Finite Group Databasebeta

← C13×#61444 #15747783

Subgroups — C13×#61444 #15747783

Order 3328.

1978 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3481C212yesmaximal, complemented
2C13×#3403C211yesmaximal, characteristic, complemented
3C13×#3389C211yesmaximal, characteristic, complemented
4C13×#3370C212yesmaximal, complemented
5C13×#3355C211yesmaximal, characteristic, complemented
6C13×#3346C212yesmaximal, complemented
7C13×#3322C212yesmaximal, complemented
8C13×#3318C212yesmaximal, complemented
9C13×#3314C212yesmaximal, complemented
10C13×#3273C211yesmaximal, characteristic, complemented
11C13×#3264C212yesmaximal, complemented
12C13×#3171C212yesmaximal, complemented
13C13×#3168C211yesmaximal, characteristic, complemented
14C13×#3105C212yesmaximal, complemented
15C13×#3102C212yesmaximal, complemented
16C13×#3100C212yesmaximal, complemented
17C13×#2965C211yesmaximal, characteristic, complemented
18C4×C13×AGL(1,ℤ/8)C212yesmaximal, complemented
19C2×C4×C13×D8C211yesmaximal, characteristic, complemented
20C2×C13×AGL(1,ℤ/8)C2212yes—
21C22×C13×D8C2211yescharacteristic
22C13×#559C2212yescomplemented
23C13×#554C2212yescomplemented
24C13×#554C2212yescomplemented
25C13×#553—22no—
26C13×#553C2212yes—
27C13×#553C2212yescomplemented
28C13×#551—22no—
29C13×#551—22no—
30C13×#546—22no—
31C13×#546C2212yes—
32C13×#546C2212yescomplemented
33D42×C13C2212yescomplemented
34C13×#532C2212yescomplemented
35C13×#529—22no—
36C13×#529C2212yescomplemented
37C13×#529C2212yescomplemented
38C13×#525—22no—
39C13×#525—22no—
40C4×C13×#41C2211yescharacteristic
41C4×C13×#41C2212yescomplemented
42C2×C4×D4×C13—22no—
43C2×C4×D4×C13C2212yescomplemented
44C2×C4×D4×C13C2212yescomplemented
45C13×#501C2212yescomplemented
46C13×#499C2211yescharacteristic, complemented
47C13×#496C2212yescomplemented
48C13×#495C2211yescharacteristic, complemented
49C13×#490C2212yescomplemented
50C13×#489C2212yescomplemented
51C13×#488C2212yescomplemented
52C13×#485C2212yescomplemented
53C13×#484C2212yescomplemented
54C13×#482C2212yescomplemented
55C13×#481C2212yescomplemented
56C13×#480C2212yescomplemented
57C13×#480C2212yescomplemented
58C13×#479C2212yescomplemented
59C13×#478C2212yescomplemented
60C13×#478C2212yescomplemented
61C13×#478C2212yescomplemented
62C13×#474C2212yescomplemented
63C13×#474C2212yescomplemented
64C13×#469C2212yescomplemented
65C13×#469C2212yescomplemented
66C13×#468C2212yescomplemented
67C13×#468C2212yescomplemented
68C13×#467C2211yescharacteristic, complemented
69C13×#466C2211yescharacteristic
70C13×#465C2212yescomplemented
71C13×#464C2212yescomplemented
72C13×#463C2212yescomplemented
73C13×#463C2212yescomplemented
74C13×#463C2212yescomplemented
75C13×#459C2212yes—
76C13×#459C2212yescomplemented
77C13×#452C2212yescomplemented
78C13×#450C2212yescomplemented
79C13×#449C2212yes—
80C13×#447C2212yes—
81C13×#447C2212yescomplemented
82C13×#447C2212yescomplemented
83C13×#446C2211yescharacteristic, complemented
84C13×#446C2211yescharacteristic, complemented
85C13×#442C2212yes—
86C13×#442C2212yescomplemented
87C13×#440C2212yescomplemented
88C13×#440C2212yescomplemented
89C4×C13×Q16C2211yescharacteristic, complemented
90C4×C13×SD16C2212yescomplemented
91C4×C13×SD16C2212yescomplemented
92C4×C13×SD16C2212yescomplemented
93C4×C13×D8C2211yescharacteristic
94C4×C13×D8C2211yescharacteristic
95C4×C13×D8C2212yescomplemented
96C4×C13×D8C2211yescharacteristic, complemented
97C4×C13×D8C2211yescharacteristic, complemented
98C4×C13×D8C2212yescomplemented
99C4×C13×D8C2212yescomplemented
100C4×C13×D8C2212yescomplemented
101C4×C13×D8C2211yescharacteristic, complemented
102C13×#436C2211yescharacteristic, complemented
103C13×#436C2211yescharacteristic, complemented
104C13×#435C2212yescomplemented
105C13×#435C2212yescomplemented
106C13×#431C2212yescomplemented
107C13×#431C2211yescharacteristic, complemented
108C13×#428C2212yescomplemented
109C2×C13×#107C2211yescharacteristic, complemented
110C13×#418C2212yescomplemented
111C13×#417C2212yescomplemented
112C2×C13×#102C2212yescomplemented
113C4×C13×M16C2212yescomplemented
114C2×C4×C8×C13C2211yescharacteristic, complemented
115C2×C13×#41—22no—
116C2×C13×#41D411yescharacteristic
117C2×C13×#41C2312yes—
118C22×D4×C13—22no—
119C22×D4×C13C2312yes—
120C22×D4×C13C2312yes—
121C23×C4×C13—22no—
122C23×C4×C13—22no—
123C13×AGL(1,ℤ/8)—28no—
124C2×C13×Q16C2311yescharacteristic
125C2×C13×SD16C2312yes—
126C2×C13×SD16C2312yes—
127C2×C13×SD16C2312yes—
128C2×C13×D8—24no—
129C2×C13×D8C2312yes—
130C2×C13×D8C2311yescharacteristic
131C2×C13×D8C2312yes—
132C2×C13×D8C2312yes—
133C2×C13×D8C2311yescharacteristic
134C2×C13×D8C2311yescharacteristic
135C2×C13×M16C2312yes—
136C2×C13×M16C2312yes—
137C22×C8×C13C2311yescharacteristic
138C22×C8×C13C2311yescharacteristic
139C13×C4⋊Q8C2312yes—
140C13×#127C2312yes—
141C13×#126—22no—
142C13×#126—22no—
143C13×#126—22no—
144C13×#126—22no—
145C13×#125—22no—
146C13×#125C2312yes—
147C13×#125C2312yes—
148C13×#124—22no—
149C13×#124—22no—
150C13×#124C2312yes—
151C13×#124C2312yes—
152C13×#123—22no—
153C13×#123—22no—
154C13×#123—22no—
155C13×#123—22no—
156C13×#123—22no—
157C13×#123—22no—
158C13×#123—22no—
159C13×#123—22no—
160C13×C22⋊Q8—22no—
161C13×C22⋊Q8—22no—
162C13×C22⋊Q8—22no—
163C13×C22⋊Q8—22no—
164C13×C22⋊Q8—22no—
165C13×C22⋊Q8C2312yes—
166C13×C22⋊Q8C2312yes—
167C13×#121—22no—
168C13×#121—22no—
169C13×#121—22no—
170C13×#121—22no—
171C13×#121—22no—
172C13×#121—22no—
173C13×#121C2312yes—
174C13×#121C2312yes—
175C13×#121C2312yes—
176C13×#121C2312yes—
177C13×#120—22no—
178C13×#120—22no—
179C13×#120—22no—
180C13×#120—22no—
181C4×Q8×C13D411yescharacteristic
182C4×Q8×C13C2312yes—
183C4×Q8×C13C2312yes—
184C4×Q8×C13C2311yescharacteristic
185C4×D4×C13—22no—
186C4×D4×C13—22no—
187C4×D4×C13—22no—
188C4×D4×C13—22no—
189C4×D4×C13—22no—
190C4×D4×C13—22no—
191C4×D4×C13—22no—
192C4×D4×C13—22no—
193C4×D4×C13—22no—
194C4×D4×C13—22no—
195C4×D4×C13—22no—
196C4×D4×C13—22no—
197C4×D4×C13—22no—
198C4×D4×C13D412yes—
199C4×D4×C13D411yescharacteristic
200C4×D4×C13C2312yes—
201C4×D4×C13C2312yes—
202C4×D4×C13C2312yes—
203C4×D4×C13C2312yes—
204C4×D4×C13C2312yes—
205C4×D4×C13C2312yes—
206C4×D4×C13C2312yes—
207C4×D4×C13C2312yes—
208C4×D4×C13C2312yes—
209C4×D4×C13C2311yescharacteristic
210C13×#117—22no—
211C13×#117—22no—
212C13×#117—22no—
213C13×#117D411yescharacteristic
214C13×#117D412yes—
215C13×#117C2312yes—
216C2×C13×C4⋊C4—22no—
217C2×C13×C4⋊C4C2312yes—
218C2×C13×C4⋊C4C2312yes—
219C2×C13×C22⋊C4—22no—
220C2×C13×C22⋊C4—22no—
221C2×C13×C22⋊C4—22no—
222C2×C13×C22⋊C4—22no—
223C2×C42×C13—22no—
224C2×C42×C13C2311yescharacteristic
225C2×C42×C13C2312yes—
226C13×#107C2311yescharacteristic
227C13×#107C2311yescharacteristic
228C13×#107C2312yes—
229C13×#107C2312yes—
230C13×#107C2311yescharacteristic
231C13×#107C2312yes—
232C13×#107C2311yescharacteristic
233C13×#106C2312yes—
234C13×#106C2312yes—
235C13×#106C2312yes—
236C13×C4⋊C8C2312yes—
237C13×C4⋊C8C2312yes—
238C13×C4⋊C8C2311yescharacteristic
239C13×C4⋊C8C2311yescharacteristic
240C13×#103C2312yes—
241C13×#103C2312yes—
242C13×#103C2312yes—
243C13×#103C2312yes—
244C13×#102C2312yes—
245C13×#102C2312yes—
246C13×#102C2312yes—
247C13×#102C2312yes—
248C13×#102C2312yes—
249C13×#102C2312yes—
250C13×#102C2312yes—
251C13×#102C2312yes—
252C13×#102C2312yes—
253C13×#102C2312yes—
254C13×#102C2312yes—
255C13×#102C2312yes—
256C13×C22⋊C8C2312yes—
257C13×C22⋊C8C2312yes—
258C13×C22⋊C8C2312yes—
259C13×#97C2312yes—
260C13×#97C2312yes—
261C4×C8×C13C2311yescharacteristic
262C4×C8×C13C2311yescharacteristic
263C4×C8×C13C2311yescharacteristic
264C4×C8×C13C2311yescharacteristic
265C4×C8×C13C2312yes—
266#61444C1311yesmaximal, characteristic, direct product factor, Sylow
267C24×C13—22no—
268C24×C13—22no—
269C13×#41—24no—
270C13×#41—42no—
271C13×#41—42no—
272C13×#41—84no—
273C2×Q8×C13—22no—
274C2×Q8×C13C2×D411yescharacteristic
275C2×Q8×C13C2412yes—
276C2×D4×C13—24no—
277C2×D4×C13—24no—
278C2×D4×C13—22no—
279C2×D4×C13—22no—
280C2×D4×C13—22no—
281C2×D4×C13—22no—
282C2×D4×C13—22no—
283C2×D4×C13—22no—
284C2×D4×C13—22no—
285C2×D4×C13—22no—
286C2×D4×C13—22no—
287C2×D4×C13—42no—
288C2×D4×C13—42no—
289C2×D4×C13—48no—
290C2×D4×C13C2×D412yes—
291C2×D4×C13C2×D411yescharacteristic
292C2×D4×C13C2412yes—
293C2×D4×C13C2412yes—
294C2×D4×C13C2412yes—
295C22×C4×C13—22no—
296C22×C4×C13—22no—
297C22×C4×C13—22no—
298C22×C4×C13—22no—
299C22×C4×C13—22no—
300C22×C4×C13—22no—
301C22×C4×C13—22no—
302C22×C4×C13—22no—
303C22×C4×C13—22no—
304C22×C4×C13—22no—
305C22×C4×C13—22no—
306C22×C4×C13—84no—
307C22×C4×C13—84no—
308C22×C4×C13C2×D411yescharacteristic
309C22×C4×C13C2×D411yescharacteristic
310C22×C4×C13C2×D412yes—
311C22×C4×C13C2×D412yes—
312C22×C4×C13C2411yescharacteristic
313C22×C4×C13C2412yes—
314C13×Q16—41no—
315C13×SD16—24no—
316C13×SD16—24no—
317C13×SD16—42no—
318C13×D8—24no—
319C13×D8—24no—
320C13×D8—22no—
321C13×D8—41no—
322C13×D8—42no—
323C13×D8#4114yescomplemented
324C13×M16—24no—
325C13×M16—42no—
326C2×C8×C13—22no—
327C2×C8×C13—41no—
328C2×C8×C13C2411yescharacteristic
329C2×C8×C13C2411yescharacteristic
330C2×C8×C13C2411yescharacteristic
331C2×C8×C13C2412yes—
332C2×C8×C13C2412yes—
333C2×C8×C13C2411yescharacteristic
334C13×C4⋊C4—22no—
335C13×C4⋊C4—22no—
336C13×C4⋊C4—22no—
337C13×C4⋊C4—22no—
338C13×C4⋊C4—22no—
339C13×C4⋊C4—22no—
340C13×C4⋊C4—22no—
341C13×C4⋊C4—22no—
342C13×C4⋊C4—22no—
343C13×C4⋊C4—22no—
344C13×C4⋊C4—22no—
345C13×C4⋊C4C2×D412yes—
346C13×C4⋊C4C2×D411yescharacteristic
347C13×C4⋊C4C2×D412yes—
348C13×C4⋊C4C2×D411yescharacteristic
349C13×C4⋊C4C2412yes—
350C13×C4⋊C4C2412yes—
351C13×C4⋊C4C2412yes—
352C13×C4⋊C4C2412yes—
353C13×C22⋊C4—22no—
354C13×C22⋊C4—22no—
355C13×C22⋊C4—22no—
356C13×C22⋊C4—22no—
357C13×C22⋊C4—22no—
358C13×C22⋊C4—22no—
359C13×C22⋊C4—22no—
360C13×C22⋊C4—22no—
361C13×C22⋊C4—22no—
362C13×C22⋊C4—22no—
363C13×C22⋊C4—22no—
364C13×C22⋊C4—22no—
365C13×C22⋊C4—22no—
366C13×C22⋊C4—22no—
367C13×C22⋊C4—22no—
368C13×C22⋊C4—22no—
369C13×C22⋊C4—22no—
370C13×C22⋊C4—22no—
371C13×C22⋊C4—22no—
372C13×C22⋊C4C2×D412yes—
373C13×C22⋊C4C2×D412yes—
374C13×C22⋊C4C2×D412yes—
375C42×C13—22no—
376C42×C13—22no—
377C42×C13—22no—
378C42×C13C2×D412yes—
379C42×C13C2×D411yescharacteristic
380C42×C13C2×D412yes—
381C42×C13C2×D411yescharacteristic
382C42×C13C2411yescharacteristic
383C42×C13C2412yes—
384C42×C13C2411yescharacteristic
385#3481C2×C1312yescomplemented
386#3403C2×C1311yescharacteristic, complemented
387#3389C2×C1311yescharacteristic, complemented
388#3370C2×C1312yescomplemented
389#3355C2×C1311yescharacteristic, complemented
390#3346C2×C1312yescomplemented
391#3322C2×C1312yescomplemented
392#3318C2×C1312yescomplemented
393#3314C2×C1312yescomplemented
394#3273C2×C1311yescharacteristic, complemented
395#3264C2×C1312yescomplemented
396#3171C2×C1312yescomplemented
397#3168C2×C1311yescharacteristic, complemented
398#3105C2×C1312yescomplemented
399#3102C2×C1312yescomplemented
400#3100C2×C1312yescomplemented
401#2965C2×C1311yescharacteristic, complemented
402C4×AGL(1,ℤ/8)C2×C1312yescomplemented
403C2×C4×D8C2×C1311yescharacteristic, complemented
404C23×C13—22no—
405C23×C13—22no—
406C23×C13—22no—
407C23×C13—44no—
408C23×C13—44no—
409C23×C13—44no—
410C23×C13—44no—
411C23×C13—82no—
412C23×C13—82no—
413C23×C13C22×D412yes—
414C23×C13C22×D411yescharacteristic
415Q8×C13—22no—
416Q8×C13—22no—
417Q8×C13—41no—
418Q8×C13—82no—
419D4×C13—24no—
420D4×C13—22no—
421D4×C13—22no—
422D4×C13—22no—
423D4×C13—22no—
424D4×C13—22no—
425D4×C13—41no—
426D4×C13—44no—
427D4×C13—44no—
428D4×C13—44no—
429D4×C13—44no—
430D4×C13—44no—
431D4×C13—44no—
432D4×C13—82no—
433D4×C13—82no—
434D4×C13—82no—
435D4×C13C2×#4114yes—
436C2×C4×C13—22no—
437C2×C4×C13—22no—
438C2×C4×C13—24no—
439C2×C4×C13—21no—
440C2×C4×C13—22no—
441C2×C4×C13—21no—
442C2×C4×C13—22no—
443C2×C4×C13—22no—
444C2×C4×C13—22no—
445C2×C4×C13—22no—
446C2×C4×C13—22no—
447C2×C4×C13—22no—
448C2×C4×C13—42no—
449C2×C4×C13—44no—
450C2×C4×C13—44no—
451C2×C4×C13—44no—
452C2×C4×C13—44no—
453C2×C4×C13—44no—
454C2×C4×C13—82no—
455C2×C4×C13—82no—
456C2×C4×C13—82no—
457C2×C4×C13—82no—
458C2×C4×C13—82no—
459C2×C4×C13—82no—
460C2×C4×C13C22×D412yes—
461C2×C4×C13C22×D412yes—
462C2×C4×C13C22×D411yescharacteristic
463C2×C4×C13C22×D411yescharacteristic
464C2×C4×C13C22×D411yescharacteristic
465C2×C4×C13C22×D411yescharacteristic
466C2×C4×C13C22×D412yes—
467C2×C4×C13C22×D411yescharacteristic
468C2×C4×C13C2511yescharacteristic
469C8×C13—21no—
470C8×C13—22no—
471C8×C13—21no—
472C8×C13—21no—
473C8×C13—22no—
474C8×C13C2×#4112yes—
475C2×AGL(1,ℤ/8)C22×C1312yes—
476C22×D8C22×C1311yescharacteristic
477#559C22×C1312yescomplemented
478#554C22×C1312yescomplemented
479#554C22×C1312yescomplemented
480#553—22no—
481#553C22×C1312yes—
482#553C22×C1312yescomplemented
483#551—22no—
484#551—22no—
485#546—22no—
486#546C22×C1312yes—
487#546C22×C1312yescomplemented
488D42C22×C1312yescomplemented
489#532C22×C1312yescomplemented
490#529—22no—
491#529C22×C1312yescomplemented
492#529C22×C1312yescomplemented
493#525—22no—
494#525—22no—
495C4×#41C22×C1311yescharacteristic
496C4×#41C22×C1312yescomplemented
497C2×C4×D4—22no—
498C2×C4×D4C22×C1312yescomplemented
499C2×C4×D4C22×C1312yescomplemented
500#501C22×C1312yescomplemented
501#499C22×C1311yescharacteristic, complemented
502#496C22×C1312yescomplemented
503#495C22×C1311yescharacteristic, complemented
504#490C22×C1312yescomplemented
505#489C22×C1312yescomplemented
506#488C22×C1312yescomplemented
507#485C22×C1312yescomplemented
508#484C22×C1312yescomplemented
509#482C22×C1312yescomplemented
510#481C22×C1312yescomplemented
511#480C22×C1312yescomplemented
512#480C22×C1312yescomplemented
513#479C22×C1312yescomplemented
514#478C22×C1312yescomplemented
515#478C22×C1312yescomplemented
516#478C22×C1312yescomplemented
517#474C22×C1312yescomplemented
518#474C22×C1312yescomplemented
519#469C22×C1312yescomplemented
520#469C22×C1312yescomplemented
521#468C22×C1312yescomplemented
522#468C22×C1312yescomplemented
523#467C22×C1311yescharacteristic, complemented
524#466C22×C1311yescharacteristic
525#465C22×C1312yescomplemented
526#464C22×C1312yescomplemented
527#463C22×C1312yescomplemented
528#463C22×C1312yescomplemented
529#463C22×C1312yescomplemented
530#459C22×C1312yes—
531#459C22×C1312yescomplemented
532#452C22×C1312yescomplemented
533#450C22×C1312yescomplemented
534#449C22×C1312yes—
535#447C22×C1312yes—
536#447C22×C1312yescomplemented
537#447C22×C1312yescomplemented
538#446C22×C1311yescharacteristic, complemented
539#446C22×C1311yescharacteristic, complemented
540#442C22×C1312yes—
541#442C22×C1312yescomplemented
542#440C22×C1312yescomplemented
543#440C22×C1312yescomplemented
544C4×Q16C22×C1311yescharacteristic, complemented
545C4×SD16C22×C1312yescomplemented
546C4×SD16C22×C1312yescomplemented
547C4×SD16C22×C1312yescomplemented
548C4×D8C22×C1311yescharacteristic
549C4×D8C22×C1311yescharacteristic
550C4×D8C22×C1311yescharacteristic, complemented
551C4×D8C22×C1311yescharacteristic, complemented
552C4×D8C22×C1312yescomplemented
553C4×D8C22×C1312yescomplemented
554C4×D8C22×C1312yescomplemented
555C4×D8C22×C1312yescomplemented
556C4×D8C22×C1311yescharacteristic, complemented
557#436C22×C1311yescharacteristic, complemented
558#436C22×C1311yescharacteristic, complemented
559#435C22×C1312yescomplemented
560#435C22×C1312yescomplemented
561#431C22×C1312yescomplemented
562#431C22×C1311yescharacteristic, complemented
563#428C22×C1312yescomplemented
564C2×#107C22×C1311yescharacteristic, complemented
565#418C22×C1312yescomplemented
566#417C22×C1312yescomplemented
567C2×#102C22×C1312yescomplemented
568C4×M16C22×C1312yescomplemented
569C2×C4×C8C22×C1311yescharacteristic, complemented
570C22×C13—21no—
571C22×C13—21no—
572C22×C13—22no—
573C22×C13—24no—
574C22×C13—22no—
575C22×C13—22no—
576C22×C13—42no—
577C22×C13—42no—
578C22×C13—42no—
579C22×C13—42no—
580C22×C13—42no—
581C22×C13—42no—
582C22×C13—42no—
583C22×C13—42no—
584C22×C13—88no—
585C22×C13—88no—
586C22×C13#57512yes—
587C22×C13C23×D411yescharacteristic
588C4×C13—22no—
589C4×C13—21no—
590C4×C13—21no—
591C4×C13—21no—
592C4×C13—22no—
593C4×C13—21no—
594C4×C13—22no—
595C4×C13—42no—
596C4×C13—42no—
597C4×C13—42no—
598C4×C13—42no—
599C4×C13—42no—
600C4×C13#57612yes—
601C4×C13C22×#4111yescharacteristic
602C4×C13#58511yescharacteristic
603C2×#41—22no—
604C2×#41D4×C1311yescharacteristic
605C2×#41C23×C1312yes—
606C22×D4—22no—
607C22×D4C23×C1312yes—
608C22×D4C23×C1312yes—
609C23×C4—22no—
610C23×C4—22no—
611AGL(1,ℤ/8)—28no—
612C2×Q16C23×C1311yescharacteristic
613C2×SD16C23×C1312yes—
614C2×SD16C23×C1312yes—
615C2×SD16C23×C1312yes—
616C2×D8—24no—
617C2×D8C23×C1312yes—
618C2×D8C23×C1311yescharacteristic
619C2×D8C23×C1312yes—
620C2×D8C23×C1312yes—
621C2×D8C23×C1311yescharacteristic
622C2×D8C23×C1311yescharacteristic
623C2×M16C23×C1312yes—
624C2×M16C23×C1312yes—
625C22×C8C23×C1311yescharacteristic
626C22×C8C23×C1311yescharacteristic
627C4⋊Q8C23×C1312yes—
628#127C23×C1312yes—
629#126—22no—
630#126—22no—
631#126—22no—
632#126—22no—
633#125—22no—
634#125C23×C1312yes—
635#125C23×C1312yes—
636#124—22no—
637#124—22no—
638#124C23×C1312yes—
639#124C23×C1312yes—
640#123—22no—
641#123—22no—
642#123—22no—
643#123—22no—
644#123—22no—
645#123—22no—
646#123—22no—
647#123—22no—
648C22⋊Q8—22no—
649C22⋊Q8—22no—
650C22⋊Q8—22no—
651C22⋊Q8—22no—
652C22⋊Q8—22no—
653C22⋊Q8C23×C1312yes—
654C22⋊Q8C23×C1312yes—
655#121—22no—
656#121—22no—
657#121—22no—
658#121—22no—
659#121—22no—
660#121—22no—
661#121C23×C1312yes—
662#121C23×C1312yes—
663#121C23×C1312yes—
664#121C23×C1312yes—
665#120—22no—
666#120—22no—
667#120—22no—
668#120—22no—
669C4×Q8D4×C1311yescharacteristic
670C4×Q8C23×C1312yes—
671C4×Q8C23×C1312yes—
672C4×Q8C23×C1311yescharacteristic
673C4×D4—22no—
674C4×D4—22no—
675C4×D4—22no—
676C4×D4—22no—
677C4×D4—22no—
678C4×D4—22no—
679C4×D4—22no—
680C4×D4—22no—
681C4×D4—22no—
682C4×D4—22no—
683C4×D4—22no—
684C4×D4—22no—
685C4×D4—22no—
686C4×D4D4×C1312yes—
687C4×D4D4×C1311yescharacteristic
688C4×D4C23×C1312yes—
689C4×D4C23×C1312yes—
690C4×D4C23×C1312yes—
691C4×D4C23×C1312yes—
692C4×D4C23×C1312yes—
693C4×D4C23×C1312yes—
694C4×D4C23×C1312yes—
695C4×D4C23×C1312yes—
696C4×D4C23×C1312yes—
697C4×D4C23×C1311yescharacteristic
698#117—22no—
699#117—22no—
700#117—22no—
701#117D4×C1311yescharacteristic
702#117D4×C1312yes—
703#117C23×C1312yes—
704C2×C4⋊C4—22no—
705C2×C4⋊C4C23×C1312yes—
706C2×C4⋊C4C23×C1312yes—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C42—22no—
712C2×C42C23×C1311yescharacteristic
713C2×C42C23×C1312yes—
714#107C23×C1311yescharacteristic
715#107C23×C1311yescharacteristic
716#107C23×C1312yes—
717#107C23×C1312yes—
718#107C23×C1311yescharacteristic
719#107C23×C1312yes—
720#107C23×C1311yescharacteristic
721#106C23×C1312yes—
722#106C23×C1312yes—
723#106C23×C1312yes—
724C4⋊C8C23×C1312yes—
725C4⋊C8C23×C1312yes—
726C4⋊C8C23×C1311yescharacteristic
727C4⋊C8C23×C1311yescharacteristic
728#103C23×C1312yes—
729#103C23×C1312yes—
730#103C23×C1312yes—
731#103C23×C1312yes—
732#102C23×C1312yes—
733#102C23×C1312yes—
734#102C23×C1312yes—
735#102C23×C1312yes—
736#102C23×C1312yes—
737#102C23×C1312yes—
738#102C23×C1312yes—
739#102C23×C1312yes—
740#102C23×C1312yes—
741#102C23×C1312yes—
742#102C23×C1312yes—
743#102C23×C1312yes—
744C22⋊C8C23×C1312yes—
745C22⋊C8C23×C1312yes—
746C22⋊C8C23×C1312yes—
747#97C23×C1312yes—
748#97C23×C1312yes—
749C4×C8C23×C1311yescharacteristic
750C4×C8C23×C1311yescharacteristic
751C4×C8C23×C1311yescharacteristic
752C4×C8C23×C1311yescharacteristic
753C4×C8C23×C1312yes—
754C2×C13—22no—
755C2×C13—42no—
756C2×C13—44no—
757C2×C13—82no—
758C2×C13—82no—
759C2×C13D4×#4111yescharacteristic
760C2×C13C2×#57511yescharacteristic
761C2×C13C2×#57611yescharacteristic
762C24—22no—
763C24—22no—
764#41—24no—
765#41—42no—
766#41—42no—
767#41—84no—
768C2×Q8—22no—
769C2×Q8C2×D4×C1311yescharacteristic
770C2×Q8C24×C1312yes—
771C2×D4—24no—
772C2×D4—24no—
773C2×D4—22no—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—22no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—48no—
785C2×D4C2×D4×C1312yes—
786C2×D4C2×D4×C1311yescharacteristic
787C2×D4C24×C1312yes—
788C2×D4C24×C1312yes—
789C2×D4C24×C1312yes—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—84no—
802C22×C4—84no—
803C22×C4C2×D4×C1311yescharacteristic
804C22×C4C2×D4×C1311yescharacteristic
805C22×C4C2×D4×C1312yes—
806C22×C4C2×D4×C1312yes—
807C22×C4C24×C1311yescharacteristic
808C22×C4C24×C1312yes—
809Q16—41no—
810SD16—24no—
811SD16—24no—
812SD16—42no—
813D8—24no—
814D8—24no—
815D8—22no—
816D8—41no—
817D8—42no—
818D8C13×#4114yescomplemented
819M16—24no—
820M16—42no—
821C2×C8—22no—
822C2×C8—41no—
823C2×C8C24×C1311yescharacteristic
824C2×C8C24×C1311yescharacteristic
825C2×C8C24×C1311yescharacteristic
826C2×C8C24×C1312yes—
827C2×C8C24×C1312yes—
828C2×C8C24×C1311yescharacteristic
829C4⋊C4—22no—
830C4⋊C4—22no—
831C4⋊C4—22no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4C2×D4×C1312yes—
841C4⋊C4C2×D4×C1311yescharacteristic
842C4⋊C4C2×D4×C1312yes—
843C4⋊C4C2×D4×C1311yescharacteristic
844C4⋊C4C24×C1312yes—
845C4⋊C4C24×C1312yes—
846C4⋊C4C24×C1312yes—
847C4⋊C4C24×C1312yes—
848C22⋊C4—22no—
849C22⋊C4—22no—
850C22⋊C4—22no—
851C22⋊C4—22no—
852C22⋊C4—22no—
853C22⋊C4—22no—
854C22⋊C4—22no—
855C22⋊C4—22no—
856C22⋊C4—22no—
857C22⋊C4—22no—
858C22⋊C4—22no—
859C22⋊C4—22no—
860C22⋊C4—22no—
861C22⋊C4—22no—
862C22⋊C4—22no—
863C22⋊C4—22no—
864C22⋊C4—22no—
865C22⋊C4—22no—
866C22⋊C4—22no—
867C22⋊C4C2×D4×C1312yes—
868C22⋊C4C2×D4×C1312yes—
869C22⋊C4C2×D4×C1312yes—
870C42—22no—
871C42—22no—
872C42—22no—
873C42C2×D4×C1312yes—
874C42C2×D4×C1311yescharacteristic
875C42C2×D4×C1312yes—
876C42C2×D4×C1311yescharacteristic
877C42C24×C1311yescharacteristic
878C42C24×C1311yescharacteristic
879C42C24×C1312yes—
880C13#6144411yescharacteristic, direct product factor, Sylow
881C23—22no—
882C23—22no—
883C23—22no—
884C23—44no—
885C23—44no—
886C23—44no—
887C23—44no—
888C23—82no—
889C23—82no—
890C23C22×D4×C1312yes—
891C23C22×D4×C1311yescharacteristic
892Q8—22no—
893Q8—22no—
894Q8—41no—
895Q8—82no—
896D4—24no—
897D4—22no—
898D4—22no—
899D4—22no—
900D4—22no—
901D4—22no—
902D4—41no—
903D4—44no—
904D4—44no—
905D4—44no—
906D4—44no—
907D4—44no—
908D4—44no—
909D4—82no—
910D4—82no—
911D4—82no—
912D4C2×C13×#4114yes—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—24no—
916C2×C4—21no—
917C2×C4—22no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—42no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—82no—
932C2×C4—82no—
933C2×C4—82no—
934C2×C4—82no—
935C2×C4—82no—
936C2×C4—82no—
937C2×C4C22×D4×C1312yes—
938C2×C4C22×D4×C1312yes—
939C2×C4C22×D4×C1311yescharacteristic
940C2×C4C22×D4×C1311yescharacteristic
941C2×C4C22×D4×C1311yescharacteristic
942C2×C4C22×D4×C1311yescharacteristic
943C2×C4C22×D4×C1312yes—
944C2×C4C22×D4×C1311yescharacteristic
945C2×C4C25×C1311yescharacteristic
946C8—21no—
947C8—22no—
948C8—21no—
949C8—21no—
950C8—22no—
951C8C2×C13×#4112yes—
952C22—21no—
953C22—21no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—24no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—88no—
967C22—88no—
968C22C13×#57512yes—
969C22C23×D4×C1311yescharacteristic
970C4—21no—
971C4—21no—
972C4—22no—
973C4—21no—
974C4—22no—
975C4—22no—
976C4—21no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4C13×#57612yes—
983C4C22×C13×#4111yescharacteristic
984C4C13×#58511yescharacteristic
985C2—22no—
986C2—42no—
987C2—44no—
988C2—82no—
989C2—82no—
990C2D4×C13×#4111yescharacteristic
991C2C2×C13×#57511yescharacteristic
992C2C2×C13×#57611yescharacteristic
subgroupG/H
centerC2×C4×C13C22×D4
commutator, Frattini, cosocleC2×C4C25×C13
socleC22×C13C23×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C13 ◁ C4×C13×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3481C2semidirect
2. C13×#3403C2semidirect
3. C13×#3389C2semidirect
4. C13×#3370C2semidirect
5. C13×#3355C2semidirect
6. C13×#3346C2semidirect
7. C13×#3322C2semidirect
8. C13×#3318C2semidirect
9. C13×#3314C2semidirect
10. C13×#3273C2semidirect
11. C13×#3264C2semidirect
12. C13×#3171C2semidirect
13. C13×#3168C2semidirect
14. C13×#3105C2semidirect
15. C13×#3102C2semidirect
16. C13×#3100C2semidirect
17. C13×#2965C2semidirect
18. C4×C13×AGL(1,ℤ/8)C2semidirect
19. C2×C4×C13×D8C2semidirect
22. C13×#559C22semidirect
23. C13×#554C22semidirect
24. C13×#554C22semidirect
27. C13×#553C22semidirect
32. C13×#546C22semidirect
33. D42×C13C22semidirect
34. C13×#532C22semidirect
36. C13×#529C22semidirect
37. C13×#529C22semidirect
41. C4×C13×#41C22semidirect
43. C2×C4×D4×C13C22semidirect
44. C2×C4×D4×C13C22semidirect
45. C13×#501C22semidirect
46. C13×#499C22semidirect
47. C13×#496C22semidirect
48. C13×#495C22semidirect
49. C13×#490C22semidirect
50. C13×#489C22semidirect
51. C13×#488C22semidirect
52. C13×#485C22semidirect
53. C13×#484C22semidirect
54. C13×#482C22semidirect
55. C13×#481C22semidirect
56. C13×#480C22semidirect
57. C13×#480C22semidirect
58. C13×#479C22semidirect
59. C13×#478C22semidirect
60. C13×#478C22semidirect
61. C13×#478C22semidirect
62. C13×#474C22semidirect
63. C13×#474C22semidirect
64. C13×#469C22semidirect
65. C13×#469C22semidirect
66. C13×#468C22semidirect
67. C13×#468C22semidirect
68. C13×#467C22semidirect
70. C13×#465C22semidirect
71. C13×#464C22semidirect
72. C13×#463C22semidirect
73. C13×#463C22semidirect
74. C13×#463C22semidirect
76. C13×#459C22semidirect
77. C13×#452C22semidirect
78. C13×#450C22semidirect
81. C13×#447C22semidirect
82. C13×#447C22semidirect
83. C13×#446C22semidirect
84. C13×#446C22semidirect
86. C13×#442C22semidirect
87. C13×#440C22semidirect
88. C13×#440C22semidirect
89. C4×C13×Q16C22semidirect
90. C4×C13×SD16C22semidirect
91. C4×C13×SD16C22semidirect
92. C4×C13×SD16C22semidirect
95. C4×C13×D8C22semidirect
96. C4×C13×D8C22semidirect
97. C4×C13×D8C22semidirect
98. C4×C13×D8C22semidirect
99. C4×C13×D8C22semidirect
100. C4×C13×D8C22semidirect
101. C4×C13×D8C22semidirect
102. C13×#436C22semidirect
103. C13×#436C22semidirect
104. C13×#435C22semidirect
105. C13×#435C22semidirect
106. C13×#431C22semidirect
107. C13×#431C22semidirect
108. C13×#428C22semidirect
109. C2×C13×#107C22semidirect
110. C13×#418C22semidirect
111. C13×#417C22semidirect
112. C2×C13×#102C22semidirect
113. C4×C13×M16C22semidirect
114. C2×C4×C8×C13C22semidirect
266. #61444C13direct (N × H)
323. C13×D8#41semidirect
385. #3481C2×C13semidirect
386. #3403C2×C13semidirect
387. #3389C2×C13semidirect
388. #3370C2×C13semidirect
389. #3355C2×C13semidirect
390. #3346C2×C13semidirect
391. #3322C2×C13semidirect
392. #3318C2×C13semidirect
393. #3314C2×C13semidirect
394. #3273C2×C13semidirect
395. #3264C2×C13semidirect
396. #3171C2×C13semidirect
397. #3168C2×C13semidirect
398. #3105C2×C13semidirect
399. #3102C2×C13semidirect
400. #3100C2×C13semidirect
401. #2965C2×C13semidirect
402. C4×AGL(1,ℤ/8)C2×C13semidirect
403. C2×C4×D8C2×C13semidirect
477. #559C22×C13semidirect
478. #554C22×C13semidirect
479. #554C22×C13semidirect
482. #553C22×C13semidirect
487. #546C22×C13semidirect
488. D42C22×C13semidirect
489. #532C22×C13semidirect
491. #529C22×C13semidirect
492. #529C22×C13semidirect
496. C4×#41C22×C13semidirect
498. C2×C4×D4C22×C13semidirect
499. C2×C4×D4C22×C13semidirect
500. #501C22×C13semidirect
501. #499C22×C13semidirect
502. #496C22×C13semidirect
503. #495C22×C13semidirect
504. #490C22×C13semidirect
505. #489C22×C13semidirect
506. #488C22×C13semidirect
507. #485C22×C13semidirect
508. #484C22×C13semidirect
509. #482C22×C13semidirect
510. #481C22×C13semidirect
511. #480C22×C13semidirect
512. #480C22×C13semidirect
513. #479C22×C13semidirect
514. #478C22×C13semidirect
515. #478C22×C13semidirect
516. #478C22×C13semidirect
517. #474C22×C13semidirect
518. #474C22×C13semidirect
519. #469C22×C13semidirect
520. #469C22×C13semidirect
521. #468C22×C13semidirect
522. #468C22×C13semidirect
523. #467C22×C13semidirect
525. #465C22×C13semidirect
526. #464C22×C13semidirect
527. #463C22×C13semidirect
528. #463C22×C13semidirect
529. #463C22×C13semidirect
531. #459C22×C13semidirect
532. #452C22×C13semidirect
533. #450C22×C13semidirect
536. #447C22×C13semidirect
537. #447C22×C13semidirect
538. #446C22×C13semidirect
539. #446C22×C13semidirect
541. #442C22×C13semidirect
542. #440C22×C13semidirect
543. #440C22×C13semidirect
544. C4×Q16C22×C13semidirect
545. C4×SD16C22×C13semidirect
546. C4×SD16C22×C13semidirect
547. C4×SD16C22×C13semidirect
550. C4×D8C22×C13semidirect
551. C4×D8C22×C13semidirect
552. C4×D8C22×C13semidirect
553. C4×D8C22×C13semidirect
554. C4×D8C22×C13semidirect
555. C4×D8C22×C13semidirect
556. C4×D8C22×C13semidirect
557. #436C22×C13semidirect
558. #436C22×C13semidirect
559. #435C22×C13semidirect
560. #435C22×C13semidirect
561. #431C22×C13semidirect
562. #431C22×C13semidirect
563. #428C22×C13semidirect
564. C2×#107C22×C13semidirect
565. #418C22×C13semidirect
566. #417C22×C13semidirect
567. C2×#102C22×C13semidirect
568. C4×M16C22×C13semidirect
569. C2×C4×C8C22×C13semidirect
818. D8C13×#41semidirect
880. C13#61444direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34812
C13×#34032
C13×#33892
C13×#33702
C13×#33552
C13×#33462
C13×#33222
C13×#33182
C13×#33142
C13×#32732
C13×#32642
C13×#31712
C13×#31682
C13×#31052
C13×#31022
C13×#31002
C13×#29652
C4×C13×AGL(1,ℤ/8)2
C2×C4×C13×D82
#6144413