Finite Group Databasebeta

← C13×#24468 #15710807

Subgroups — C13×#24468 #15710807

Order 3328.

1502 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3488C211yesmaximal, characteristic, complemented
2C13×#3055C211yesmaximal, characteristic, complemented
3C2×C13×#453C211yesmaximal, characteristic, complemented
4C13×#3006C211yesmaximal, characteristic, complemented
5C2×C13×#421C211yesmaximal, characteristic, complemented
6C13×#2619C211yesmaximal, characteristic, complemented
7C13×#2040C211yesmaximal, characteristic, complemented
8C13×#2037C211yesmaximal, characteristic, complemented
9C13×#2006C211yesmaximal, characteristic, complemented
10C13×#2002C211yesmaximal, characteristic, complemented
11C13×#1900C211yesmaximal, characteristic, complemented
12C13×#1897C211yesmaximal, characteristic, complemented
13C13×#1883C211yesmaximal, characteristic, complemented
14C13×#1860C211yesmaximal, characteristic, complemented
15C13×#1792C211yesmaximal, characteristic, complemented
16C2×C13×H(5,𝔽2)C2211yescharacteristic
17C22×C13×#41C2211yescharacteristic
18C2×C13×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C13×AGL(1,ℤ/8)C2211yescharacteristic, complemented
20C2×C13×AGL(1,ℤ/8)C2211yescharacteristic, complemented
21C22×C13×M16C2211yescharacteristic, complemented
22C13×#550—21no—
23C13×#548—21no—
24C13×#546—21no—
25C13×#546—22no—
26D42×C13—22no—
27D42×C13—21no—
28C13×#537—21no—
29C13×#537C2211yescharacteristic
30C13×#535—21no—
31C13×#535C2211yescharacteristic
32C2×C13×#127C2211yescharacteristic, complemented
33C13×#525—21no—
34C13×#525C2211yescharacteristic
35C2×C13×#121—21no—
36C2×C13×#121C2211yescharacteristic
37C2×C13×#121C2211yescharacteristic, complemented
38C13×#520C2211yescharacteristic
39C2×C13×#117C2211yescharacteristic, complemented
40C13×#469—21no—
41C13×#468—21no—
42C13×#466—21no—
43C13×#465—21no—
44C13×#453—24no—
45C13×#449—21no—
46C13×#449—21no—
47C13×#448—21no—
48C13×#447—21no—
49C13×#428C2211yescharacteristic, complemented
50C13×#421—24no—
51C2×C13×#104C2211yescharacteristic
52C2×C13×#104C2211yescharacteristic
53C2×C13×#104C2211yescharacteristic, complemented
54C2×C13×#104C2211yescharacteristic, complemented
55C2×C13×#104C2211yescharacteristic, complemented
56C2×C13×#104C2211yescharacteristic, complemented
57C13×#418C2211yescharacteristic, complemented
58C13×#417C2211yescharacteristic
59C13×#417C2211yescharacteristic, complemented
60C13×#417C2211yescharacteristic, complemented
61C2×C13×#100C2211yescharacteristic, complemented
62C2×C13×#100C2211yescharacteristic, complemented
63C13×#407C2211yescharacteristic, complemented
64C13×#394—22no—
65C13×#392—22no—
66C13×#390C2211yescharacteristic, complemented
67C13×#390C2211yescharacteristic, complemented
68C13×#382C2211yescharacteristic, complemented
69C13×#343C2211yescharacteristic, complemented
70C13×#343C2211yescharacteristic, complemented
71C13×#339C2211yescharacteristic, complemented
72C13×#339C2211yescharacteristic, complemented
73C13×H(5,𝔽2)—22no—
74C13×H(5,𝔽2)—22no—
75C13×H(5,𝔽2)—41no—
76C13×H(5,𝔽2)—41no—
77C2×C13×#41—21no—
78C2×C13×#41—21no—
79C2×C13×#41—21no—
80C2×C13×#41—21no—
81C2×C13×#41—22no—
82C2×C13×#41—22no—
83C2×C13×#41—41no—
84C2×C13×#41—41no—
85C2×C13×#41D411yescharacteristic, complemented
86C2×C13×#41D411yescharacteristic, complemented
87C2×C13×#41C2311yescharacteristic
88C2×C13×#41C2311yescharacteristic
89C2×C13×#41C2311yescharacteristic
90C22×Q8×C13D411yescharacteristic, complemented
91C22×D4×C13—21no—
92C22×D4×C13—22no—
93C22×D4×C13—22no—
94C22×D4×C13—21no—
95C22×D4×C13—21no—
96C22×D4×C13—21no—
97C22×D4×C13—22no—
98C22×D4×C13D412yes—
99C22×D4×C13D411yescharacteristic, complemented
100C22×D4×C13C2311yescharacteristic
101C22×D4×C13C2311yescharacteristic
102C23×C4×C13—21no—
103C23×C4×C13C2311yescharacteristic
104C13×AGL(1,ℤ/8)—22no—
105C13×AGL(1,ℤ/8)—22no—
106C13×AGL(1,ℤ/8)—22no—
107C13×AGL(1,ℤ/8)—41no—
108C13×AGL(1,ℤ/8)—41no—
109C13×AGL(1,ℤ/8)—41no—
110C2×C13×SD16—21no—
111C2×C13×SD16—21no—
112C2×C13×SD16—21no—
113C2×C13×D8—21no—
114C2×C13×D8—21no—
115C2×C13×D8—21no—
116C2×C13×M16—21no—
117C2×C13×M16—22no—
118C2×C13×M16—41no—
119C2×C13×M16C2311yescharacteristic
120C2×C13×M16C2311yescharacteristic
121C2×C13×M16C2311yescharacteristic
122C2×C13×M16C2311yescharacteristic
123C22×C8×C13—21no—
124C13×#127—22no—
125C13×#127—21no—
126C13×#127—22no—
127C13×#127—41no—
128C13×#124—22no—
129C13×#124—21no—
130C13×#123—22no—
131C13×#123—21no—
132C13×C22⋊Q8—22no—
133C13×C22⋊Q8—21no—
134C13×C22⋊Q8—21no—
135C13×C22⋊Q8D411yescharacteristic, complemented
136C13×C22⋊Q8D411yescharacteristic, complemented
137C13×#121—22no—
138C13×#121—22no—
139C13×#121—22no—
140C13×#121—22no—
141C13×#121—22no—
142C13×#121—21no—
143C13×#121—21no—
144C13×#121—21no—
145C13×#121—21no—
146C13×#121—21no—
147C13×#121—21no—
148C13×#121—22no—
149C13×#121—21no—
150C13×#121—21no—
151C13×#121—21no—
152C13×#121—21no—
153C13×#121—21no—
154C13×#121—21no—
155C13×#121D411yescharacteristic, complemented
156C13×#121D411yescharacteristic, complemented
157C13×#120—22no—
158C13×#120—22no—
159C13×#120—22no—
160C13×#120—21no—
161C13×#120—22no—
162C4×Q8×C13—21no—
163C4×D4×C13—22no—
164C4×D4×C13—22no—
165C4×D4×C13—21no—
166C4×D4×C13—22no—
167C4×D4×C13—21no—
168C4×D4×C13—21no—
169C13×#117—21no—
170C13×#117—22no—
171C13×#117—41no—
172C13×#117C2311yescharacteristic
173C2×C13×C4⋊C4—21no—
174C2×C13×C4⋊C4—21no—
175C2×C13×C4⋊C4C2311yescharacteristic
176C2×C13×C4⋊C4C2311yescharacteristic
177C2×C13×C22⋊C4—22no—
178C2×C13×C22⋊C4—21no—
179C2×C13×C22⋊C4—21no—
180C2×C13×C22⋊C4—22no—
181C2×C13×C22⋊C4—22no—
182C2×C13×C22⋊C4D412yes—
183C2×C42×C13C2311yescharacteristic
184C2×C42×C13C2311yescharacteristic
185C13×#107—21no—
186C13×#106—21no—
187C13×#104—22no—
188C13×#104—22no—
189C13×#104—22no—
190C13×#104—22no—
191C13×#104—41no—
192C13×#104D414yescomplemented
193C13×#103—21no—
194C13×#103—21no—
195C13×#103—21no—
196C13×#102—21no—
197C13×#102—21no—
198C13×#102—21no—
199C13×#102—21no—
200C13×#102—21no—
201C13×#100—22no—
202C13×#100—41no—
203C13×C22⋊C8—21no—
204C13×C22⋊C8—21no—
205C13×#95—22no—
206#24468C1311yesmaximal, characteristic, direct product factor, Sylow
207C24×C13—22no—
208C24×C13—21no—
209C24×C13—21no—
210C24×C13C2×D412yes—
211C24×C13C2×D411yescharacteristic
212C13×#41—21no—
213C13×#41—21no—
214C13×#41—22no—
215C13×#41—22no—
216C13×#41—21no—
217C13×#41—21no—
218C13×#41—21no—
219C13×#41—21no—
220C13×#41—21no—
221C13×#41—21no—
222C13×#41—21no—
223C13×#41—21no—
224C13×#41—42no—
225C13×#41—42no—
226C13×#41—41no—
227C13×#41—41no—
228C13×#41—42no—
229C13×#41—42no—
230C13×#41—42no—
231C13×#41—42no—
232C13×#41—42no—
233C13×#41—42no—
234C13×#41C2×D412yes—
235C13×#41#4112yes—
236C2×Q8×C13—21no—
237C2×Q8×C13—22no—
238C2×Q8×C13—41no—
239C2×Q8×C13C2×D411yescharacteristic
240C2×Q8×C13C2×D411yescharacteristic
241C2×Q8×C13C2×D411yescharacteristic
242C2×D4×C13—21no—
243C2×D4×C13—22no—
244C2×D4×C13—22no—
245C2×D4×C13—22no—
246C2×D4×C13—22no—
247C2×D4×C13—21no—
248C2×D4×C13—21no—
249C2×D4×C13—21no—
250C2×D4×C13—21no—
251C2×D4×C13—21no—
252C2×D4×C13—22no—
253C2×D4×C13—22no—
254C2×D4×C13—22no—
255C2×D4×C13—21no—
256C2×D4×C13—22no—
257C2×D4×C13—21no—
258C2×D4×C13—21no—
259C2×D4×C13—21no—
260C2×D4×C13—21no—
261C2×D4×C13—21no—
262C2×D4×C13—21no—
263C2×D4×C13—21no—
264C2×D4×C13—21no—
265C2×D4×C13—21no—
266C2×D4×C13—21no—
267C2×D4×C13—21no—
268C2×D4×C13—21no—
269C2×D4×C13—21no—
270C2×D4×C13—41no—
271C2×D4×C13—42no—
272C2×D4×C13—42no—
273C2×D4×C13—44no—
274C2×D4×C13—42no—
275C2×D4×C13—42no—
276C2×D4×C13—44no—
277C2×D4×C13—44no—
278C2×D4×C13—42no—
279C2×D4×C13—42no—
280C2×D4×C13—41no—
281C2×D4×C13—41no—
282C2×D4×C13—82no—
283C2×D4×C13—82no—
284C2×D4×C13—82no—
285C2×D4×C13—82no—
286C2×D4×C13—84no—
287C2×D4×C13C2×D411yescharacteristic
288C2×D4×C13C2×D411yescharacteristic
289C2×D4×C13C2×D411yescharacteristic
290C22×C4×C13—21no—
291C22×C4×C13—21no—
292C22×C4×C13—21no—
293C22×C4×C13—21no—
294C22×C4×C13—21no—
295C22×C4×C13—22no—
296C22×C4×C13—21no—
297C22×C4×C13—21no—
298C22×C4×C13—22no—
299C22×C4×C13—21no—
300C22×C4×C13—21no—
301C22×C4×C13—21no—
302C22×C4×C13—21no—
303C22×C4×C13—21no—
304C22×C4×C13—21no—
305C22×C4×C13—42no—
306C22×C4×C13—42no—
307C22×C4×C13C2×D411yescharacteristic
308C22×C4×C13C2×D411yescharacteristic
309C22×C4×C13C2×D411yescharacteristic
310C22×C4×C13C2×D411yescharacteristic
311C22×C4×C13C2×D411yescharacteristic
312C22×C4×C13C2×D412yes—
313C22×C4×C13C2411yescharacteristic
314C13×SD16—42no—
315C13×SD16—42no—
316C13×SD16—42no—
317C13×D8—42no—
318C13×D8—42no—
319C13×D8—42no—
320C13×M16—21no—
321C13×M16—21no—
322C13×M16—21no—
323C13×M16—21no—
324C13×M16—21no—
325C13×M16—21no—
326C13×M16—21no—
327C13×M16—42no—
328C13×M16C2×D412yescomplemented
329C2×C8×C13—21no—
330C2×C8×C13—21no—
331C2×C8×C13—21no—
332C2×C8×C13—21no—
333C2×C8×C13—42no—
334C13×C4⋊C4—22no—
335C13×C4⋊C4—22no—
336C13×C4⋊C4—21no—
337C13×C4⋊C4—21no—
338C13×C4⋊C4—21no—
339C13×C4⋊C4—21no—
340C13×C4⋊C4—21no—
341C13×C4⋊C4—21no—
342C13×C4⋊C4—42no—
343C13×C4⋊C4C2×D411yescharacteristic
344C13×C4⋊C4C2×D411yescharacteristic
345C13×C22⋊C4—22no—
346C13×C22⋊C4—22no—
347C13×C22⋊C4—22no—
348C13×C22⋊C4—22no—
349C13×C22⋊C4—22no—
350C13×C22⋊C4—21no—
351C13×C22⋊C4—21no—
352C13×C22⋊C4—21no—
353C13×C22⋊C4—21no—
354C13×C22⋊C4—22no—
355C13×C22⋊C4—22no—
356C13×C22⋊C4—21no—
357C13×C22⋊C4—42no—
358C13×C22⋊C4—41no—
359C13×C22⋊C4—41no—
360C13×C22⋊C4—82no—
361C13×C22⋊C4—82no—
362C42×C13—22no—
363C42×C13—21no—
364C42×C13—21no—
365C42×C13—21no—
366C42×C13—21no—
367C42×C13C2×D412yescomplemented
368#3488C2×C1311yescharacteristic, complemented
369#3055C2×C1311yescharacteristic, complemented
370C2×#453C2×C1311yescharacteristic, complemented
371#3006C2×C1311yescharacteristic, complemented
372C2×#421C2×C1311yescharacteristic, complemented
373#2619C2×C1311yescharacteristic, complemented
374#2040C2×C1311yescharacteristic, complemented
375#2037C2×C1311yescharacteristic, complemented
376#2006C2×C1311yescharacteristic, complemented
377#2002C2×C1311yescharacteristic, complemented
378#1900C2×C1311yescharacteristic, complemented
379#1897C2×C1311yescharacteristic, complemented
380#1883C2×C1311yescharacteristic, complemented
381#1860C2×C1311yescharacteristic, complemented
382#1792C2×C1311yescharacteristic, complemented
383C23×C13—21no—
384C23×C13—21no—
385C23×C13—21no—
386C23×C13—22no—
387C23×C13—21no—
388C23×C13—21no—
389C23×C13—22no—
390C23×C13—22no—
391C23×C13—41no—
392C23×C13—41no—
393C23×C13—42no—
394C23×C13—42no—
395C23×C13—44no—
396C23×C13—42no—
397C23×C13—42no—
398C23×C13—42no—
399C23×C13—42no—
400C23×C13—41no—
401C23×C13—41no—
402C23×C13—41no—
403C23×C13—81no—
404C23×C13—82no—
405C23×C13—82no—
406C23×C13#12011yescharacteristic
407C23×C13#12011yescharacteristic
408C23×C13C22×D411yescharacteristic
409Q8×C13—21no—
410Q8×C13—21no—
411Q8×C13—21no—
412Q8×C13—21no—
413Q8×C13—21no—
414Q8×C13—42no—
415Q8×C13#12112yes—
416D4×C13—22no—
417D4×C13—22no—
418D4×C13—21no—
419D4×C13—21no—
420D4×C13—21no—
421D4×C13—21no—
422D4×C13—21no—
423D4×C13—42no—
424D4×C13—42no—
425D4×C13—44no—
426D4×C13—42no—
427D4×C13—44no—
428D4×C13—44no—
429D4×C13—42no—
430D4×C13—41no—
431D4×C13—41no—
432D4×C13—41no—
433D4×C13—41no—
434D4×C13—41no—
435D4×C13—41no—
436D4×C13—41no—
437D4×C13—41no—
438D4×C13—41no—
439D4×C13—41no—
440D4×C13—41no—
441D4×C13—41no—
442D4×C13—81no—
443D4×C13—82no—
444D4×C13—82no—
445D4×C13—82no—
446D4×C13—82no—
447D4×C13—88no—
448D4×C13—82no—
449D4×C13—82no—
450D4×C13#12112yes—
451C2×C4×C13—21no—
452C2×C4×C13—21no—
453C2×C4×C13—21no—
454C2×C4×C13—21no—
455C2×C4×C13—21no—
456C2×C4×C13—21no—
457C2×C4×C13—21no—
458C2×C4×C13—21no—
459C2×C4×C13—21no—
460C2×C4×C13—22no—
461C2×C4×C13—21no—
462C2×C4×C13—21no—
463C2×C4×C13—22no—
464C2×C4×C13—21no—
465C2×C4×C13—22no—
466C2×C4×C13—21no—
467C2×C4×C13—21no—
468C2×C4×C13—21no—
469C2×C4×C13—22no—
470C2×C4×C13—42no—
471C2×C4×C13—42no—
472C2×C4×C13—42no—
473C2×C4×C13—44no—
474C2×C4×C13—41no—
475C2×C4×C13—41no—
476C2×C4×C13—41no—
477C2×C4×C13—41no—
478C2×C4×C13—41no—
479C2×C4×C13—41no—
480C2×C4×C13—42no—
481C2×C4×C13—41no—
482C2×C4×C13—41no—
483C2×C4×C13—42no—
484C2×C4×C13—41no—
485C2×C4×C13—41no—
486C2×C4×C13—82no—
487C2×C4×C13#12011yescharacteristic
488C2×C4×C13#12011yescharacteristic
489C2×C4×C13C22×D411yescharacteristic
490C2×C4×C13C22×D411yescharacteristic
491C2×C4×C13C22×D411yescharacteristic
492C2×C4×C13C2×#4111yescharacteristic
493C2×C4×C13H(5,𝔽2)11yescharacteristic
494C2×C4×C13H(5,𝔽2)11yescharacteristic
495C8×C13—22no—
496C8×C13—41no—
497C8×C13—41no—
498C8×C13—41no—
499C2×H(5,𝔽2)C22×C1311yescharacteristic
500C22×#41C22×C1311yescharacteristic
501C2×AGL(1,ℤ/8)C22×C1311yescharacteristic
502C2×AGL(1,ℤ/8)C22×C1311yescharacteristic, complemented
503C2×AGL(1,ℤ/8)C22×C1311yescharacteristic, complemented
504C22×M16C22×C1311yescharacteristic, complemented
505#550—21no—
506#548—21no—
507#546—21no—
508#546—22no—
509D42—22no—
510D42—21no—
511#537—21no—
512#537C22×C1311yescharacteristic
513#535—21no—
514#535C22×C1311yescharacteristic
515C2×#127C22×C1311yescharacteristic, complemented
516#525—21no—
517#525C22×C1311yescharacteristic
518C2×#121—21no—
519C2×#121C22×C1311yescharacteristic
520C2×#121C22×C1311yescharacteristic, complemented
521#520C22×C1311yescharacteristic
522C2×#117C22×C1311yescharacteristic, complemented
523#469—21no—
524#468—21no—
525#466—21no—
526#465—21no—
527#453—24no—
528#449—21no—
529#449—21no—
530#448—21no—
531#447—21no—
532#428C22×C1311yescharacteristic, complemented
533#421—24no—
534C2×#104C22×C1311yescharacteristic
535C2×#104C22×C1311yescharacteristic
536C2×#104C22×C1311yescharacteristic, complemented
537C2×#104C22×C1311yescharacteristic, complemented
538C2×#104C22×C1311yescharacteristic, complemented
539C2×#104C22×C1311yescharacteristic, complemented
540#418C22×C1311yescharacteristic, complemented
541#417C22×C1311yescharacteristic
542#417C22×C1311yescharacteristic, complemented
543#417C22×C1311yescharacteristic, complemented
544C2×#100C22×C1311yescharacteristic, complemented
545C2×#100C22×C1311yescharacteristic, complemented
546#407C22×C1311yescharacteristic, complemented
547#394—22no—
548#392—22no—
549#390C22×C1311yescharacteristic, complemented
550#390C22×C1311yescharacteristic, complemented
551#382C22×C1311yescharacteristic, complemented
552#343C22×C1311yescharacteristic, complemented
553#343C22×C1311yescharacteristic, complemented
554#339C22×C1311yescharacteristic, complemented
555#339C22×C1311yescharacteristic, complemented
556C22×C13—21no—
557C22×C13—21no—
558C22×C13—21no—
559C22×C13—21no—
560C22×C13—22no—
561C22×C13—21no—
562C22×C13—21no—
563C22×C13—21no—
564C22×C13—21no—
565C22×C13—41no—
566C22×C13—41no—
567C22×C13—41no—
568C22×C13—41no—
569C22×C13—42no—
570C22×C13—42no—
571C22×C13—41no—
572C22×C13—41no—
573C22×C13—41no—
574C22×C13—42no—
575C22×C13—41no—
576C22×C13—81no—
577C22×C13—81no—
578C22×C13—82no—
579C22×C13—82no—
580C22×C13—82no—
581C22×C13—82no—
582C22×C13—84no—
583C22×C13—81no—
584C22×C13—81no—
585C22×C13—81no—
586C22×C13—164no—
587C22×C13C2×#12011yescharacteristic
588C22×C13D4211yescharacteristic
589C22×C13#54611yescharacteristic
590C4×C13—21no—
591C4×C13—21no—
592C4×C13—22no—
593C4×C13—42no—
594C4×C13—41no—
595C4×C13—41no—
596C4×C13—42no—
597C4×C13—41no—
598C4×C13—41no—
599C4×C13—81no—
600C4×C13—81no—
601C4×C13C2×#12111yescharacteristic
602C4×C13#53411yescharacteristic
603C4×C13D4211yescharacteristic
604C4×C13#54611yescharacteristic
605H(5,𝔽2)—22no—
606H(5,𝔽2)—22no—
607H(5,𝔽2)—41no—
608H(5,𝔽2)—41no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—41no—
616C2×#41—41no—
617C2×#41D4×C1311yescharacteristic, complemented
618C2×#41D4×C1311yescharacteristic, complemented
619C2×#41C23×C1311yescharacteristic
620C2×#41C23×C1311yescharacteristic
621C2×#41C23×C1311yescharacteristic
622C22×Q8D4×C1311yescharacteristic, complemented
623C22×D4—21no—
624C22×D4—22no—
625C22×D4—22no—
626C22×D4—21no—
627C22×D4—21no—
628C22×D4—21no—
629C22×D4—22no—
630C22×D4D4×C1312yes—
631C22×D4D4×C1311yescharacteristic, complemented
632C22×D4C23×C1311yescharacteristic
633C22×D4C23×C1311yescharacteristic
634C23×C4—21no—
635C23×C4C23×C1311yescharacteristic
636AGL(1,ℤ/8)—22no—
637AGL(1,ℤ/8)—22no—
638AGL(1,ℤ/8)—22no—
639AGL(1,ℤ/8)—41no—
640AGL(1,ℤ/8)—41no—
641AGL(1,ℤ/8)—41no—
642C2×SD16—21no—
643C2×SD16—21no—
644C2×SD16—21no—
645C2×D8—21no—
646C2×D8—21no—
647C2×D8—21no—
648C2×M16—21no—
649C2×M16—22no—
650C2×M16—41no—
651C2×M16C23×C1311yescharacteristic
652C2×M16C23×C1311yescharacteristic
653C2×M16C23×C1311yescharacteristic
654C2×M16C23×C1311yescharacteristic
655C22×C8—21no—
656#127—22no—
657#127—21no—
658#127—22no—
659#127—41no—
660#124—22no—
661#124—21no—
662#123—22no—
663#123—21no—
664C22⋊Q8—22no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8D4×C1311yescharacteristic, complemented
668C22⋊Q8D4×C1311yescharacteristic, complemented
669#121—22no—
670#121—22no—
671#121—22no—
672#121—22no—
673#121—22no—
674#121—21no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—22no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—21no—
685#121—21no—
686#121—21no—
687#121D4×C1311yescharacteristic, complemented
688#121D4×C1311yescharacteristic, complemented
689#120—22no—
690#120—22no—
691#120—22no—
692#120—21no—
693#120—22no—
694C4×Q8—21no—
695C4×D4—22no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—22no—
699C4×D4—21no—
700C4×D4—21no—
701#117—21no—
702#117—22no—
703#117—41no—
704#117C23×C1311yescharacteristic
705C2×C4⋊C4—21no—
706C2×C4⋊C4—21no—
707C2×C4⋊C4C23×C1311yescharacteristic
708C2×C4⋊C4C23×C1311yescharacteristic
709C2×C22⋊C4—22no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4D4×C1312yes—
715C2×C42C23×C1311yescharacteristic
716C2×C42C23×C1311yescharacteristic
717#107—21no—
718#106—21no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—41no—
724#104D4×C1314yescomplemented
725#103—21no—
726#103—21no—
727#103—21no—
728#102—21no—
729#102—21no—
730#102—21no—
731#102—21no—
732#102—21no—
733#100—22no—
734#100—41no—
735C22⋊C8—21no—
736C22⋊C8—21no—
737#95—22no—
738C2×C13—21no—
739C2×C13—21no—
740C2×C13—41no—
741C2×C13—41no—
742C2×C13—42no—
743C2×C13—81no—
744C2×C13—82no—
745C2×C13—81no—
746C2×C13—161no—
747C2×C13#241011yescharacteristic
748C2×C13#301911yescharacteristic
749C2×C13#302111yescharacteristic
750C24—22no—
751C24—21no—
752C24—21no—
753C24C2×D4×C1312yes—
754C24C2×D4×C1311yescharacteristic
755#41—21no—
756#41—21no—
757#41—22no—
758#41—22no—
759#41—21no—
760#41—21no—
761#41—21no—
762#41—21no—
763#41—21no—
764#41—21no—
765#41—21no—
766#41—21no—
767#41—42no—
768#41—42no—
769#41—41no—
770#41—41no—
771#41—42no—
772#41—42no—
773#41—42no—
774#41—42no—
775#41—42no—
776#41—42no—
777#41C2×D4×C1312yes—
778#41C13×#4112yes—
779C2×Q8—21no—
780C2×Q8—22no—
781C2×Q8—41no—
782C2×Q8C2×D4×C1311yescharacteristic
783C2×Q8C2×D4×C1311yescharacteristic
784C2×Q8C2×D4×C1311yescharacteristic
785C2×D4—21no—
786C2×D4—22no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—21no—
799C2×D4—22no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—41no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—44no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—44no—
820C2×D4—44no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—41no—
824C2×D4—41no—
825C2×D4—82no—
826C2×D4—82no—
827C2×D4—82no—
828C2×D4—82no—
829C2×D4—84no—
830C2×D4C2×D4×C1311yescharacteristic
831C2×D4C2×D4×C1311yescharacteristic
832C2×D4C2×D4×C1311yescharacteristic
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—22no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4C2×D4×C1311yescharacteristic
851C22×C4C2×D4×C1311yescharacteristic
852C22×C4C2×D4×C1311yescharacteristic
853C22×C4C2×D4×C1311yescharacteristic
854C22×C4C2×D4×C1311yescharacteristic
855C22×C4C2×D4×C1312yes—
856C22×C4C24×C1311yescharacteristic
857SD16—42no—
858SD16—42no—
859SD16—42no—
860D8—42no—
861D8—42no—
862D8—42no—
863M16—21no—
864M16—21no—
865M16—21no—
866M16—21no—
867M16—21no—
868M16—21no—
869M16—21no—
870M16—42no—
871M16C2×D4×C1312yescomplemented
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—42no—
877C4⋊C4—22no—
878C4⋊C4—22no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—42no—
886C4⋊C4C2×D4×C1311yescharacteristic
887C4⋊C4C2×D4×C1311yescharacteristic
888C22⋊C4—22no—
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—21no—
894C22⋊C4—21no—
895C22⋊C4—21no—
896C22⋊C4—21no—
897C22⋊C4—22no—
898C22⋊C4—22no—
899C22⋊C4—21no—
900C22⋊C4—42no—
901C22⋊C4—41no—
902C22⋊C4—41no—
903C22⋊C4—82no—
904C22⋊C4—82no—
905C42—22no—
906C42—21no—
907C42—21no—
908C42—21no—
909C42—21no—
910C42C2×D4×C1312yescomplemented
911C13#2446811yescharacteristic, direct product factor, Sylow
912C23—21no—
913C23—21no—
914C23—21no—
915C23—22no—
916C23—21no—
917C23—21no—
918C23—22no—
919C23—22no—
920C23—41no—
921C23—41no—
922C23—42no—
923C23—42no—
924C23—44no—
925C23—42no—
926C23—42no—
927C23—42no—
928C23—42no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—81no—
933C23—82no—
934C23—82no—
935C23C13×#12011yescharacteristic
936C23C13×#12011yescharacteristic
937C23C22×D4×C1311yescharacteristic
938Q8—21no—
939Q8—21no—
940Q8—21no—
941Q8—21no—
942Q8—21no—
943Q8—42no—
944Q8C13×#12112yes—
945D4—22no—
946D4—22no—
947D4—21no—
948D4—21no—
949D4—21no—
950D4—21no—
951D4—21no—
952D4—42no—
953D4—42no—
954D4—44no—
955D4—42no—
956D4—44no—
957D4—44no—
958D4—42no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—41no—
965D4—41no—
966D4—41no—
967D4—41no—
968D4—41no—
969D4—41no—
970D4—41no—
971D4—82no—
972D4—81no—
973D4—82no—
974D4—82no—
975D4—82no—
976D4—88no—
977D4—82no—
978D4—82no—
979D4C13×#12112yes—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—44no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—42no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—42no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—82no—
1016C2×C4C13×#12011yescharacteristic
1017C2×C4C13×#12011yescharacteristic
1018C2×C4C22×D4×C1311yescharacteristic
1019C2×C4C22×D4×C1311yescharacteristic
1020C2×C4C22×D4×C1311yescharacteristic
1021C2×C4C2×C13×#4111yescharacteristic
1022C2×C4C13×H(5,𝔽2)11yescharacteristic
1023C2×C4C13×H(5,𝔽2)11yescharacteristic
1024C8—22no—
1025C8—41no—
1026C8—41no—
1027C8—41no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—21no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—22no—
1037C22—41no—
1038C22—41no—
1039C22—42no—
1040C22—41no—
1041C22—41no—
1042C22—41no—
1043C22—42no—
1044C22—41no—
1045C22—41no—
1046C22—41no—
1047C22—42no—
1048C22—81no—
1049C22—81no—
1050C22—82no—
1051C22—82no—
1052C22—82no—
1053C22—82no—
1054C22—84no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—164no—
1059C22C2×C13×#12011yescharacteristic
1060C22D42×C1311yescharacteristic
1061C22C13×#54611yescharacteristic
1062C4—21no—
1063C4—21no—
1064C4—22no—
1065C4—42no—
1066C4—42no—
1067C4—41no—
1068C4—41no—
1069C4—41no—
1070C4—41no—
1071C4—81no—
1072C4—81no—
1073C4C2×C13×#12111yescharacteristic
1074C4C13×#53411yescharacteristic
1075C4D42×C1311yescharacteristic
1076C4C13×#54611yescharacteristic
1077C2—21no—
1078C2—21no—
1079C2—41no—
1080C2—41no—
1081C2—42no—
1082C2—81no—
1083C2—82no—
1084C2—81no—
1085C2—161no—
1086C2C13×#241011yescharacteristic
1087C2C13×#301911yescharacteristic
1088C2C13×#302111yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3488C2semidirect
2. C13×#3055C2semidirect
3. C2×C13×#453C2semidirect
4. C13×#3006C2semidirect
5. C2×C13×#421C2semidirect
6. C13×#2619C2semidirect
7. C13×#2040C2semidirect
8. C13×#2037C2semidirect
9. C13×#2006C2semidirect
10. C13×#2002C2semidirect
11. C13×#1900C2semidirect
12. C13×#1897C2semidirect
13. C13×#1883C2semidirect
14. C13×#1860C2semidirect
15. C13×#1792C2semidirect
19. C2×C13×AGL(1,ℤ/8)C22semidirect
20. C2×C13×AGL(1,ℤ/8)C22semidirect
21. C22×C13×M16C22semidirect
32. C2×C13×#127C22semidirect
37. C2×C13×#121C22semidirect
39. C2×C13×#117C22semidirect
49. C13×#428C22semidirect
53. C2×C13×#104C22semidirect
54. C2×C13×#104C22semidirect
55. C2×C13×#104C22semidirect
56. C2×C13×#104C22semidirect
57. C13×#418C22semidirect
59. C13×#417C22semidirect
60. C13×#417C22semidirect
61. C2×C13×#100C22semidirect
62. C2×C13×#100C22semidirect
63. C13×#407C22semidirect
66. C13×#390C22semidirect
67. C13×#390C22semidirect
68. C13×#382C22semidirect
69. C13×#343C22semidirect
70. C13×#343C22semidirect
71. C13×#339C22semidirect
72. C13×#339C22semidirect
85. C2×C13×#41D4semidirect
86. C2×C13×#41D4semidirect
90. C22×Q8×C13D4semidirect
99. C22×D4×C13D4semidirect
135. C13×C22⋊Q8D4semidirect
136. C13×C22⋊Q8D4semidirect
155. C13×#121D4semidirect
156. C13×#121D4semidirect
192. C13×#104D4semidirect
206. #24468C13direct (N × H)
328. C13×M16C2×D4semidirect
367. C42×C13C2×D4semidirect
368. #3488C2×C13semidirect
369. #3055C2×C13semidirect
370. C2×#453C2×C13semidirect
371. #3006C2×C13semidirect
372. C2×#421C2×C13semidirect
373. #2619C2×C13semidirect
374. #2040C2×C13semidirect
375. #2037C2×C13semidirect
376. #2006C2×C13semidirect
377. #2002C2×C13semidirect
378. #1900C2×C13semidirect
379. #1897C2×C13semidirect
380. #1883C2×C13semidirect
381. #1860C2×C13semidirect
382. #1792C2×C13semidirect
502. C2×AGL(1,ℤ/8)C22×C13semidirect
503. C2×AGL(1,ℤ/8)C22×C13semidirect
504. C22×M16C22×C13semidirect
515. C2×#127C22×C13semidirect
520. C2×#121C22×C13semidirect
522. C2×#117C22×C13semidirect
532. #428C22×C13semidirect
536. C2×#104C22×C13semidirect
537. C2×#104C22×C13semidirect
538. C2×#104C22×C13semidirect
539. C2×#104C22×C13semidirect
540. #418C22×C13semidirect
542. #417C22×C13semidirect
543. #417C22×C13semidirect
544. C2×#100C22×C13semidirect
545. C2×#100C22×C13semidirect
546. #407C22×C13semidirect
549. #390C22×C13semidirect
550. #390C22×C13semidirect
551. #382C22×C13semidirect
552. #343C22×C13semidirect
553. #343C22×C13semidirect
554. #339C22×C13semidirect
555. #339C22×C13semidirect
617. C2×#41D4×C13semidirect
618. C2×#41D4×C13semidirect
622. C22×Q8D4×C13semidirect
631. C22×D4D4×C13semidirect
667. C22⋊Q8D4×C13semidirect
668. C22⋊Q8D4×C13semidirect
687. #121D4×C13semidirect
688. #121D4×C13semidirect
724. #104D4×C13semidirect
871. M16C2×D4×C13semidirect
910. C42C2×D4×C13semidirect
911. C13#24468direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34882
C13×#30552
C2×C13×#4532
C13×#30062
C2×C13×#4212
C13×#26192
C13×#20402
C13×#20372
C13×#20062
C13×#20022
C13×#19002
C13×#18972
C13×#18832
C13×#18602
C13×#17922
#2446813