Finite Group Databasebeta

← C13×#32713 #15719052

Subgroups — C13×#32713 #15719052

Order 3328.

906 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2616C211yesmaximal, characteristic, complemented
2C13×#2615C211yesmaximal, characteristic
3C13×#2077C211yesmaximal, characteristic, complemented
4C13×#2076C211yesmaximal, characteristic, complemented
5C13×#2075C211yesmaximal, characteristic, complemented
6C13×#2036C211yesmaximal, characteristic, complemented
7C13×#2036C211yesmaximal, characteristic, complemented
8C13×#2035C211yesmaximal, characteristic, complemented
9C13×#2034C211yesmaximal, characteristic, complemented
10C13×#2033C211yesmaximal, characteristic, complemented
11C13×#2033C211yesmaximal, characteristic, complemented
12C13×#2000C211yesmaximal, characteristic, complemented
13C13×#2000C211yesmaximal, characteristic, complemented
14C13×#2000C211yesmaximal, characteristic, complemented
15C13×#1780C211yesmaximal, characteristic, complemented
16C22×C13×#41C2211yescharacteristic
17C22×C13×SD16C2211yescharacteristic
18C2×C13×C22⋊Q8C2211yescharacteristic
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×C13×C22⋊Q8C2211yescharacteristic
21C2×C13×#121C2211yescharacteristic
22C2×C13×#121C2211yescharacteristic
23C2×C13×#121C2211yescharacteristic
24C2×C13×#107C2211yescharacteristic
25C2×C13×#107C2211yescharacteristic
26C2×C13×#106C2211yescharacteristic
27C2×C13×#103C2211yescharacteristic
28C2×C13×#103C2211yescharacteristic
29C2×C13×#103C2211yescharacteristic
30C2×C13×#102C2211yescharacteristic
31C2×C13×#102C2211yescharacteristic
32C2×C13×#102C2211yescharacteristic
33C2×C13×C22⋊C8C2211yescharacteristic
34C2×C13×C22⋊C8C2211yescharacteristic
35C2×C13×C22⋊C8C2211yescharacteristic
36C2×C13×C22⋊C8C2211yescharacteristic
37C2×C13×C22⋊C8C2211yescharacteristic
38C2×C13×C22⋊C8C2211yescharacteristic
39C13×#395—21no—
40C13×#394—21no—
41C13×#394—21no—
42C13×#394—21no—
43C13×#393—21no—
44C13×#392—21no—
45C13×#392—21no—
46C13×#392—21no—
47C13×#380C2211yescharacteristic
48C13×#380C2211yescharacteristic
49C13×#380C2211yescharacteristic
50C13×#380C2211yescharacteristic
51C13×#380C2211yescharacteristic
52C13×#380C2211yescharacteristic
53C13×#340C2211yescharacteristic
54C13×#340C2211yescharacteristic
55C13×#340C2211yescharacteristic
56C13×#340C2211yescharacteristic
57C13×#340C2211yescharacteristic
58C13×#340C2211yescharacteristic
59C2×C13×#41—41no—
60C2×C13×#41—41no—
61C2×C13×#41—41no—
62C2×C13×#41—41no—
63C2×C13×#41—41no—
64C2×C13×#41—41no—
65C22×Q8×C13D411yescharacteristic
66C22×Q8×C13C2311yescharacteristic
67C22×D4×C13—21no—
68C22×D4×C13—21no—
69C22×D4×C13—21no—
70C22×D4×C13D411yescharacteristic
71C22×D4×C13D411yescharacteristic
72C22×D4×C13D411yescharacteristic
73C22×D4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C2×C13×SD16—41no—
78C2×C13×SD16—41no—
79C2×C13×SD16—41no—
80C22×C8×C13C2311yescharacteristic
81C22×C8×C13C2311yescharacteristic
82C22×C8×C13C2311yescharacteristic
83C22×C8×C13C2311yescharacteristic
84C13×C22⋊Q8—41no—
85C13×C22⋊Q8—41no—
86C13×C22⋊Q8—41no—
87C13×C22⋊Q8—41no—
88C13×C22⋊Q8—41no—
89C13×C22⋊Q8—41no—
90C13×#121—41no—
91C13×#121—41no—
92C13×#121—41no—
93C13×#121—41no—
94C13×#121—41no—
95C13×#121—41no—
96C2×C13×C4⋊C4—21no—
97C2×C13×C4⋊C4—21no—
98C2×C13×C4⋊C4—21no—
99C2×C13×C4⋊C4C2311yescharacteristic
100C2×C13×C4⋊C4C2311yescharacteristic
101C2×C13×C4⋊C4C2311yescharacteristic
102C2×C13×C4⋊C4C2311yescharacteristic
103C2×C13×C4⋊C4C2311yescharacteristic
104C2×C13×C4⋊C4C2311yescharacteristic
105C2×C13×C22⋊C4—21no—
106C2×C13×C22⋊C4—21no—
107C2×C13×C22⋊C4—21no—
108C2×C13×C22⋊C4—21no—
109C2×C13×C22⋊C4—21no—
110C2×C13×C22⋊C4—21no—
111C2×C13×C22⋊C4—21no—
112C2×C13×C22⋊C4—21no—
113C2×C13×C22⋊C4—21no—
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4—21no—
116C2×C13×C22⋊C4—21no—
117C13×#107—41no—
118C13×#107—41no—
119C13×#106—41no—
120C13×#103—41no—
121C13×#103—41no—
122C13×#103—41no—
123C13×#102—41no—
124C13×#102—41no—
125C13×#102—41no—
126C13×C22⋊C8—41no—
127C13×C22⋊C8—41no—
128C13×C22⋊C8—41no—
129C13×C22⋊C8—41no—
130C13×C22⋊C8—41no—
131C13×C22⋊C8—41no—
132C13×#95—21no—
133C13×#95—21no—
134C13×#95—21no—
135C13×#95—21no—
136C13×#95—21no—
137C13×#95—21no—
138#32713C1311yesmaximal, characteristic, direct product factor, Sylow
139C24×C13—21no—
140C24×C13C2×D411yescharacteristic
141C24×C13C2×D411yescharacteristic
142C24×C13C2×D411yescharacteristic
143C13×#41—44no—
144C13×#41—44no—
145C13×#41—44no—
146C13×#41—44no—
147C2×Q8×C13—21no—
148C2×Q8×C13—21no—
149C2×Q8×C13—21no—
150C2×Q8×C13—21no—
151C2×Q8×C13—21no—
152C2×Q8×C13—21no—
153C2×Q8×C13—41no—
154C2×Q8×C13—41no—
155C2×Q8×C13—41no—
156C2×D4×C13—21no—
157C2×D4×C13—21no—
158C2×D4×C13—21no—
159C2×D4×C13—21no—
160C2×D4×C13—21no—
161C2×D4×C13—21no—
162C2×D4×C13—41no—
163C2×D4×C13—41no—
164C2×D4×C13—41no—
165C2×D4×C13—41no—
166C2×D4×C13—41no—
167C2×D4×C13—41no—
168C2×D4×C13—41no—
169C2×D4×C13—41no—
170C2×D4×C13—41no—
171C2×D4×C13—42no—
172C2×D4×C13—42no—
173C2×D4×C13—42no—
174C2×D4×C13—81no—
175C2×D4×C13—81no—
176C2×D4×C13—81no—
177C2×D4×C13—81no—
178C2×D4×C13—81no—
179C2×D4×C13—81no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
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—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13C2×D411yescharacteristic
207C22×C4×C13C2×D411yescharacteristic
208C22×C4×C13C2411yescharacteristic
209C13×SD16—44no—
210C2×C8×C13—21no—
211C2×C8×C13—21no—
212C2×C8×C13—21no—
213C2×C8×C13—21no—
214C2×C8×C13—21no—
215C2×C8×C13—21no—
216C2×C8×C13—21no—
217C2×C8×C13—21no—
218C2×C8×C13—21no—
219C2×C8×C13—21no—
220C2×C8×C13—21no—
221C2×C8×C13—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—42no—
235C13×C4⋊C4—42no—
236C13×C4⋊C4—42no—
237C13×C22⋊C4—42no—
238C13×C22⋊C4—42no—
239C13×C22⋊C4—42no—
240C13×C22⋊C4—42no—
241C13×C22⋊C4—42no—
242C13×C22⋊C4—42no—
243C13×C22⋊C4—81no—
244C13×C22⋊C4—81no—
245C13×C22⋊C4—81no—
246C13×C22⋊C4—81no—
247C13×C22⋊C4—81no—
248C13×C22⋊C4—81no—
249#2616C2×C1311yescharacteristic, complemented
250#2615C2×C1311yescharacteristic
251#2077C2×C1311yescharacteristic, complemented
252#2076C2×C1311yescharacteristic, complemented
253#2075C2×C1311yescharacteristic, complemented
254#2036C2×C1311yescharacteristic, complemented
255#2036C2×C1311yescharacteristic, complemented
256#2035C2×C1311yescharacteristic, complemented
257#2034C2×C1311yescharacteristic, complemented
258#2033C2×C1311yescharacteristic, complemented
259#2033C2×C1311yescharacteristic, complemented
260#2000C2×C1311yescharacteristic, complemented
261#2000C2×C1311yescharacteristic, complemented
262#2000C2×C1311yescharacteristic, complemented
263#1780C2×C1311yescharacteristic, complemented
264C23×C13—21no—
265C23×C13—21no—
266C23×C13—21no—
267C23×C13—21no—
268C23×C13—21no—
269C23×C13—21no—
270C23×C13—21no—
271C23×C13—21no—
272C23×C13—21no—
273C23×C13—21no—
274C23×C13—21no—
275C23×C13—21no—
276C23×C13—21no—
277C23×C13—21no—
278C23×C13—21no—
279C23×C13—21no—
280C23×C13—21no—
281C23×C13—21no—
282C23×C13—21no—
283C23×C13—21no—
284C23×C13—21no—
285C23×C13—41no—
286C23×C13—41no—
287C23×C13—41no—
288C23×C13—41no—
289C23×C13—41no—
290C23×C13—41no—
291C23×C13—41no—
292C23×C13C22×D411yescharacteristic
293Q8×C13—44no—
294Q8×C13—41no—
295Q8×C13—41no—
296Q8×C13—41no—
297Q8×C13—41no—
298D4×C13—44no—
299D4×C13—44no—
300D4×C13—44no—
301D4×C13—41no—
302D4×C13—41no—
303D4×C13—41no—
304D4×C13—41no—
305D4×C13—84no—
306D4×C13—84no—
307D4×C13—84no—
308C2×C4×C13—21no—
309C2×C4×C13—21no—
310C2×C4×C13—21no—
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—41no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×C4×C13—41no—
322C2×C4×C13—41no—
323C2×C4×C13—41no—
324C2×C4×C13—41no—
325C2×C4×C13—41no—
326C2×C4×C13—41no—
327C2×C4×C13—41no—
328C2×C4×C13—41no—
329C2×C4×C13—41no—
330C2×C4×C13—41no—
331C2×C4×C13—41no—
332C2×C4×C13—41no—
333C2×C4×C13—41no—
334C2×C4×C13—41no—
335C2×C4×C13—41no—
336C2×C4×C13—41no—
337C2×C4×C13—41no—
338C2×C4×C13—41no—
339C2×C4×C13—41no—
340C2×C4×C13—41no—
341C2×C4×C13—41no—
342C2×C4×C13—41no—
343C2×C4×C13—41no—
344C2×C4×C13—41no—
345C2×C4×C13—41no—
346C2×C4×C13—41no—
347C2×C4×C13—41no—
348C2×C4×C13—41no—
349C2×C4×C13—41no—
350C2×C4×C13H(5,𝔽2)11yescharacteristic
351C2×C4×C13H(5,𝔽2)11yescharacteristic
352C2×C4×C13H(5,𝔽2)11yescharacteristic
353C2×C4×C13H(5,𝔽2)11yescharacteristic
354C2×C4×C13H(5,𝔽2)11yescharacteristic
355C2×C4×C13H(5,𝔽2)11yescharacteristic
356C8×C13—41no—
357C8×C13—41no—
358C8×C13—41no—
359C8×C13—41no—
360C22×#41C22×C1311yescharacteristic
361C22×SD16C22×C1311yescharacteristic
362C2×C22⋊Q8C22×C1311yescharacteristic
363C2×C22⋊Q8C22×C1311yescharacteristic
364C2×C22⋊Q8C22×C1311yescharacteristic
365C2×#121C22×C1311yescharacteristic
366C2×#121C22×C1311yescharacteristic
367C2×#121C22×C1311yescharacteristic
368C2×#107C22×C1311yescharacteristic
369C2×#107C22×C1311yescharacteristic
370C2×#106C22×C1311yescharacteristic
371C2×#103C22×C1311yescharacteristic
372C2×#103C22×C1311yescharacteristic
373C2×#103C22×C1311yescharacteristic
374C2×#102C22×C1311yescharacteristic
375C2×#102C22×C1311yescharacteristic
376C2×#102C22×C1311yescharacteristic
377C2×C22⋊C8C22×C1311yescharacteristic
378C2×C22⋊C8C22×C1311yescharacteristic
379C2×C22⋊C8C22×C1311yescharacteristic
380C2×C22⋊C8C22×C1311yescharacteristic
381C2×C22⋊C8C22×C1311yescharacteristic
382C2×C22⋊C8C22×C1311yescharacteristic
383#395—21no—
384#394—21no—
385#394—21no—
386#394—21no—
387#393—21no—
388#392—21no—
389#392—21no—
390#392—21no—
391#380C22×C1311yescharacteristic
392#380C22×C1311yescharacteristic
393#380C22×C1311yescharacteristic
394#380C22×C1311yescharacteristic
395#380C22×C1311yescharacteristic
396#380C22×C1311yescharacteristic
397#340C22×C1311yescharacteristic
398#340C22×C1311yescharacteristic
399#340C22×C1311yescharacteristic
400#340C22×C1311yescharacteristic
401#340C22×C1311yescharacteristic
402#340C22×C1311yescharacteristic
403C22×C13—41no—
404C22×C13—41no—
405C22×C13—41no—
406C22×C13—41no—
407C22×C13—41no—
408C22×C13—41no—
409C22×C13—41no—
410C22×C13—41no—
411C22×C13—41no—
412C22×C13—41no—
413C22×C13—41no—
414C22×C13—41no—
415C22×C13—41no—
416C22×C13—41no—
417C22×C13—41no—
418C22×C13—41no—
419C22×C13—41no—
420C22×C13—41no—
421C22×C13—41no—
422C22×C13—41no—
423C22×C13—41no—
424C22×C13—81no—
425C22×C13—81no—
426C22×C13—81no—
427C22×C13—81no—
428C22×C13—81no—
429C22×C13—81no—
430C22×C13—81no—
431C22×C13#53411yescharacteristic
432C22×C13#53411yescharacteristic
433C22×C13#53411yescharacteristic
434C22×C13#57611yescharacteristic
435C22×C13#57711yescharacteristic
436C22×C13#57711yescharacteristic
437C22×C13#57811yescharacteristic
438C4×C13—41no—
439C4×C13—41no—
440C4×C13—41no—
441C4×C13—81no—
442C4×C13—81no—
443C4×C13—81no—
444C4×C13—81no—
445C4×C13—81no—
446C4×C13—81no—
447C4×C13—81no—
448C4×C13#56011yescharacteristic
449C4×C13#56011yescharacteristic
450C4×C13#56011yescharacteristic
451C4×C13H(3,𝔽4)11yescharacteristic
452C2×#41—41no—
453C2×#41—41no—
454C2×#41—41no—
455C2×#41—41no—
456C2×#41—41no—
457C2×#41—41no—
458C22×Q8D4×C1311yescharacteristic
459C22×Q8C23×C1311yescharacteristic
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4D4×C1311yescharacteristic
464C22×D4D4×C1311yescharacteristic
465C22×D4D4×C1311yescharacteristic
466C22×D4C23×C1311yescharacteristic
467C23×C4C23×C1311yescharacteristic
468C23×C4C23×C1311yescharacteristic
469C23×C4C23×C1311yescharacteristic
470C2×SD16—41no—
471C2×SD16—41no—
472C2×SD16—41no—
473C22×C8C23×C1311yescharacteristic
474C22×C8C23×C1311yescharacteristic
475C22×C8C23×C1311yescharacteristic
476C22×C8C23×C1311yescharacteristic
477C22⋊Q8—41no—
478C22⋊Q8—41no—
479C22⋊Q8—41no—
480C22⋊Q8—41no—
481C22⋊Q8—41no—
482C22⋊Q8—41no—
483#121—41no—
484#121—41no—
485#121—41no—
486#121—41no—
487#121—41no—
488#121—41no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4C23×C1311yescharacteristic
493C2×C4⋊C4C23×C1311yescharacteristic
494C2×C4⋊C4C23×C1311yescharacteristic
495C2×C4⋊C4C23×C1311yescharacteristic
496C2×C4⋊C4C23×C1311yescharacteristic
497C2×C4⋊C4C23×C1311yescharacteristic
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510#107—41no—
511#107—41no—
512#106—41no—
513#103—41no—
514#103—41no—
515#103—41no—
516#102—41no—
517#102—41no—
518#102—41no—
519C22⋊C8—41no—
520C22⋊C8—41no—
521C22⋊C8—41no—
522C22⋊C8—41no—
523C22⋊C8—41no—
524C22⋊C8—41no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531C2×C13—81no—
532C2×C13—81no—
533C2×C13—81no—
534C2×C13—161no—
535C2×C13#281211yescharacteristic
536C2×C13#319811yescharacteristic
537C2×C13#319811yescharacteristic
538C2×C13#320011yescharacteristic
539C2×C13#320111yescharacteristic
540C2×C13#320111yescharacteristic
541C2×C13#320311yescharacteristic
542C24—21no—
543C24C2×D4×C1311yescharacteristic
544C24C2×D4×C1311yescharacteristic
545C24C2×D4×C1311yescharacteristic
546#41—44no—
547#41—44no—
548#41—44no—
549#41—44no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—41no—
557C2×Q8—41no—
558C2×Q8—41no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—41no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—41no—
569C2×D4—41no—
570C2×D4—41no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—81no—
578C2×D4—81no—
579C2×D4—81no—
580C2×D4—81no—
581C2×D4—81no—
582C2×D4—81no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4C2×D4×C1311yescharacteristic
609C22×C4C2×D4×C1311yescharacteristic
610C22×C4C2×D4×C1311yescharacteristic
611C22×C4C24×C1311yescharacteristic
612SD16—44no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—42no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C22⋊C4—81no—
650C22⋊C4—81no—
651C22⋊C4—81no—
652C13#3271311yescharacteristic, direct product factor, Sylow
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23C22×D4×C1311yescharacteristic
682Q8—44no—
683Q8—41no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687D4—44no—
688D4—44no—
689D4—44no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—84no—
695D4—84no—
696D4—84no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4C13×H(5,𝔽2)11yescharacteristic
740C2×C4C13×H(5,𝔽2)11yescharacteristic
741C2×C4C13×H(5,𝔽2)11yescharacteristic
742C2×C4C13×H(5,𝔽2)11yescharacteristic
743C2×C4C13×H(5,𝔽2)11yescharacteristic
744C2×C4C13×H(5,𝔽2)11yescharacteristic
745C8—41no—
746C8—41no—
747C8—41no—
748C8—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22C13×#53411yescharacteristic
778C22C13×#53411yescharacteristic
779C22C13×#53411yescharacteristic
780C22C13×#57611yescharacteristic
781C22C13×#57711yescharacteristic
782C22C13×#57711yescharacteristic
783C22C13×#57811yescharacteristic
784C4—41no—
785C4—41no—
786C4—41no—
787C4—81no—
788C4—81no—
789C4—81no—
790C4—81no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4C13×#56011yescharacteristic
795C4C13×#56011yescharacteristic
796C4C13×#56011yescharacteristic
797C4C13×H(3,𝔽4)11yescharacteristic
798C2—81no—
799C2—81no—
800C2—81no—
801C2—161no—
802C2C13×#281211yescharacteristic
803C2C13×#319811yescharacteristic
804C2C13×#319811yescharacteristic
805C2C13×#320011yescharacteristic
806C2C13×#320111yescharacteristic
807C2C13×#320111yescharacteristic
808C2C13×#320311yescharacteristic
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#2615C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C22×C13×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2616C2semidirect
3. C13×#2077C2semidirect
4. C13×#2076C2semidirect
5. C13×#2075C2semidirect
6. C13×#2036C2semidirect
7. C13×#2036C2semidirect
8. C13×#2035C2semidirect
9. C13×#2034C2semidirect
10. C13×#2033C2semidirect
11. C13×#2033C2semidirect
12. C13×#2000C2semidirect
13. C13×#2000C2semidirect
14. C13×#2000C2semidirect
15. C13×#1780C2semidirect
138. #32713C13direct (N × H)
249. #2616C2×C13semidirect
251. #2077C2×C13semidirect
252. #2076C2×C13semidirect
253. #2075C2×C13semidirect
254. #2036C2×C13semidirect
255. #2036C2×C13semidirect
256. #2035C2×C13semidirect
257. #2034C2×C13semidirect
258. #2033C2×C13semidirect
259. #2033C2×C13semidirect
260. #2000C2×C13semidirect
261. #2000C2×C13semidirect
262. #2000C2×C13semidirect
263. #1780C2×C13semidirect
652. C13#32713direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26162
C13×#26152
C13×#20772
C13×#20762
C13×#20752
C13×#20362
C13×#20352
C13×#20342
C13×#20332
C13×#20002
C13×#17802
#3271313