Finite Group Databasebeta

← C13×#61052 #15747391

Subgroups — C13×#61052 #15747391

Order 3328.

2722 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#577C211yesmaximal, characteristic, complemented
2C22×C13×#135C211yesmaximal, characteristic, complemented
3C13×#3487C211yesmaximal, characteristic, complemented
4C13×#3485C211yesmaximal, characteristic, complemented
5C13×#3284C214yesmaximal, complemented
6C13×#3282C214yesmaximal, complemented
7C13×#3269C214yesmaximal, complemented
8C13×#3268C214yesmaximal, complemented
9C13×#3154C211yesmaximal, characteristic, complemented
10C13×#3057C211yesmaximal, characteristic, complemented
11C13×#3050C211yesmaximal, characteristic, complemented
12C13×#3044C211yesmaximal, characteristic, complemented
13C13×#3041C211yesmaximal, characteristic, complemented
14C13×#3011C211yesmaximal, characteristic, complemented
15C13×#3008C211yesmaximal, characteristic, complemented
16C13×#3005C211yesmaximal, characteristic, complemented
17C13×#3005C211yesmaximal, characteristic, complemented
18C13×#2949C211yesmaximal, characteristic, complemented
19C13×#2929C211yesmaximal, characteristic, complemented
20C2×C13×2−1+4C2211yescharacteristic
21C2×C13×H(5,𝔽2)C2211yescharacteristic
22C22×C13×#41C2211yescharacteristic
23C22×C13×#41C2211yescharacteristic, complemented
24C13×#577—28no—
25C2×C13×#137C2211yescharacteristic
26C2×C13×#137C2212yescomplemented
27C2×C13×#137C2211yescharacteristic, complemented
28C2×C13×AGL(1,ℤ/8)C2211yescharacteristic
29C2×C13×AGL(1,ℤ/8)C2211yescharacteristic
30C2×C13×AGL(1,ℤ/8)C2212yescomplemented
31C2×C13×#135—28no—
32C2×C13×#135C2211yescharacteristic
33C2×C13×#135C2214yescomplemented
34C2×C13×#135C2214yescomplemented
35C2×C13×#135C2212yescomplemented
36C22×C13×Q16C2211yescharacteristic, complemented
37C22×C13×SD16C2211yescharacteristic
38C22×C13×SD16C2212yescomplemented
39C22×C13×SD16C2211yescharacteristic, complemented
40C22×C13×D8C2211yescharacteristic
41C2×C13×#131C2211yescharacteristic
42C23×C8×C13C2211yescharacteristic, complemented
43C13×#550—22no—
44C13×#550C2214yescomplemented
45C13×#548—22no—
46C13×#548C2214yescomplemented
47C13×#547—22no—
48C13×#547C2214yescomplemented
49C13×#546—22no—
50C13×#546C2214yescomplemented
51C13×#536C2211yescharacteristic
52C13×#536C2211yescharacteristic
53C13×#535—22no—
54C13×#535C2211yescharacteristic
55C13×#535C2211yescharacteristic, complemented
56C13×#534—22no—
57C13×#525—22no—
58C13×#525C2211yescharacteristic
59C13×#525C2211yescharacteristic
60C13×#525C2211yescharacteristic, complemented
61C2×C13×#123—22no—
62C13×#519C2211yescharacteristic, complemented
63C13×#518C2211yescharacteristic
64C13×#497C2212yescomplemented
65C13×#496C2212yescomplemented
66C13×#495C2212yescomplemented
67C13×#492C2212yescomplemented
68C13×#468C2214yescomplemented
69C13×#467C2212yescomplemented
70C13×#466C2212yescomplemented
71C13×#465C2212yescomplemented
72C13×#465C2214yescomplemented
73C13×#465C2212yescomplemented
74C13×#464C2214yescomplemented
75C13×#463C2214yescomplemented
76C13×#462C2214yescomplemented
77C13×#459C2214yescomplemented
78C13×#452C2214yescomplemented
79C13×#452C2214yescomplemented
80C13×#452C2214yescomplemented
81C13×#451C2214yescomplemented
82C13×#449C2214yescomplemented
83C13×#449C2214yescomplemented
84C13×#449C2214yescomplemented
85C13×#447C2214yescomplemented
86C13×#440C2214yescomplemented
87C4×C13×SD16C2214yescomplemented
88C13×#435C2214yescomplemented
89C8×D4×C13C2214yescomplemented
90C13×#427C2211yescharacteristic, complemented
91C13×#424C2211yescharacteristic, complemented
92C13×#419C2211yescharacteristic, complemented
93C13×#419C2211yescharacteristic, complemented
94C13×#418C2211yescharacteristic
95C13×#418C2211yescharacteristic, complemented
96C13×#416C2211yescharacteristic
97C13×#416C2211yescharacteristic, complemented
98C13×#408C2211yescharacteristic
99C13×#407C2211yescharacteristic, complemented
100C13×#405C2211yescharacteristic, complemented
101C13×2−1+4—24no—
102C13×2−1+4—42no—
103C13×H(5,𝔽2)—24no—
104C13×H(5,𝔽2)—42no—
105C2×C13×#41—21no—
106C2×C13×#41—22no—
107C2×C13×#41—21no—
108C2×C13×#41—22no—
109C2×C13×#41—22no—
110C2×C13×#41—24no—
111C2×C13×#41—24no—
112C2×C13×#41—42no—
113C2×C13×#41—42no—
114C2×C13×#41C2311yescharacteristic
115C2×C13×#41C2311yescharacteristic
116C2×C13×#41C2312yes—
117C2×C13×#41C2314yes—
118C2×C13×#41C2314yes—
119C2×C13×#41C2312yes—
120C2×C13×#41C2311yescharacteristic
121C22×Q8×C13—21no—
122C22×Q8×C13C2311yescharacteristic
123C22×Q8×C13C2312yes—
124C22×Q8×C13C2311yescharacteristic
125C22×D4×C13—21no—
126C22×D4×C13—21no—
127C22×D4×C13—22no—
128C22×D4×C13—21no—
129C22×D4×C13C2311yescharacteristic
130C22×D4×C13C2312yes—
131C22×D4×C13C2311yescharacteristic
132C23×C4×C13—21no—
133C23×C4×C13—21no—
134C23×C4×C13C2311yescharacteristic
135C13×#137—24no—
136C13×#137—28no—
137C13×#137—42no—
138C13×AGL(1,ℤ/8)—24no—
139C13×AGL(1,ℤ/8)—28no—
140C13×AGL(1,ℤ/8)—42no—
141C13×#135—216no—
142C13×#135—216no—
143C13×#135—28no—
144C13×#135—24no—
145C2×C13×Q16—24no—
146C2×C13×Q16C2314yes—
147C2×C13×Q16C2312yes—
148C2×C13×Q16C2311yescharacteristic
149C2×C13×Q16C2312yes—
150C2×C13×SD16—28no—
151C2×C13×SD16—24no—
152C2×C13×SD16D418yescomplemented
153C2×C13×SD16C2312yes—
154C2×C13×SD16C2312yes—
155C2×C13×SD16C2311yescharacteristic
156C2×C13×SD16C2312yes—
157C2×C13×SD16C2311yescharacteristic
158C2×C13×SD16C2312yes—
159C2×C13×SD16C2312yes—
160C2×C13×SD16C2312yes—
161C2×C13×SD16C2312yes—
162C2×C13×SD16C2312yes—
163C2×C13×D8—24no—
164C2×C13×D8C2314yes—
165C2×C13×D8C2312yes—
166C2×C13×D8C2311yescharacteristic
167C2×C13×D8C2312yes—
168C13×#131—24no—
169C2×C13×M16C2311yescharacteristic
170C2×C13×M16C2311yescharacteristic
171C2×C13×M16C2312yes—
172C22×C8×C13—24no—
173C22×C8×C13C2311yescharacteristic
174C22×C8×C13C2312yes—
175C22×C8×C13C2312yes—
176C22×C8×C13C2312yes—
177C22×C8×C13C2311yescharacteristic
178C13×C4⋊Q8—21no—
179C13×C4⋊Q8C2312yes—
180C13×#127—24no—
181C13×#127—21no—
182C13×#127C2312yes—
183C13×#124—21no—
184C13×#124—21no—
185C13×#124—24no—
186C13×#124C2312yes—
187C13×#124C2312yes—
188C13×#123—22no—
189C13×#123—21no—
190C13×#123—21no—
191C13×#123—24no—
192C13×#123—22no—
193C13×#123—24no—
194C13×#123—24no—
195C13×#123D412yes—
196C13×C22⋊Q8—24no—
197C13×C22⋊Q8—22no—
198C13×C22⋊Q8D412yes—
199C13×C22⋊Q8C2314yes—
200C13×C22⋊Q8C2312yes—
201C13×C22⋊Q8C2312yes—
202C13×#121—24no—
203C13×#121—24no—
204C13×#121—22no—
205C13×#121—24no—
206C13×#121—24no—
207C13×#121—24no—
208C13×#121D412yes—
209C13×#121C2314yes—
210C13×#121C2312yes—
211C13×#121C2312yes—
212C13×#120—21no—
213C13×#120—21no—
214C13×#120—22no—
215C13×#120—24no—
216C13×#120—22no—
217C13×#120D412yes—
218C4×Q8×C13—22no—
219C4×Q8×C13C2314yes—
220C4×D4×C13—22no—
221C4×D4×C13—22no—
222C4×D4×C13—22no—
223C4×D4×C13—24no—
224C4×D4×C13—24no—
225C4×D4×C13C2314yes—
226C4×D4×C13C2314yes—
227C13×#117—22no—
228C13×#117C2311yescharacteristic
229C13×#117C2311yescharacteristic
230C13×#117C2311yescharacteristic
231C2×C13×C4⋊C4—24no—
232C2×C13×C22⋊C4—22no—
233C2×C13×C22⋊C4—24no—
234C13×#107C2312yes—
235C13×#106C2312yes—
236C13×C4⋊C8C2314yes—
237C13×#103C2312yes—
238C13×#103C2312yes—
239C13×#103C2314yes—
240C13×#103C2314yes—
241C13×#102C2312yes—
242C13×#102C2312yes—
243C13×#102C2314yes—
244C13×#102C2314yes—
245C13×C22⋊C8C2314yes—
246C13×C22⋊C8C2314yes—
247C13×#97C2312yes—
248C4×C8×C13C2312yes—
249#61052C1311yesmaximal, characteristic, direct product factor, Sylow
250C24×C13—21no—
251C24×C13—22no—
252C24×C13—21no—
253C24×C13C2×D411yescharacteristic
254C13×#41—22no—
255C13×#41—22no—
256C13×#41—28no—
257C13×#41—24no—
258C13×#41—28no—
259C13×#41—24no—
260C13×#41—22no—
261C13×#41—22no—
262C13×#41—22no—
263C13×#41—22no—
264C13×#41—44no—
265C13×#41—44no—
266C13×#41—42no—
267C13×#41—42no—
268C13×#41—48no—
269C13×#41—48no—
270C13×#41—48no—
271C13×#41—44no—
272C13×#41—44no—
273C2×Q8×C13—21no—
274C2×Q8×C13—22no—
275C2×Q8×C13—21no—
276C2×Q8×C13—22no—
277C2×Q8×C13—24no—
278C2×Q8×C13—22no—
279C2×Q8×C13—22no—
280C2×Q8×C13—42no—
281C2×Q8×C13—44no—
282C2×Q8×C13C2×D414yes—
283C2×Q8×C13C2×D411yescharacteristic
284C2×Q8×C13C2411yescharacteristic
285C2×Q8×C13C2412yes—
286C2×Q8×C13C2411yescharacteristic
287C2×Q8×C13C2412yes—
288C2×D4×C13—24no—
289C2×D4×C13—21no—
290C2×D4×C13—24no—
291C2×D4×C13—21no—
292C2×D4×C13—22no—
293C2×D4×C13—24no—
294C2×D4×C13—22no—
295C2×D4×C13—22no—
296C2×D4×C13—24no—
297C2×D4×C13—22no—
298C2×D4×C13—21no—
299C2×D4×C13—22no—
300C2×D4×C13—22no—
301C2×D4×C13—21no—
302C2×D4×C13—24no—
303C2×D4×C13—22no—
304C2×D4×C13—22no—
305C2×D4×C13—42no—
306C2×D4×C13—44no—
307C2×D4×C13—44no—
308C2×D4×C13—48no—
309C2×D4×C13—44no—
310C2×D4×C13C2×D412yes—
311C2×D4×C13C2×D411yescharacteristic
312C2×D4×C13C2×D414yes—
313C2×D4×C13C2×D414yes—
314C2×D4×C13C2411yescharacteristic
315C2×D4×C13C2412yes—
316C2×D4×C13C2411yescharacteristic
317C2×D4×C13C2412yes—
318C22×C4×C13—21no—
319C22×C4×C13—22no—
320C22×C4×C13—22no—
321C22×C4×C13—22no—
322C22×C4×C13—21no—
323C22×C4×C13—24no—
324C22×C4×C13—22no—
325C22×C4×C13—22no—
326C22×C4×C13—21no—
327C22×C4×C13—24no—
328C22×C4×C13—21no—
329C22×C4×C13—24no—
330C22×C4×C13—44no—
331C22×C4×C13—44no—
332C22×C4×C13C2×D412yes—
333C22×C4×C13C2×D411yescharacteristic
334C22×C4×C13C2412yes—
335C22×C4×C13C2412yes—
336C22×C4×C13C2411yescharacteristic
337C13×Q16—28no—
338C13×Q16—24no—
339C13×Q16—22no—
340C13×Q16—42no—
341C13×SD16—24no—
342C13×SD16—24no—
343C13×SD16—22no—
344C13×SD16—24no—
345C13×SD16—24no—
346C13×SD16—22no—
347C13×SD16—42no—
348C13×SD16—42no—
349C13×SD16C2×D418yes—
350C13×SD16C2×D418yes—
351C13×D8—28no—
352C13×D8—24no—
353C13×D8—22no—
354C13×D8—42no—
355C13×M16—22no—
356C13×M16—22no—
357C13×M16—24no—
358C2×C8×C13—22no—
359C2×C8×C13—24no—
360C2×C8×C13—24no—
361C2×C8×C13—24no—
362C2×C8×C13C2×D414yes—
363C2×C8×C13C2412yes—
364C2×C8×C13C2412yes—
365C2×C8×C13C2412yes—
366C2×C8×C13C2411yescharacteristic
367C2×C8×C13C2411yescharacteristic
368C13×C4⋊C4—22no—
369C13×C4⋊C4—24no—
370C13×C4⋊C4—24no—
371C13×C4⋊C4—24no—
372C13×C4⋊C4—22no—
373C13×C4⋊C4C2×D414yes—
374C13×C4⋊C4C2×D412yes—
375C13×C4⋊C4C2412yes—
376C13×C4⋊C4C2412yes—
377C13×C22⋊C4—21no—
378C13×C22⋊C4—24no—
379C13×C22⋊C4—21no—
380C13×C22⋊C4—22no—
381C13×C22⋊C4—22no—
382C13×C22⋊C4—22no—
383C13×C22⋊C4—24no—
384C13×C22⋊C4—24no—
385C13×C22⋊C4—22no—
386C13×C22⋊C4—24no—
387C13×C22⋊C4—24no—
388C13×C22⋊C4C2×D412yes—
389C13×C22⋊C4C2×D414yes—
390C13×C22⋊C4C2×D414yes—
391C42×C13—24no—
392C42×C13—21no—
393C42×C13—21no—
394C42×C13C2412yes—
395C2×#577C2×C1311yescharacteristic, complemented
396C22×#135C2×C1311yescharacteristic, complemented
397#3487C2×C1311yescharacteristic, complemented
398#3485C2×C1311yescharacteristic, complemented
399#3284C2×C1314yescomplemented
400#3282C2×C1314yescomplemented
401#3269C2×C1314yescomplemented
402#3268C2×C1314yescomplemented
403#3154C2×C1311yescharacteristic, complemented
404#3057C2×C1311yescharacteristic, complemented
405#3050C2×C1311yescharacteristic, complemented
406#3044C2×C1311yescharacteristic, complemented
407#3041C2×C1311yescharacteristic, complemented
408#3011C2×C1311yescharacteristic, complemented
409#3008C2×C1311yescharacteristic, complemented
410#3005C2×C1311yescharacteristic, complemented
411#3005C2×C1311yescharacteristic, complemented
412#2949C2×C1311yescharacteristic, complemented
413#2929C2×C1311yescharacteristic, complemented
414C23×C13—22no—
415C23×C13—22no—
416C23×C13—24no—
417C23×C13—21no—
418C23×C13—22no—
419C23×C13—21no—
420C23×C13—42no—
421C23×C13—44no—
422C23×C13—42no—
423C23×C13—82no—
424C23×C13—82no—
425C23×C13—84no—
426C23×C13C22×D412yes—
427C23×C13C22×D412yes—
428C23×C13C22×D411yescharacteristic
429Q8×C13—24no—
430Q8×C13—22no—
431Q8×C13—22no—
432Q8×C13—21no—
433Q8×C13—22no—
434Q8×C13—21no—
435Q8×C13—21no—
436Q8×C13—22no—
437Q8×C13—21no—
438Q8×C13—44no—
439Q8×C13—42no—
440Q8×C13C22×D414yes—
441D4×C13—24no—
442D4×C13—24no—
443D4×C13—22no—
444D4×C13—21no—
445D4×C13—22no—
446D4×C13—21no—
447D4×C13—22no—
448D4×C13—21no—
449D4×C13—22no—
450D4×C13—21no—
451D4×C13—44no—
452D4×C13—44no—
453D4×C13—48no—
454D4×C13—44no—
455D4×C13—44no—
456D4×C13—48no—
457D4×C13—42no—
458D4×C13—42no—
459D4×C13—42no—
460D4×C13—84no—
461D4×C13—82no—
462D4×C13—84no—
463D4×C13—82no—
464D4×C13C22×D414yes—
465C2×C4×C13—22no—
466C2×C4×C13—24no—
467C2×C4×C13—22no—
468C2×C4×C13—24no—
469C2×C4×C13—22no—
470C2×C4×C13—22no—
471C2×C4×C13—22no—
472C2×C4×C13—22no—
473C2×C4×C13—22no—
474C2×C4×C13—22no—
475C2×C4×C13—21no—
476C2×C4×C13—22no—
477C2×C4×C13—21no—
478C2×C4×C13—48no—
479C2×C4×C13—44no—
480C2×C4×C13—48no—
481C2×C4×C13—44no—
482C2×C4×C13—44no—
483C2×C4×C13—42no—
484C2×C4×C13—42no—
485C2×C4×C13—42no—
486C2×C4×C13—84no—
487C2×C4×C13C22×D414yes—
488C2×C4×C13C22×D412yes—
489C2×C4×C13C22×D412yes—
490C2×C4×C13C22×D411yescharacteristic
491C2×C4×C13C22×D412yes—
492C2×C4×C13H(5,𝔽2)12yes—
493C2×C4×C13C2511yescharacteristic
494C8×C13—22no—
495C8×C13—22no—
496C8×C13—22no—
497C8×C13C22×D412yes—
498C8×C13C22×D412yes—
499C2×2−1+4C22×C1311yescharacteristic
500C2×H(5,𝔽2)C22×C1311yescharacteristic
501C22×#41C22×C1311yescharacteristic
502C22×#41C22×C1311yescharacteristic, complemented
503#577—28no—
504C2×#137C22×C1311yescharacteristic
505C2×#137C22×C1312yescomplemented
506C2×#137C22×C1311yescharacteristic, complemented
507C2×AGL(1,ℤ/8)C22×C1311yescharacteristic
508C2×AGL(1,ℤ/8)C22×C1311yescharacteristic
509C2×AGL(1,ℤ/8)C22×C1312yescomplemented
510C2×#135—28no—
511C2×#135C22×C1311yescharacteristic
512C2×#135C22×C1314yescomplemented
513C2×#135C22×C1314yescomplemented
514C2×#135C22×C1312yescomplemented
515C22×Q16C22×C1311yescharacteristic, complemented
516C22×SD16C22×C1311yescharacteristic
517C22×SD16C22×C1311yescharacteristic, complemented
518C22×SD16C22×C1312yescomplemented
519C22×D8C22×C1311yescharacteristic
520C2×#131C22×C1311yescharacteristic
521C23×C8C22×C1311yescharacteristic, complemented
522#550—22no—
523#550C22×C1314yescomplemented
524#548—22no—
525#548C22×C1314yescomplemented
526#547—22no—
527#547C22×C1314yescomplemented
528#546—22no—
529#546C22×C1314yescomplemented
530#536C22×C1311yescharacteristic
531#536C22×C1311yescharacteristic
532#535—22no—
533#535C22×C1311yescharacteristic
534#535C22×C1311yescharacteristic, complemented
535#534—22no—
536#525—22no—
537#525C22×C1311yescharacteristic
538#525C22×C1311yescharacteristic
539#525C22×C1311yescharacteristic, complemented
540C2×#123—22no—
541#519C22×C1311yescharacteristic, complemented
542#518C22×C1311yescharacteristic
543#497C22×C1312yescomplemented
544#496C22×C1312yescomplemented
545#495C22×C1312yescomplemented
546#492C22×C1312yescomplemented
547#468C22×C1314yescomplemented
548#467C22×C1312yescomplemented
549#466C22×C1312yescomplemented
550#465C22×C1312yescomplemented
551#465C22×C1314yescomplemented
552#465C22×C1312yescomplemented
553#464C22×C1314yescomplemented
554#463C22×C1314yescomplemented
555#462C22×C1314yescomplemented
556#459C22×C1314yescomplemented
557#452C22×C1314yescomplemented
558#452C22×C1314yescomplemented
559#452C22×C1314yescomplemented
560#451C22×C1314yescomplemented
561#449C22×C1314yescomplemented
562#449C22×C1314yescomplemented
563#449C22×C1314yescomplemented
564#447C22×C1314yescomplemented
565#440C22×C1314yescomplemented
566C4×SD16C22×C1314yescomplemented
567#435C22×C1314yescomplemented
568C8×D4C22×C1314yescomplemented
569#427C22×C1311yescharacteristic, complemented
570#424C22×C1311yescharacteristic, complemented
571#419C22×C1311yescharacteristic, complemented
572#419C22×C1311yescharacteristic, complemented
573#418C22×C1311yescharacteristic
574#418C22×C1311yescharacteristic, complemented
575#416C22×C1311yescharacteristic
576#416C22×C1311yescharacteristic, complemented
577#408C22×C1311yescharacteristic
578#407C22×C1311yescharacteristic, complemented
579#405C22×C1311yescharacteristic, complemented
580C22×C13—22no—
581C22×C13—22no—
582C22×C13—24no—
583C22×C13—22no—
584C22×C13—22no—
585C22×C13—22no—
586C22×C13—24no—
587C22×C13—44no—
588C22×C13—44no—
589C22×C13—42no—
590C22×C13—44no—
591C22×C13—42no—
592C22×C13—41no—
593C22×C13—42no—
594C22×C13—41no—
595C22×C13—84no—
596C22×C13—84no—
597C22×C13—164no—
598C22×C13D4212yes—
599C22×C13C23×D411yescharacteristic
600C4×C13—24no—
601C4×C13—22no—
602C4×C13—24no—
603C4×C13—22no—
604C4×C13—42no—
605C4×C13—42no—
606C4×C13—41no—
607C4×C13—42no—
608C4×C13—41no—
609C4×C13D4212yes—
610C4×C13C23×D411yescharacteristic
611C4×C13C2×H(5,𝔽2)11yescharacteristic
6122−1+4—24no—
6132−1+4—42no—
614H(5,𝔽2)—24no—
615H(5,𝔽2)—42no—
616C2×#41—21no—
617C2×#41—22no—
618C2×#41—21no—
619C2×#41—22no—
620C2×#41—22no—
621C2×#41—24no—
622C2×#41—24no—
623C2×#41—42no—
624C2×#41—42no—
625C2×#41C23×C1311yescharacteristic
626C2×#41C23×C1311yescharacteristic
627C2×#41C23×C1314yes—
628C2×#41C23×C1312yes—
629C2×#41C23×C1314yes—
630C2×#41C23×C1312yes—
631C2×#41C23×C1311yescharacteristic
632C22×Q8—21no—
633C22×Q8C23×C1311yescharacteristic
634C22×Q8C23×C1312yes—
635C22×Q8C23×C1311yescharacteristic
636C22×D4—21no—
637C22×D4—21no—
638C22×D4—22no—
639C22×D4—21no—
640C22×D4C23×C1311yescharacteristic
641C22×D4C23×C1312yes—
642C22×D4C23×C1311yescharacteristic
643C23×C4—21no—
644C23×C4—21no—
645C23×C4C23×C1311yescharacteristic
646#137—24no—
647#137—28no—
648#137—42no—
649AGL(1,ℤ/8)—24no—
650AGL(1,ℤ/8)—28no—
651AGL(1,ℤ/8)—42no—
652#135—216no—
653#135—216no—
654#135—28no—
655#135—24no—
656C2×Q16—24no—
657C2×Q16C23×C1314yes—
658C2×Q16C23×C1311yescharacteristic
659C2×Q16C23×C1312yes—
660C2×Q16C23×C1312yes—
661C2×SD16—28no—
662C2×SD16—24no—
663C2×SD16D4×C1318yescomplemented
664C2×SD16C23×C1311yescharacteristic
665C2×SD16C23×C1312yes—
666C2×SD16C23×C1312yes—
667C2×SD16C23×C1312yes—
668C2×SD16C23×C1312yes—
669C2×SD16C23×C1311yescharacteristic
670C2×SD16C23×C1312yes—
671C2×SD16C23×C1312yes—
672C2×SD16C23×C1312yes—
673C2×SD16C23×C1312yes—
674C2×D8—24no—
675C2×D8C23×C1314yes—
676C2×D8C23×C1311yescharacteristic
677C2×D8C23×C1312yes—
678C2×D8C23×C1312yes—
679#131—24no—
680C2×M16C23×C1311yescharacteristic
681C2×M16C23×C1312yes—
682C2×M16C23×C1311yescharacteristic
683C22×C8—24no—
684C22×C8C23×C1311yescharacteristic
685C22×C8C23×C1312yes—
686C22×C8C23×C1312yes—
687C22×C8C23×C1312yes—
688C22×C8C23×C1311yescharacteristic
689C4⋊Q8—21no—
690C4⋊Q8C23×C1312yes—
691#127—24no—
692#127—21no—
693#127C23×C1312yes—
694#124—21no—
695#124—21no—
696#124—24no—
697#124C23×C1312yes—
698#124C23×C1312yes—
699#123—22no—
700#123—21no—
701#123—21no—
702#123—24no—
703#123—22no—
704#123—24no—
705#123—24no—
706#123D4×C1312yes—
707C22⋊Q8—24no—
708C22⋊Q8—22no—
709C22⋊Q8D4×C1312yes—
710C22⋊Q8C23×C1312yes—
711C22⋊Q8C23×C1312yes—
712C22⋊Q8C23×C1314yes—
713#121—24no—
714#121—24no—
715#121—22no—
716#121—24no—
717#121—24no—
718#121—24no—
719#121D4×C1312yes—
720#121C23×C1312yes—
721#121C23×C1312yes—
722#121C23×C1314yes—
723#120—21no—
724#120—21no—
725#120—22no—
726#120—24no—
727#120—22no—
728#120D4×C1312yes—
729C4×Q8—22no—
730C4×Q8C23×C1314yes—
731C4×D4—22no—
732C4×D4—22no—
733C4×D4—22no—
734C4×D4—24no—
735C4×D4—24no—
736C4×D4C23×C1314yes—
737C4×D4C23×C1314yes—
738#117—22no—
739#117C23×C1311yescharacteristic
740#117C23×C1311yescharacteristic
741#117C23×C1311yescharacteristic
742C2×C4⋊C4—24no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—24no—
745#107C23×C1312yes—
746#106C23×C1312yes—
747C4⋊C8C23×C1314yes—
748#103C23×C1312yes—
749#103C23×C1312yes—
750#103C23×C1314yes—
751#103C23×C1314yes—
752#102C23×C1312yes—
753#102C23×C1312yes—
754#102C23×C1314yes—
755#102C23×C1314yes—
756C22⋊C8C23×C1314yes—
757C22⋊C8C23×C1314yes—
758#97C23×C1312yes—
759C4×C8C23×C1312yes—
760C2×C13—22no—
761C2×C13—42no—
762C2×C13—42no—
763C2×C13—44no—
764C2×C13—81no—
765C2×C13—82no—
766C2×C13—81no—
767C2×C13C2×D4211yescharacteristic
768C2×C13#358412yes—
769C24—21no—
770C24—22no—
771C24—21no—
772C24C2×D4×C1311yescharacteristic
773#41—22no—
774#41—22no—
775#41—28no—
776#41—24no—
777#41—28no—
778#41—24no—
779#41—22no—
780#41—22no—
781#41—22no—
782#41—22no—
783#41—44no—
784#41—44no—
785#41—42no—
786#41—42no—
787#41—48no—
788#41—48no—
789#41—48no—
790#41—44no—
791#41—44no—
792C2×Q8—21no—
793C2×Q8—22no—
794C2×Q8—21no—
795C2×Q8—22no—
796C2×Q8—24no—
797C2×Q8—22no—
798C2×Q8—22no—
799C2×Q8—42no—
800C2×Q8—44no—
801C2×Q8C2×D4×C1314yes—
802C2×Q8C2×D4×C1311yescharacteristic
803C2×Q8C24×C1311yescharacteristic
804C2×Q8C24×C1312yes—
805C2×Q8C24×C1311yescharacteristic
806C2×Q8C24×C1312yes—
807C2×D4—24no—
808C2×D4—21no—
809C2×D4—24no—
810C2×D4—21no—
811C2×D4—22no—
812C2×D4—24no—
813C2×D4—22no—
814C2×D4—22no—
815C2×D4—24no—
816C2×D4—22no—
817C2×D4—21no—
818C2×D4—22no—
819C2×D4—22no—
820C2×D4—21no—
821C2×D4—24no—
822C2×D4—22no—
823C2×D4—22no—
824C2×D4—42no—
825C2×D4—44no—
826C2×D4—44no—
827C2×D4—48no—
828C2×D4—44no—
829C2×D4C2×D4×C1312yes—
830C2×D4C2×D4×C1311yescharacteristic
831C2×D4C2×D4×C1314yes—
832C2×D4C2×D4×C1314yes—
833C2×D4C24×C1311yescharacteristic
834C2×D4C24×C1312yes—
835C2×D4C24×C1311yescharacteristic
836C2×D4C24×C1312yes—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—24no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—21no—
846C22×C4—24no—
847C22×C4—21no—
848C22×C4—24no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4C2×D4×C1312yes—
852C22×C4C2×D4×C1311yescharacteristic
853C22×C4C24×C1312yes—
854C22×C4C24×C1312yes—
855C22×C4C24×C1311yescharacteristic
856Q16—28no—
857Q16—24no—
858Q16—22no—
859Q16—42no—
860SD16—24no—
861SD16—24no—
862SD16—22no—
863SD16—24no—
864SD16—24no—
865SD16—22no—
866SD16—42no—
867SD16—42no—
868SD16C2×D4×C1318yes—
869SD16C2×D4×C1318yes—
870D8—28no—
871D8—24no—
872D8—22no—
873D8—42no—
874M16—22no—
875M16—22no—
876M16—24no—
877C2×C8—22no—
878C2×C8—24no—
879C2×C8—24no—
880C2×C8—24no—
881C2×C8C2×D4×C1314yes—
882C2×C8C24×C1312yes—
883C2×C8C24×C1312yes—
884C2×C8C24×C1312yes—
885C2×C8C24×C1311yescharacteristic
886C2×C8C24×C1311yescharacteristic
887C4⋊C4—22no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—22no—
892C4⋊C4C2×D4×C1314yes—
893C4⋊C4C2×D4×C1312yes—
894C4⋊C4C24×C1312yes—
895C4⋊C4C24×C1312yes—
896C22⋊C4—21no—
897C22⋊C4—24no—
898C22⋊C4—21no—
899C22⋊C4—22no—
900C22⋊C4—22no—
901C22⋊C4—22no—
902C22⋊C4—24no—
903C22⋊C4—24no—
904C22⋊C4—22no—
905C22⋊C4—24no—
906C22⋊C4—24no—
907C22⋊C4C2×D4×C1312yes—
908C22⋊C4C2×D4×C1314yes—
909C22⋊C4C2×D4×C1314yes—
910C42—24no—
911C42—21no—
912C42—21no—
913C42C24×C1312yes—
914C13#6105211yescharacteristic, direct product factor, Sylow
915C23—22no—
916C23—22no—
917C23—24no—
918C23—21no—
919C23—22no—
920C23—21no—
921C23—42no—
922C23—44no—
923C23—42no—
924C23—82no—
925C23—82no—
926C23—84no—
927C23C22×D4×C1312yes—
928C23C22×D4×C1312yes—
929C23C22×D4×C1311yescharacteristic
930Q8—24no—
931Q8—22no—
932Q8—22no—
933Q8—21no—
934Q8—22no—
935Q8—21no—
936Q8—21no—
937Q8—22no—
938Q8—21no—
939Q8—44no—
940Q8—42no—
941Q8C22×D4×C1314yes—
942D4—24no—
943D4—24no—
944D4—22no—
945D4—21no—
946D4—22no—
947D4—21no—
948D4—22no—
949D4—21no—
950D4—22no—
951D4—21no—
952D4—44no—
953D4—44no—
954D4—48no—
955D4—44no—
956D4—44no—
957D4—48no—
958D4—42no—
959D4—42no—
960D4—42no—
961D4—84no—
962D4—82no—
963D4—84no—
964D4—82no—
965D4C22×D4×C1314yes—
966C2×C4—22no—
967C2×C4—24no—
968C2×C4—22no—
969C2×C4—24no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—48no—
980C2×C4—44no—
981C2×C4—48no—
982C2×C4—44no—
983C2×C4—44no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4—84no—
988C2×C4C22×D4×C1314yes—
989C2×C4C22×D4×C1312yes—
990C2×C4C22×D4×C1312yes—
991C2×C4C22×D4×C1311yescharacteristic
992C2×C4C22×D4×C1312yes—
993C2×C4C13×H(5,𝔽2)12yes—
994C2×C4C25×C1311yescharacteristic
995C8—22no—
996C8—22no—
997C8—22no—
998C8C22×D4×C1312yes—
999C8C22×D4×C1312yes—
1000C22—22no—
1001C22—22no—
1002C22—24no—
1003C22—22no—
1004C22—22no—
1005C22—22no—
1006C22—24no—
1007C22—44no—
1008C22—44no—
1009C22—42no—
1010C22—44no—
1011C22—42no—
1012C22—41no—
1013C22—42no—
1014C22—41no—
1015C22—84no—
1016C22—84no—
1017C22—164no—
1018C22D42×C1312yes—
1019C22C23×D4×C1311yescharacteristic
1020C4—24no—
1021C4—22no—
1022C4—24no—
1023C4—22no—
1024C4—42no—
1025C4—42no—
1026C4—41no—
1027C4—42no—
1028C4—41no—
1029C4D42×C1312yes—
1030C4C23×D4×C1311yescharacteristic
1031C4C2×C13×H(5,𝔽2)11yescharacteristic
1032C2—22no—
1033C2—42no—
1034C2—42no—
1035C2—44no—
1036C2—82no—
1037C2—81no—
1038C2—81no—
1039C2C2×D42×C1311yescharacteristic
1040C2C13×#358412yes—
subgroupG/H
center, socleC22×C13C23×D4
commutator, Frattini, cosocleC2×C4C25×C13
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C13×#525 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#577C2semidirect
2. C22×C13×#135C2semidirect
3. C13×#3487C2semidirect
4. C13×#3485C2semidirect
5. C13×#3284C2semidirect
6. C13×#3282C2semidirect
7. C13×#3269C2semidirect
8. C13×#3268C2semidirect
9. C13×#3154C2semidirect
10. C13×#3057C2semidirect
11. C13×#3050C2semidirect
12. C13×#3044C2semidirect
13. C13×#3041C2semidirect
14. C13×#3011C2semidirect
15. C13×#3008C2semidirect
16. C13×#3005C2semidirect
17. C13×#3005C2semidirect
18. C13×#2949C2semidirect
19. C13×#2929C2semidirect
23. C22×C13×#41C22semidirect
26. C2×C13×#137C22semidirect
27. C2×C13×#137C22semidirect
30. C2×C13×AGL(1,ℤ/8)C22semidirect
33. C2×C13×#135C22semidirect
34. C2×C13×#135C22semidirect
35. C2×C13×#135C22semidirect
36. C22×C13×Q16C22semidirect
38. C22×C13×SD16C22semidirect
39. C22×C13×SD16C22semidirect
42. C23×C8×C13C22semidirect
44. C13×#550C22semidirect
46. C13×#548C22semidirect
48. C13×#547C22semidirect
50. C13×#546C22semidirect
55. C13×#535C22semidirect
60. C13×#525C22semidirect
62. C13×#519C22semidirect
64. C13×#497C22semidirect
65. C13×#496C22semidirect
66. C13×#495C22semidirect
67. C13×#492C22semidirect
68. C13×#468C22semidirect
69. C13×#467C22semidirect
70. C13×#466C22semidirect
71. C13×#465C22semidirect
72. C13×#465C22semidirect
73. C13×#465C22semidirect
74. C13×#464C22semidirect
75. C13×#463C22semidirect
76. C13×#462C22semidirect
77. C13×#459C22semidirect
78. C13×#452C22semidirect
79. C13×#452C22semidirect
80. C13×#452C22semidirect
81. C13×#451C22semidirect
82. C13×#449C22semidirect
83. C13×#449C22semidirect
84. C13×#449C22semidirect
85. C13×#447C22semidirect
86. C13×#440C22semidirect
87. C4×C13×SD16C22semidirect
88. C13×#435C22semidirect
89. C8×D4×C13C22semidirect
90. C13×#427C22semidirect
91. C13×#424C22semidirect
92. C13×#419C22semidirect
93. C13×#419C22semidirect
95. C13×#418C22semidirect
97. C13×#416C22semidirect
99. C13×#407C22semidirect
100. C13×#405C22semidirect
152. C2×C13×SD16D4semidirect
249. #61052C13direct (N × H)
395. C2×#577C2×C13semidirect
396. C22×#135C2×C13semidirect
397. #3487C2×C13semidirect
398. #3485C2×C13semidirect
399. #3284C2×C13semidirect
400. #3282C2×C13semidirect
401. #3269C2×C13semidirect
402. #3268C2×C13semidirect
403. #3154C2×C13semidirect
404. #3057C2×C13semidirect
405. #3050C2×C13semidirect
406. #3044C2×C13semidirect
407. #3041C2×C13semidirect
408. #3011C2×C13semidirect
409. #3008C2×C13semidirect
410. #3005C2×C13semidirect
411. #3005C2×C13semidirect
412. #2949C2×C13semidirect
413. #2929C2×C13semidirect
502. C22×#41C22×C13semidirect
505. C2×#137C22×C13semidirect
506. C2×#137C22×C13semidirect
509. C2×AGL(1,ℤ/8)C22×C13semidirect
512. C2×#135C22×C13semidirect
513. C2×#135C22×C13semidirect
514. C2×#135C22×C13semidirect
515. C22×Q16C22×C13semidirect
517. C22×SD16C22×C13semidirect
518. C22×SD16C22×C13semidirect
521. C23×C8C22×C13semidirect
523. #550C22×C13semidirect
525. #548C22×C13semidirect
527. #547C22×C13semidirect
529. #546C22×C13semidirect
534. #535C22×C13semidirect
539. #525C22×C13semidirect
541. #519C22×C13semidirect
543. #497C22×C13semidirect
544. #496C22×C13semidirect
545. #495C22×C13semidirect
546. #492C22×C13semidirect
547. #468C22×C13semidirect
548. #467C22×C13semidirect
549. #466C22×C13semidirect
550. #465C22×C13semidirect
551. #465C22×C13semidirect
552. #465C22×C13semidirect
553. #464C22×C13semidirect
554. #463C22×C13semidirect
555. #462C22×C13semidirect
556. #459C22×C13semidirect
557. #452C22×C13semidirect
558. #452C22×C13semidirect
559. #452C22×C13semidirect
560. #451C22×C13semidirect
561. #449C22×C13semidirect
562. #449C22×C13semidirect
563. #449C22×C13semidirect
564. #447C22×C13semidirect
565. #440C22×C13semidirect
566. C4×SD16C22×C13semidirect
567. #435C22×C13semidirect
568. C8×D4C22×C13semidirect
569. #427C22×C13semidirect
570. #424C22×C13semidirect
571. #419C22×C13semidirect
572. #419C22×C13semidirect
574. #418C22×C13semidirect
576. #416C22×C13semidirect
578. #407C22×C13semidirect
579. #405C22×C13semidirect
663. C2×SD16D4×C13semidirect
914. C13#61052direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5772
C22×C13×#1352
C13×#34872
C13×#34852
C13×#32842
C13×#32822
C13×#32692
C13×#32682
C13×#31542
C13×#30572
C13×#30502
C13×#30442
C13×#30412
C13×#30112
C13×#30082
C13×#30052
C13×#29492
C13×#29292
#6105213