C4C2×D411yescharacteristic
244C13×C4⋊C4C2×D411yescharacteristic
245C13×C4⋊C4C2×D411yescharacteristic
246C13×C22⋊C4—21no—
247C13×C22⋊C4—21no—
248C13×C22⋊C4—21no—
249C13×C22⋊C4—21no—
250C13×C22⋊C4—21no—
251C13×C22⋊C4—21no—
252C13×C22⋊C4—21no—
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—82no—
268C42×C13—21no—
269C42×C13—21no—
270C42×C13—21no—
271C42×C13—21no—
272C42×C13—21no—
273C42×C13—21no—
274C42×C13—21no—
275C42×C13C2×D411yescharacteristic
276C42×C13C2×D411yescharacteristic
277C42×C13C2×D411yescharacteristic
278C42×C13C2×D411yescharacteristic
279#3564C2×C1311yescharacteristic
280#3218C2×C1311yescharacteristic, complemented
281#3209C2×C1311yescharacteristic, complemented
282#2821C2×C1311yescharacteristic, complemented
283#1606C2×C1312yes—
284#1605C2×C1312yescomplemented
285#1603C2×C1312yescomplemented
286#1602C2×C1312yescomplemented
287#1521C2×C1311yescharacteristic, complemented
288#1515C2×C1311yescharacteristic, complemented
289#1473C2×C1311yescharacteristic, complemented
290C23×C13—21no—
291C23×C13—21no—
292C23×C13—22no—
293C23×C13—41no—
294C23×C13—41no—
295C23×C13C22×D411yescharacteristic
296Q8×C13—41no—
297Q8×C13—41no—
298Q8×C13—41no—
299Q8×C13—42no—
300Q8×C13—42no—
301Q8×C13—42no—
302Q8×C13—42no—
303Q8×C13—81no—
304Q8×C13—81no—
305Q8×C13—81no—
306D4×C13—41no—
307D4×C13—42no—
308D4×C13—81no—
309D4×C13—81no—
310C2×C4×C13—22no—
311C2×C4×C13—21no—
312C2×C4×C13—21no—
313C2×C4×C13—21no—
314C2×C4×C13—21no—
315C2×C4×C13—21no—
316C2×C4×C13—21no—
317C2×C4×C13—21no—
318C2×C4×C13—21no—
319C2×C4×C13—21no—
320C2×C4×C13—21no—
321C2×C4×C13—22no—
322C2×C4×C13—41no—
323C2×C4×C13—41no—
324C2×C4×C13—41no—
325C2×C4×C13—41no—
326C2×C4×C13—42no—
327C2×C4×C13—42no—
328C2×C4×C13—42no—
329C2×C4×C13—42no—
330C2×C4×C13—42no—
331C2×C4×C13—42no—
332C2×C4×C13—81no—
333C2×C4×C13—81no—
334C2×C4×C13—81no—
335C2×C4×C13—81no—
336C2×C4×C13—81no—
337C2×C4×C13#12011yescharacteristic
338C2×C4×C13#12011yescharacteristic
339C2×C4×C13#12011yescharacteristic
340C2×C4×C13#12011yescharacteristic
341C2×C4×C13C22×D411yescharacteristic
342C2×C4×C13C22×D411yescharacteristic
343C8×C13—42no—
344C8×C13—42no—
345#563—21no—
346#563—21no—
347#556—21no—
348#554—21no—
349#552—21no—
350#552—21no—
351#551—21no—
352#551—21no—
353#544C22×C1311yescharacteristic
354#543C22×C1311yescharacteristic
355#542—21no—
356#541—21no—
357#541—21no—
358#539—21no—
359#539C22×C1311yescharacteristic
360#538C22×C1311yescharacteristic
361#533C22×C1311yescharacteristic
362C2×C4⋊Q8C22×C1311yescharacteristic
363#529C22×C1311yescharacteristic
364C2×#126C22×C1311yescharacteristic
365#497—21no—
366#494—21no—
367#491—21no—
368#487—21no—
369#462—21no—
370#462—21no—
371#462—21no—
372#461—21no—
373#451C22×C1312yes—
374#451C22×C1312yes—
375#451C22×C1312yes—
376#448C22×C1312yes—
377#432C22×C1311yescharacteristic
378#431C22×C1311yescharacteristic
379#400—21no—
380#399—21no—
381#398—21no—
382#397—21no—
383#395C22×C1312yes—
384#393C22×C1312yes—
385#383C22×C1311yescharacteristic
386#328C22×C1312yes—
387#328C22×C1312yes—
388#328C22×C1312yes—
389#327C22×C1312yes—
390#324C22×C1312yes—
391#323C22×C1312yes—
392C22×C13—21no—
393C22×C13—21no—
394C22×C13—41no—
395C22×C13—41no—
396C22×C13—41no—
397C22×C13—41no—
398C22×C13—41no—
399C22×C13—41no—
400C22×C13—82no—
401C22×C13C2×#12011yescharacteristic
402C22×C13#57812yes—
403C4×C13—21no—
404C4×C13—21no—
405C4×C13—21no—
406C4×C13—21no—
407C4×C13—21no—
408C4×C13—21no—
409C4×C13—41no—
410C4×C13—41no—
411C4×C13—41no—
412C4×C13—41no—
413C4×C13—41no—
414C4×C13—41no—
415C4×C13—41no—
416C4×C13—41no—
417C4×C13—41no—
418C4×C13—41no—
419C4×C13—82no—
420C4×C13—82no—
421C22×Q8C23×C1312yes—
422C2×Q16—22no—
423C2×Q16—22no—
424C2×Q16—22no—
425C2×SD16—22no—
426C4⋊Q8—21no—
427C4⋊Q8—21no—
428C4⋊Q8—21no—
429C4⋊Q8—21no—
430C4⋊Q8—21no—
431C4⋊Q8—21no—
432C4⋊Q8—21no—
433C4⋊Q8D4×C1311yescharacteristic
434C4⋊Q8D4×C1311yescharacteristic
435#126—21no—
436#126—21no—
437#126—21no—
438#126—21no—
439#126—21no—
440#126—21no—
441#126—21no—
442#126—21no—
443#126—21no—
444#126—21no—
445#126—21no—
446#126—21no—
447#126—21no—
448#125—21no—
449#125—21no—
450#125—21no—
451#125—21no—
452#125—21no—
453#125—21no—
454#125—21no—
455#125—21no—
456#125—21no—
457#125D4×C1311yescharacteristic
458#124—21no—
459#124—21no—
460#124—21no—
461#124D4×C1311yescharacteristic
462#123—21no—
463#123—21no—
464#123—21no—
465#123—21no—
466#123—21no—
467#123—21no—
468#123—21no—
469#123—21no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—21no—
483C22⋊Q8—21no—
484C22⋊Q8C23×C1311yescharacteristic
485C22⋊Q8C23×C1311yescharacteristic
486C22⋊Q8C23×C1311yescharacteristic
487#121—21no—
488#121C23×C1311yescharacteristic
489#120—21no—
490C4×Q8—21no—
491C4×Q8—21no—
492C4×Q8—21no—
493C4×Q8D4×C1311yescharacteristic
494C4×Q8D4×C1311yescharacteristic
495C4×Q8D4×C1311yescharacteristic
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—21no—
499C4×D4—21no—
500C4×D4—21no—
501C4×D4D4×C1311yescharacteristic
502#117—21no—
503#117—21no—
504#117—21no—
505#117—21no—
506#117—21no—
507#117—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4D4×C1311yescharacteristic
513C2×C4⋊C4D4×C1311yescharacteristic
514C2×C4⋊C4C23×C1311yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4D4×C1311yescharacteristic
518C2×C22⋊C4D4×C1311yescharacteristic
519C2×C22⋊C4C23×C1311yescharacteristic
520C2×C42C23×C1311yescharacteristic
521C4⋊C8—21no—
522C4⋊C8—21no—
523#103—22no—
524#103—22no—
525#103—22no—
526#103—22no—
527C22⋊C8C23×C1312yes—
528C22⋊C8C23×C1312yes—
529#97—21no—
530C4×C8—21no—
531#95—21no—
532#95—21no—
533#95—22no—
534#95—22no—
535#95C23×C1312yes—
536C2×C13—22no—
537C2×C13—81no—
538C2×C13—81no—
539C2×C13#301111yescharacteristic
540C2×C13#302211yescharacteristic
541C2×C13#302711yescharacteristic
542C24C2×D4×C1311yescharacteristic
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—82no—
549C2×Q8C2×D4×C1311yescharacteristic
550C2×Q8C2×D4×C1311yescharacteristic
551C2×Q8C2×D4×C1311yescharacteristic
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4C2×D4×C1311yescharacteristic
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4C2×D4×C1311yescharacteristic
564C22×C4C2×D4×C1311yescharacteristic
565C22×C4C2×D4×C1311yescharacteristic
566C22×C4C2×D4×C1311yescharacteristic
567C22×C4C2×D4×C1311yescharacteristic
568C22×C4C24×C1311yescharacteristic
569Q16—82no—
570Q16—82no—
571Q16—82no—
572SD16—82no—
573C2×C8—22no—
574C2×C8—22no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—41no—
605C4⋊C4—41no—
606C4⋊C4—41no—
607C4⋊C4—41no—
608C4⋊C4—82no—
609C4⋊C4C2×D4×C1311yescharacteristic
610C4⋊C4C2×D4×C1311yescharacteristic
611C4⋊C4C2×D4×C1311yescharacteristic
612C4⋊C4C2×D4×C1311yescharacteristic
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—82no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42C2×D4×C1311yescharacteristic
643C42C2×D4×C1311yescharacteristic
644C42C2×D4×C1311yescharacteristic
645C42C2×D4×C1311yescharacteristic
646C13#1846511yescharacteristic, direct product factor, Sylow
647C23—21no—
648C23—21no—
649C23—22no—
650C23—41no—
651C23—41no—
652C23C22×D4×C1311yescharacteristic
653Q8—41no—
654Q8—41no—
655Q8—41no—
656Q8—42no—
657Q8—42no—
658Q8—42no—
659Q8—42no—
660Q8—81no—
661Q8—81no—
662Q8—81no—
663D4—41no—
664D4—42no—
665D4—81no—
666D4—81no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4C13×#12011yescharacteristic
695C2×C4C13×#12011yescharacteristic
696C2×C4C13×#12011yescharacteristic
697C2×C4C13×#12011yescharacteristic
698C2×C4C22×D4×C1311yescharacteristic
699C2×C4C22×D4×C1311yescharacteristic
700C8—42no—
701C8—42no—
702C22—21no—
703C22—21no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—82no—
711C22C2×C13×#12011yescharacteristic
712C22C13×#57812yes—
713C4—21no—
714C4—21no—
715C4—21no—
716C4—21no—
717C4—21no—
718C4—21no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—82no—
730C4—82no—
731C2—22no—
732C2—81no—
733C2—81no—
734C2C13×#301111yescharacteristic
735C2C13×#302211yescharacteristic
736C2C13×#302711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#538C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3218C2semidirect
3. C13×#3209C2semidirect
4. C13×#2821C2semidirect
6. C13×#1605C2semidirect
7. C13×#1603C2semidirect
8. C13×#1602C2semidirect
9. C13×#1521C2semidirect
10. C13×#1515C2semidirect
11. C13×#1473C2semidirect
174. #18465C13direct (N × H)
280. #3218C2×C13semidirect
281. #3209C2×C13semidirect
282. #2821C2×C13semidirect
284. #1605C2×C13semidirect
285. #1603C2×C13semidirect
286. #1602C2×C13semidirect
287. #1521C2×C13semidirect
288. #1515C2×C13semidirect
289. #1473C2×C13semidirect
646. C13#18465direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35642
C13×#32182
C13×#32092
C13×#28212
C13×#16062
C13×#16052
C13×#16032
C13×#16022
C13×#15212
C13×#15152
C13×#14732
#1846513