Finite Group Databasebeta

← C13×#32731 #15719070

Subgroups — C13×#32731 #15719070

Order 3328.

782 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2625C211yesmaximal, characteristic, complemented
2C13×#2619C211yesmaximal, characteristic
3C13×#2101C211yesmaximal, characteristic, complemented
4C13×#2097C211yesmaximal, characteristic, complemented
5C13×#2067C211yesmaximal, characteristic, complemented
6C13×#2065C211yesmaximal, characteristic, complemented
7C13×#2055C211yesmaximal, characteristic, complemented
8C13×#2055C211yesmaximal, characteristic, complemented
9C13×#2041C211yesmaximal, characteristic, complemented
10C13×#2034C211yesmaximal, characteristic, complemented
11C13×#2033C211yesmaximal, characteristic, complemented
12C13×#2014C211yesmaximal, characteristic, complemented
13C13×#2000C211yesmaximal, characteristic, complemented
14C13×#2000C211yesmaximal, characteristic, complemented
15C13×#1798C211yesmaximal, characteristic, complemented
16C22×C13×SD16C2211yescharacteristic
17C22×C13×SD16C2211yescharacteristic
18C2×C13×#127C2211yescharacteristic
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×C13×#121C2211yescharacteristic
21C2×C13×#121C2211yescharacteristic
22C2×C13×#117C2211yescharacteristic
23C2×C13×#107C2211yescharacteristic
24C2×C13×#106C2211yescharacteristic
25C2×C13×C4⋊C8C2211yescharacteristic
26C2×C13×C4⋊C8C2211yescharacteristic
27C2×C13×#103C2211yescharacteristic
28C2×C13×#103C2211yescharacteristic
29C2×C13×#102C2211yescharacteristic
30C2×C13×#102C2211yescharacteristic
31C2×C13×#102C2211yescharacteristic
32C2×C13×#102C2211yescharacteristic
33C2×C13×#102C2211yescharacteristic
34C2×C13×#102C2211yescharacteristic
35C2×C13×C22⋊C8C2211yescharacteristic
36C2×C13×C22⋊C8C2211yescharacteristic
37C13×#400—21no—
38C13×#398—21no—
39C13×#397—21no—
40C13×#397—21no—
41C13×#394—21no—
42C13×#394—21no—
43C13×#392—21no—
44C13×#392—21no—
45C13×#391C2211yescharacteristic
46C13×#391C2211yescharacteristic
47C13×#390C2211yescharacteristic
48C13×#390C2211yescharacteristic
49C13×#389C2211yescharacteristic
50C13×#389C2211yescharacteristic
51C13×#382C2211yescharacteristic
52C13×#380C2211yescharacteristic
53C13×#340C2211yescharacteristic
54C13×#340C2211yescharacteristic
55C13×#340C2211yescharacteristic
56C13×#340C2211yescharacteristic
57C13×#336C2211yescharacteristic
58C13×#336C2211yescharacteristic
59C22×Q8×C13C2311yescharacteristic
60C22×D4×C13—21no—
61C22×D4×C13—21no—
62C22×D4×C13—21no—
63C22×D4×C13—21no—
64C22×D4×C13C2311yescharacteristic
65C22×D4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C2×C13×SD16—41no—
68C2×C13×SD16—41no—
69C2×C13×SD16—41no—
70C2×C13×SD16—41no—
71C2×C13×SD16—41no—
72C2×C13×SD16—41no—
73C22×C8×C13C2311yescharacteristic
74C22×C8×C13C2311yescharacteristic
75C22×C8×C13C2311yescharacteristic
76C22×C8×C13C2311yescharacteristic
77C13×#127—41no—
78C13×#127—41no—
79C13×C22⋊Q8—41no—
80C13×C22⋊Q8—41no—
81C13×#121—41no—
82C13×#121—41no—
83C13×#121—41no—
84C13×#121—41no—
85C13×#117—41no—
86C13×#117—41no—
87C2×C13×C4⋊C4—21no—
88C2×C13×C4⋊C4—21no—
89C2×C13×C4⋊C4—21no—
90C2×C13×C4⋊C4D411yescharacteristic
91C2×C13×C4⋊C4D411yescharacteristic
92C2×C13×C4⋊C4C2311yescharacteristic
93C2×C13×C4⋊C4C2311yescharacteristic
94C2×C13×C4⋊C4C2311yescharacteristic
95C2×C13×C4⋊C4C2311yescharacteristic
96C2×C13×C4⋊C4C2311yescharacteristic
97C2×C13×C22⋊C4—21no—
98C2×C13×C22⋊C4—21no—
99C2×C13×C22⋊C4—21no—
100C2×C13×C22⋊C4—21no—
101C2×C13×C22⋊C4—21no—
102C2×C13×C22⋊C4—21no—
103C2×C13×C22⋊C4—21no—
104C2×C13×C22⋊C4—21no—
105C2×C13×C22⋊C4D411yescharacteristic
106C2×C13×C22⋊C4D411yescharacteristic
107C2×C42×C13C2311yescharacteristic
108C2×C42×C13C2311yescharacteristic
109C13×#107—41no—
110C13×#106—41no—
111C13×C4⋊C8—41no—
112C13×C4⋊C8—41no—
113C13×#103—41no—
114C13×#103—41no—
115C13×#102—41no—
116C13×#102—41no—
117C13×#102—41no—
118C13×#102—41no—
119C13×#102—41no—
120C13×#102—41no—
121C13×C22⋊C8—41no—
122C13×C22⋊C8—41no—
123C13×#95—21no—
124C13×#95—21no—
125C13×#95—21no—
126C13×#95—21no—
127C13×#95—21no—
128C13×#95—21no—
129C13×#95—21no—
130C13×#95—21no—
131C13×#95—21no—
132#32731C1311yesmaximal, characteristic, direct product factor, Sylow
133C24×C13—21no—
134C24×C13—21no—
135C24×C13C2×D411yescharacteristic
136C2×Q8×C13—21no—
137C2×Q8×C13—21no—
138C2×Q8×C13—21no—
139C2×Q8×C13—21no—
140C2×Q8×C13—21no—
141C2×Q8×C13—21no—
142C2×D4×C13—21no—
143C2×D4×C13—21no—
144C2×D4×C13—21no—
145C2×D4×C13—21no—
146C2×D4×C13—21no—
147C2×D4×C13—21no—
148C2×D4×C13—21no—
149C2×D4×C13—21no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C2×D4×C13—21no—
154C2×D4×C13—42no—
155C2×D4×C13—42no—
156C2×D4×C13—42no—
157C2×D4×C13—42no—
158C2×D4×C13—81no—
159C2×D4×C13—81no—
160C2×D4×C13—81no—
161C2×D4×C13—81no—
162C2×D4×C13—81no—
163C2×D4×C13—81no—
164C2×D4×C13—81no—
165C2×D4×C13—81no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13C2×D411yescharacteristic
179C22×C4×C13C2×D411yescharacteristic
180C22×C4×C13C2×D411yescharacteristic
181C22×C4×C13C2×D411yescharacteristic
182C22×C4×C13C2×D411yescharacteristic
183C22×C4×C13C2411yescharacteristic
184C13×SD16—44no—
185C13×SD16—44no—
186C2×C8×C13—21no—
187C2×C8×C13—21no—
188C2×C8×C13—21no—
189C2×C8×C13—21no—
190C2×C8×C13—21no—
191C2×C8×C13—21no—
192C2×C8×C13—21no—
193C2×C8×C13—21no—
194C2×C8×C13—21no—
195C2×C8×C13—21no—
196C2×C8×C13—21no—
197C2×C8×C13—21no—
198C13×C4⋊C4—21no—
199C13×C4⋊C4—21no—
200C13×C4⋊C4—21no—
201C13×C4⋊C4—21no—
202C13×C4⋊C4—21no—
203C13×C4⋊C4—21no—
204C13×C4⋊C4—21no—
205C13×C4⋊C4—21no—
206C13×C4⋊C4—21no—
207C13×C4⋊C4—21no—
208C13×C4⋊C4—41no—
209C13×C4⋊C4—41no—
210C13×C4⋊C4—42no—
211C13×C4⋊C4—81no—
212C13×C4⋊C4—81no—
213C13×C22⋊C4—41no—
214C13×C22⋊C4—41no—
215C13×C22⋊C4—42no—
216C13×C22⋊C4—42no—
217C13×C22⋊C4—42no—
218C13×C22⋊C4—81no—
219C13×C22⋊C4—81no—
220C13×C22⋊C4—81no—
221C13×C22⋊C4—81no—
222C13×C22⋊C4—81no—
223C42×C13—21no—
224C42×C13—21no—
225C42×C13—21no—
226C42×C13—21no—
227#2625C2×C1311yescharacteristic, complemented
228#2619C2×C1311yescharacteristic
229#2101C2×C1311yescharacteristic, complemented
230#2097C2×C1311yescharacteristic, complemented
231#2067C2×C1311yescharacteristic, complemented
232#2065C2×C1311yescharacteristic, complemented
233#2055C2×C1311yescharacteristic, complemented
234#2055C2×C1311yescharacteristic, complemented
235#2041C2×C1311yescharacteristic, complemented
236#2034C2×C1311yescharacteristic, complemented
237#2033C2×C1311yescharacteristic, complemented
238#2014C2×C1311yescharacteristic, complemented
239#2000C2×C1311yescharacteristic, complemented
240#2000C2×C1311yescharacteristic, complemented
241#1798C2×C1311yescharacteristic, complemented
242C23×C13—21no—
243C23×C13—21no—
244C23×C13—21no—
245C23×C13—21no—
246C23×C13—21no—
247C23×C13—21no—
248C23×C13—21no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13—41no—
252C23×C13—41no—
253C23×C13—41no—
254C23×C13—41no—
255C23×C13—41no—
256C23×C13—41no—
257C23×C13—41no—
258C23×C13—41no—
259C23×C13—41no—
260C23×C13—41no—
261C23×C13—41no—
262C23×C13—41no—
263C23×C13C22×D411yescharacteristic
264Q8×C13—41no—
265Q8×C13—41no—
266Q8×C13—41no—
267Q8×C13—41no—
268D4×C13—41no—
269D4×C13—41no—
270D4×C13—41no—
271D4×C13—41no—
272D4×C13—41no—
273D4×C13—41no—
274D4×C13—41no—
275D4×C13—41no—
276D4×C13—84no—
277D4×C13—84no—
278D4×C13—84no—
279D4×C13—84no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—21no—
283C2×C4×C13—21no—
284C2×C4×C13—21no—
285C2×C4×C13—21no—
286C2×C4×C13—21no—
287C2×C4×C13—21no—
288C2×C4×C13—21no—
289C2×C4×C13—21no—
290C2×C4×C13—21no—
291C2×C4×C13—21no—
292C2×C4×C13—21no—
293C2×C4×C13—21no—
294C2×C4×C13—21no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—41no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
306C2×C4×C13—41no—
307C2×C4×C13—41no—
308C2×C4×C13—41no—
309C2×C4×C13—41no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—41no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13—41no—
316C2×C4×C13—41no—
317C2×C4×C13H(5,𝔽2)11yescharacteristic
318C2×C4×C13H(5,𝔽2)11yescharacteristic
319C2×C4×C13H(5,𝔽2)11yescharacteristic
320C2×C4×C13H(5,𝔽2)11yescharacteristic
321C2×C4×C13H(5,𝔽2)11yescharacteristic
322C2×C4×C132−1+411yescharacteristic
323C8×C13—41no—
324C8×C13—41no—
325C8×C13—41no—
326C8×C13—41no—
327C22×SD16C22×C1311yescharacteristic
328C22×SD16C22×C1311yescharacteristic
329C2×#127C22×C1311yescharacteristic
330C2×C22⋊Q8C22×C1311yescharacteristic
331C2×#121C22×C1311yescharacteristic
332C2×#121C22×C1311yescharacteristic
333C2×#117C22×C1311yescharacteristic
334C2×#107C22×C1311yescharacteristic
335C2×#106C22×C1311yescharacteristic
336C2×C4⋊C8C22×C1311yescharacteristic
337C2×C4⋊C8C22×C1311yescharacteristic
338C2×#103C22×C1311yescharacteristic
339C2×#103C22×C1311yescharacteristic
340C2×#102C22×C1311yescharacteristic
341C2×#102C22×C1311yescharacteristic
342C2×#102C22×C1311yescharacteristic
343C2×#102C22×C1311yescharacteristic
344C2×#102C22×C1311yescharacteristic
345C2×#102C22×C1311yescharacteristic
346C2×C22⋊C8C22×C1311yescharacteristic
347C2×C22⋊C8C22×C1311yescharacteristic
348#400—21no—
349#398—21no—
350#397—21no—
351#397—21no—
352#394—21no—
353#394—21no—
354#392—21no—
355#392—21no—
356#391C22×C1311yescharacteristic
357#391C22×C1311yescharacteristic
358#390C22×C1311yescharacteristic
359#390C22×C1311yescharacteristic
360#389C22×C1311yescharacteristic
361#389C22×C1311yescharacteristic
362#382C22×C1311yescharacteristic
363#380C22×C1311yescharacteristic
364#340C22×C1311yescharacteristic
365#340C22×C1311yescharacteristic
366#340C22×C1311yescharacteristic
367#340C22×C1311yescharacteristic
368#336C22×C1311yescharacteristic
369#336C22×C1311yescharacteristic
370C22×C13—41no—
371C22×C13—41no—
372C22×C13—41no—
373C22×C13—41no—
374C22×C13—41no—
375C22×C13—41no—
376C22×C13—41no—
377C22×C13—81no—
378C22×C13—81no—
379C22×C13—81no—
380C22×C13—81no—
381C22×C13—81no—
382C22×C13—81no—
383C22×C13—81no—
384C22×C13—81no—
385C22×C13—81no—
386C22×C13—81no—
387C22×C13—81no—
388C22×C13—81no—
389C22×C13—81no—
390C22×C13—81no—
391C22×C13#53411yescharacteristic
392C22×C13#53511yescharacteristic
393C22×C13#53711yescharacteristic
394C22×C13#57611yescharacteristic
395C22×C13#57711yescharacteristic
396C22×C13#57711yescharacteristic
397C22×C13#57711yescharacteristic
398C4×C13—41no—
399C4×C13—41no—
400C4×C13—41no—
401C4×C13—41no—
402C4×C13—41no—
403C4×C13—81no—
404C4×C13—81no—
405C4×C13—81no—
406C4×C13—81no—
407C4×C13—81no—
408C4×C13—81no—
409C4×C13#56011yescharacteristic
410C4×C13#56011yescharacteristic
411C4×C13#56211yescharacteristic
412C4×C13#56211yescharacteristic
413C22×Q8C23×C1311yescharacteristic
414C22×D4—21no—
415C22×D4—21no—
416C22×D4—21no—
417C22×D4—21no—
418C22×D4C23×C1311yescharacteristic
419C22×D4C23×C1311yescharacteristic
420C23×C4C23×C1311yescharacteristic
421C2×SD16—41no—
422C2×SD16—41no—
423C2×SD16—41no—
424C2×SD16—41no—
425C2×SD16—41no—
426C2×SD16—41no—
427C22×C8C23×C1311yescharacteristic
428C22×C8C23×C1311yescharacteristic
429C22×C8C23×C1311yescharacteristic
430C22×C8C23×C1311yescharacteristic
431#127—41no—
432#127—41no—
433C22⋊Q8—41no—
434C22⋊Q8—41no—
435#121—41no—
436#121—41no—
437#121—41no—
438#121—41no—
439#117—41no—
440#117—41no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4D4×C1311yescharacteristic
445C2×C4⋊C4D4×C1311yescharacteristic
446C2×C4⋊C4C23×C1311yescharacteristic
447C2×C4⋊C4C23×C1311yescharacteristic
448C2×C4⋊C4C23×C1311yescharacteristic
449C2×C4⋊C4C23×C1311yescharacteristic
450C2×C4⋊C4C23×C1311yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4D4×C1311yescharacteristic
460C2×C22⋊C4D4×C1311yescharacteristic
461C2×C42C23×C1311yescharacteristic
462C2×C42C23×C1311yescharacteristic
463#107—41no—
464#106—41no—
465C4⋊C8—41no—
466C4⋊C8—41no—
467#103—41no—
468#103—41no—
469#102—41no—
470#102—41no—
471#102—41no—
472#102—41no—
473#102—41no—
474#102—41no—
475C22⋊C8—41no—
476C22⋊C8—41no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486C2×C13—81no—
487C2×C13—161no—
488C2×C13—161no—
489C2×C13#281311yescharacteristic
490C2×C13#319811yescharacteristic
491C2×C13#320011yescharacteristic
492C2×C13#322211yescharacteristic
493C2×C13#322411yescharacteristic
494C2×C13#325711yescharacteristic
495C2×C13#326011yescharacteristic
496C24—21no—
497C24—21no—
498C24C2×D4×C1311yescharacteristic
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—81no—
522C2×D4—81no—
523C2×D4—81no—
524C2×D4—81no—
525C2×D4—81no—
526C2×D4—81no—
527C2×D4—81no—
528C2×D4—81no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4C2×D4×C1311yescharacteristic
542C22×C4C2×D4×C1311yescharacteristic
543C22×C4C2×D4×C1311yescharacteristic
544C22×C4C2×D4×C1311yescharacteristic
545C22×C4C2×D4×C1311yescharacteristic
546C22×C4C24×C1311yescharacteristic
547SD16—44no—
548SD16—44no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—41no—
572C4⋊C4—41no—
573C4⋊C4—42no—
574C4⋊C4—81no—
575C4⋊C4—81no—
576C22⋊C4—41no—
577C22⋊C4—41no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—81no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C22⋊C4—81no—
585C22⋊C4—81no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C13#3273111yescharacteristic, direct product factor, Sylow
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23C22×D4×C1311yescharacteristic
613Q8—41no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—41no—
621D4—41no—
622D4—41no—
623D4—41no—
624D4—41no—
625D4—84no—
626D4—84no—
627D4—84no—
628D4—84no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4C13×H(5,𝔽2)11yescharacteristic
667C2×C4C13×H(5,𝔽2)11yescharacteristic
668C2×C4C13×H(5,𝔽2)11yescharacteristic
669C2×C4C13×H(5,𝔽2)11yescharacteristic
670C2×C4C13×H(5,𝔽2)11yescharacteristic
671C2×C4C13×2−1+411yescharacteristic
672C8—41no—
673C8—41no—
674C8—41no—
675C8—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22C13×#53411yescharacteristic
698C22C13×#53511yescharacteristic
699C22C13×#53711yescharacteristic
700C22C13×#57611yescharacteristic
701C22C13×#57711yescharacteristic
702C22C13×#57711yescharacteristic
703C22C13×#57711yescharacteristic
704C4—41no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—81no—
710C4—81no—
711C4—81no—
712C4—81no—
713C4—81no—
714C4—81no—
715C4C13×#56011yescharacteristic
716C4C13×#56011yescharacteristic
717C4C13×#56211yescharacteristic
718C4C13×#56211yescharacteristic
719C2—81no—
720C2—161no—
721C2—161no—
722C2C13×#281311yescharacteristic
723C2C13×#319811yescharacteristic
724C2C13×#320011yescharacteristic
725C2C13×#322211yescharacteristic
726C2C13×#322411yescharacteristic
727C2C13×#325711yescharacteristic
728C2C13×#326011yescharacteristic
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#2619C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C13×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2625C2semidirect
3. C13×#2101C2semidirect
4. C13×#2097C2semidirect
5. C13×#2067C2semidirect
6. C13×#2065C2semidirect
7. C13×#2055C2semidirect
8. C13×#2055C2semidirect
9. C13×#2041C2semidirect
10. C13×#2034C2semidirect
11. C13×#2033C2semidirect
12. C13×#2014C2semidirect
13. C13×#2000C2semidirect
14. C13×#2000C2semidirect
15. C13×#1798C2semidirect
132. #32731C13direct (N × H)
227. #2625C2×C13semidirect
229. #2101C2×C13semidirect
230. #2097C2×C13semidirect
231. #2067C2×C13semidirect
232. #2065C2×C13semidirect
233. #2055C2×C13semidirect
234. #2055C2×C13semidirect
235. #2041C2×C13semidirect
236. #2034C2×C13semidirect
237. #2033C2×C13semidirect
238. #2014C2×C13semidirect
239. #2000C2×C13semidirect
240. #2000C2×C13semidirect
241. #1798C2×C13semidirect
590. C13#32731direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26252
C13×#26192
C13×#21012
C13×#20972
C13×#20672
C13×#20652
C13×#20552
C13×#20412
C13×#20342
C13×#20332
C13×#20142
C13×#20002
C13×#17982
#3273113