Finite Group Databasebeta

← C13×#24467 #15710806

Subgroups — C13×#24467 #15710806

Order 3328.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3488C211yesmaximal, characteristic
2C13×#3056C211yesmaximal, characteristic, complemented
3C2×C13×#455C211yesmaximal, characteristic, complemented
4C13×#3007C211yesmaximal, characteristic, complemented
5C22×C13×#104C211yesmaximal, characteristic, complemented
6C13×#2850C211yesmaximal, characteristic, complemented
7C13×#2040C211yesmaximal, characteristic, complemented
8C13×#2037C211yesmaximal, characteristic, complemented
9C13×#2007C211yesmaximal, characteristic, complemented
10C13×#2004C211yesmaximal, characteristic, complemented
11C13×#1900C211yesmaximal, characteristic, complemented
12C13×#1896C211yesmaximal, characteristic, complemented
13C13×#1882C211yesmaximal, characteristic, complemented
14C13×#1860C211yesmaximal, characteristic, complemented
15C13×#1792C211yesmaximal, characteristic, complemented
16C2×C13×H(5,𝔽2)C2211yescharacteristic
17C22×C13×#41C2211yescharacteristic
18C2×C13×#137C2211yescharacteristic
19C2×C13×#137C2211yescharacteristic, complemented
20C2×C13×#137C2211yescharacteristic, 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×#124C2211yescharacteristic, complemented
33C13×#525—21no—
34C13×#525C2211yescharacteristic
35C2×C13×C22⋊Q8C2211yescharacteristic, complemented
36C2×C13×#121—21no—
37C2×C13×#121C2211yescharacteristic
38C13×#520C2211yescharacteristic
39C22×C42×C13C2211yescharacteristic, complemented
40C13×#470—21no—
41C13×#468—21no—
42C13×#467—21no—
43C13×#465—21no—
44C13×#455—24no—
45C13×#452—21no—
46C13×#452—21no—
47C13×#451—21no—
48C13×#450—21no—
49C13×#428C2211yescharacteristic, complemented
50C2×C13×#104—24no—
51C2×C13×#104C2211yescharacteristic
52C2×C13×#104C2211yescharacteristic
53C2×C13×#104C2211yescharacteristic, complemented
54C2×C13×#104C2211yescharacteristic, complemented
55C2×C13×#104C2211yescharacteristic, complemented
56C2×C13×#104C2211yescharacteristic, complemented
57C13×#419C2211yescharacteristic, complemented
58C13×#417C2211yescharacteristic
59C13×#417C2211yescharacteristic, complemented
60C13×#417C2211yescharacteristic, complemented
61C2×C13×#100C2211yescharacteristic, complemented
62C2×C13×#100C2211yescharacteristic, complemented
63C13×#407C2211yescharacteristic, complemented
64C13×#391C2211yescharacteristic, complemented
65C13×#390C2211yescharacteristic, complemented
66C13×#388—22no—
67C13×#386—22no—
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
86C2×C13×#41D411yescharacteristic
87C2×C13×#41C2311yescharacteristic
88C2×C13×#41C2311yescharacteristic
89C2×C13×#41C2311yescharacteristic
90C22×Q8×C13D411yescharacteristic
91C22×Q8×C13C2311yescharacteristic
92C22×D4×C13—21no—
93C22×D4×C13—22no—
94C22×D4×C13—22no—
95C22×D4×C13—21no—
96C22×D4×C13—21no—
97C22×D4×C13D411yescharacteristic
98C22×D4×C13D412yes—
99C22×D4×C13C2311yescharacteristic
100C23×C4×C13—21no—
101C23×C4×C13—21no—
102C23×C4×C13C2311yescharacteristic
103C13×#137—22no—
104C13×#137—22no—
105C13×#137—22no—
106C13×#137—41no—
107C13×#137—41no—
108C13×#137—41no—
109C2×C13×Q16—21no—
110C2×C13×Q16—21no—
111C2×C13×Q16—21no—
112C2×C13×SD16—21no—
113C2×C13×SD16—21no—
114C2×C13×SD16—21no—
115C2×C13×M16—21no—
116C2×C13×M16—22no—
117C2×C13×M16—41no—
118C2×C13×M16C2311yescharacteristic
119C2×C13×M16C2311yescharacteristic
120C2×C13×M16C2311yescharacteristic
121C2×C13×M16C2311yescharacteristic
122C22×C8×C13—21no—
123C13×#127—22no—
124C13×#127—21no—
125C13×#124—22no—
126C13×#124—21no—
127C13×#124—22no—
128C13×#124—41no—
129C13×#123—22no—
130C13×#123—21no—
131C13×C22⋊Q8—22no—
132C13×C22⋊Q8—21no—
133C13×C22⋊Q8—21no—
134C13×C22⋊Q8—21no—
135C13×C22⋊Q8—21no—
136C13×C22⋊Q8—21no—
137C13×C22⋊Q8—21no—
138C13×C22⋊Q8D411yescharacteristic
139C13×C22⋊Q8D411yescharacteristic
140C13×#121—22no—
141C13×#121—22no—
142C13×#121—22no—
143C13×#121—22no—
144C13×#121—22no—
145C13×#121—21no—
146C13×#121—21no—
147C13×#121—21no—
148C13×#121—21no—
149C13×#121—21no—
150C13×#121—21no—
151C13×#121—22no—
152C13×#121—21no—
153C13×#121—21no—
154C13×#121D411yescharacteristic
155C13×#121D411yescharacteristic
156C13×#120—22no—
157C13×#120—22no—
158C13×#120—22no—
159C13×#120—21no—
160C13×#120—22no—
161C4×Q8×C13—21no—
162C4×D4×C13—22no—
163C4×D4×C13—22no—
164C4×D4×C13—21no—
165C4×D4×C13—22no—
166C4×D4×C13—21no—
167C4×D4×C13—21no—
168C13×#117—21no—
169C13×#117C2311yescharacteristic
170C2×C13×C4⋊C4—21no—
171C2×C13×C4⋊C4—21no—
172C2×C13×C4⋊C4C2311yescharacteristic
173C2×C13×C4⋊C4C2311yescharacteristic
174C2×C13×C22⋊C4—22no—
175C2×C13×C22⋊C4—21no—
176C2×C13×C22⋊C4—22no—
177C2×C13×C22⋊C4—22no—
178C2×C13×C22⋊C4D412yes—
179C2×C42×C13—22no—
180C2×C42×C13—21no—
181C2×C42×C13—41no—
182C2×C42×C13C2311yescharacteristic
183C2×C42×C13C2311yescharacteristic
184C13×#107—21no—
185C13×#106—21no—
186C13×#104—22no—
187C13×#104—22no—
188C13×#104—22no—
189C13×#104—22no—
190C13×#104—41no—
191C13×#104D414yescomplemented
192C13×#103—21no—
193C13×#103—21no—
194C13×#103—21no—
195C13×#103—21no—
196C13×#103—21no—
197C13×#102—21no—
198C13×#102—21no—
199C13×#102—21no—
200C13×#100—22no—
201C13×#100—41no—
202C13×C22⋊C8—21no—
203C13×C22⋊C8—21no—
204C13×#95—22no—
205C13×#95—22no—
206#24467C1311yesmaximal, characteristic, direct product factor, Sylow
207C24×C13—22no—
208C24×C13—21no—
209C24×C13C2×D411yescharacteristic
210C24×C13C2×D412yes—
211C13×#41—21no—
212C13×#41—21no—
213C13×#41—22no—
214C13×#41—22no—
215C13×#41—21no—
216C13×#41—21no—
217C13×#41—21no—
218C13×#41—21no—
219C13×#41—21no—
220C13×#41—21no—
221C13×#41—21no—
222C13×#41—21no—
223C13×#41—42no—
224C13×#41—42no—
225C13×#41—41no—
226C13×#41—41no—
227C13×#41—42no—
228C13×#41—42no—
229C13×#41—42no—
230C13×#41—42no—
231C13×#41—42no—
232C13×#41—42no—
233C13×#41C2×D412yes—
234C13×#41#4112yes—
235C2×Q8×C13—21no—
236C2×Q8×C13—22no—
237C2×Q8×C13—21no—
238C2×Q8×C13—21no—
239C2×Q8×C13—21no—
240C2×Q8×C13—21no—
241C2×Q8×C13—21no—
242C2×Q8×C13—21no—
243C2×Q8×C13—41no—
244C2×Q8×C13C2×D411yescharacteristic
245C2×Q8×C13C2×D411yescharacteristic
246C2×Q8×C13C2×D411yescharacteristic
247C2×D4×C13—21no—
248C2×D4×C13—22no—
249C2×D4×C13—22no—
250C2×D4×C13—22no—
251C2×D4×C13—22no—
252C2×D4×C13—21no—
253C2×D4×C13—21no—
254C2×D4×C13—21no—
255C2×D4×C13—21no—
256C2×D4×C13—21no—
257C2×D4×C13—22no—
258C2×D4×C13—22no—
259C2×D4×C13—22no—
260C2×D4×C13—21no—
261C2×D4×C13—22no—
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—41no—
270C2×D4×C13—42no—
271C2×D4×C13—42no—
272C2×D4×C13—42no—
273C2×D4×C13—42no—
274C2×D4×C13—44no—
275C2×D4×C13—44no—
276C2×D4×C13—42no—
277C2×D4×C13—42no—
278C2×D4×C13—44no—
279C2×D4×C13—84no—
280C2×D4×C13C2×D411yescharacteristic
281C2×D4×C13C2×D411yescharacteristic
282C2×D4×C13C2×D411yescharacteristic
283C22×C4×C13—21no—
284C22×C4×C13—21no—
285C22×C4×C13—21no—
286C22×C4×C13—21no—
287C22×C4×C13—21no—
288C22×C4×C13—22no—
289C22×C4×C13—21no—
290C22×C4×C13—21no—
291C22×C4×C13—21no—
292C22×C4×C13—22no—
293C22×C4×C13—21no—
294C22×C4×C13—21no—
295C22×C4×C13—21no—
296C22×C4×C13—21no—
297C22×C4×C13—21no—
298C22×C4×C13—21no—
299C22×C4×C13—42no—
300C22×C4×C13—42no—
301C22×C4×C13—42no—
302C22×C4×C13—42no—
303C22×C4×C13—42no—
304C22×C4×C13C2×D411yescharacteristic
305C22×C4×C13C2×D411yescharacteristic
306C22×C4×C13C2×D411yescharacteristic
307C22×C4×C13C2×D411yescharacteristic
308C22×C4×C13C2×D411yescharacteristic
309C22×C4×C13C2×D412yes—
310C22×C4×C13C2411yescharacteristic
311C13×Q16—42no—
312C13×Q16—42no—
313C13×Q16—42no—
314C13×SD16—42no—
315C13×SD16—42no—
316C13×SD16—42no—
317C13×M16—21no—
318C13×M16—21no—
319C13×M16—21no—
320C13×M16—21no—
321C13×M16—21no—
322C13×M16—21no—
323C13×M16—21no—
324C13×M16—42no—
325C13×M16C2×D412yescomplemented
326C2×C8×C13—21no—
327C2×C8×C13—21no—
328C2×C8×C13—21no—
329C2×C8×C13—21no—
330C2×C8×C13—42no—
331C13×C4⋊C4—22no—
332C13×C4⋊C4—22no—
333C13×C4⋊C4—21no—
334C13×C4⋊C4—21no—
335C13×C4⋊C4—21no—
336C13×C4⋊C4—21no—
337C13×C4⋊C4—21no—
338C13×C4⋊C4—21no—
339C13×C4⋊C4—41no—
340C13×C4⋊C4—41no—
341C13×C4⋊C4C2×D411yescharacteristic
342C13×C4⋊C4C2×D411yescharacteristic
343C13×C22⋊C4—22no—
344C13×C22⋊C4—22no—
345C13×C22⋊C4—22no—
346C13×C22⋊C4—22no—
347C13×C22⋊C4—22no—
348C13×C22⋊C4—21no—
349C13×C22⋊C4—21no—
350C13×C22⋊C4—21no—
351C13×C22⋊C4—21no—
352C13×C22⋊C4—22no—
353C13×C22⋊C4—22no—
354C13×C22⋊C4—21no—
355C13×C22⋊C4—44no—
356C13×C22⋊C4—44no—
357C13×C22⋊C4—41no—
358C13×C22⋊C4—41no—
359C42×C13—22no—
360C42×C13—21no—
361C42×C13—21no—
362C42×C13—21no—
363C42×C13—21no—
364C42×C13—42no—
365C42×C13C2×D412yescomplemented
366#3488C2×C1311yescharacteristic
367#3056C2×C1311yescharacteristic, complemented
368C2×#455C2×C1311yescharacteristic, complemented
369#3007C2×C1311yescharacteristic, complemented
370C22×#104C2×C1311yescharacteristic, complemented
371#2850C2×C1311yescharacteristic, complemented
372#2040C2×C1311yescharacteristic, complemented
373#2037C2×C1311yescharacteristic, complemented
374#2007C2×C1311yescharacteristic, complemented
375#2004C2×C1311yescharacteristic, complemented
376#1900C2×C1311yescharacteristic, complemented
377#1896C2×C1311yescharacteristic, complemented
378#1882C2×C1311yescharacteristic, complemented
379#1860C2×C1311yescharacteristic, complemented
380#1792C2×C1311yescharacteristic, complemented
381C23×C13—21no—
382C23×C13—21no—
383C23×C13—21no—
384C23×C13—22no—
385C23×C13—22no—
386C23×C13—21no—
387C23×C13—21no—
388C23×C13—22no—
389C23×C13—22no—
390C23×C13—41no—
391C23×C13—42no—
392C23×C13—44no—
393C23×C13—42no—
394C23×C13—42no—
395C23×C13—42no—
396C23×C13—81no—
397C23×C13—82no—
398C23×C13—82no—
399C23×C13#12011yescharacteristic
400C23×C13#12011yescharacteristic
401C23×C13C22×D411yescharacteristic
402Q8×C13—21no—
403Q8×C13—21no—
404Q8×C13—21no—
405Q8×C13—21no—
406Q8×C13—21no—
407Q8×C13—42no—
408Q8×C13—41no—
409Q8×C13—41no—
410Q8×C13—41no—
411Q8×C13—41no—
412Q8×C13#12112yes—
413D4×C13—22no—
414D4×C13—22no—
415D4×C13—21no—
416D4×C13—21no—
417D4×C13—21no—
418D4×C13—21no—
419D4×C13—21no—
420D4×C13—42no—
421D4×C13—42no—
422D4×C13—44no—
423D4×C13—42no—
424D4×C13—44no—
425D4×C13—41no—
426D4×C13—41no—
427D4×C13—41no—
428D4×C13—41no—
429D4×C13—44no—
430D4×C13—42no—
431D4×C13—41no—
432D4×C13—41no—
433D4×C13—41no—
434D4×C13—41no—
435D4×C13—81no—
436D4×C13—82no—
437D4×C13—82no—
438D4×C13—82no—
439D4×C13—82no—
440D4×C13#12112yes—
441C2×C4×C13—21no—
442C2×C4×C13—21no—
443C2×C4×C13—21no—
444C2×C4×C13—21no—
445C2×C4×C13—21no—
446C2×C4×C13—21no—
447C2×C4×C13—21no—
448C2×C4×C13—21no—
449C2×C4×C13—21no—
450C2×C4×C13—22no—
451C2×C4×C13—21no—
452C2×C4×C13—21no—
453C2×C4×C13—22no—
454C2×C4×C13—22no—
455C2×C4×C13—21no—
456C2×C4×C13—22no—
457C2×C4×C13—21no—
458C2×C4×C13—21no—
459C2×C4×C13—21no—
460C2×C4×C13—22no—
461C2×C4×C13—42no—
462C2×C4×C13—42no—
463C2×C4×C13—42no—
464C2×C4×C13—44no—
465C2×C4×C13—41no—
466C2×C4×C13—41no—
467C2×C4×C13—41no—
468C2×C4×C13—48no—
469C2×C4×C13—41no—
470C2×C4×C13—41no—
471C2×C4×C13—41no—
472C2×C4×C13—41no—
473C2×C4×C13—41no—
474C2×C4×C13—42no—
475C2×C4×C13—42no—
476C2×C4×C13—41no—
477C2×C4×C13—41no—
478C2×C4×C13—41no—
479C2×C4×C13—41no—
480C2×C4×C13—82no—
481C2×C4×C13#12011yescharacteristic
482C2×C4×C13#12011yescharacteristic
483C2×C4×C13C22×D411yescharacteristic
484C2×C4×C13C22×D411yescharacteristic
485C2×C4×C13C22×D411yescharacteristic
486C2×C4×C13C2×#4111yescharacteristic
487C2×C4×C13H(5,𝔽2)11yescharacteristic
488C2×C4×C13H(5,𝔽2)11yescharacteristic
489C8×C13—22no—
490C8×C13—41no—
491C8×C13—41no—
492C8×C13—41no—
493C2×H(5,𝔽2)C22×C1311yescharacteristic
494C22×#41C22×C1311yescharacteristic
495C2×#137C22×C1311yescharacteristic
496C2×#137C22×C1311yescharacteristic, complemented
497C2×#137C22×C1311yescharacteristic, complemented
498C22×M16C22×C1311yescharacteristic, complemented
499#550—21no—
500#548—21no—
501#546—21no—
502#546—22no—
503D42—22no—
504D42—21no—
505#537—21no—
506#537C22×C1311yescharacteristic
507#535—21no—
508#535C22×C1311yescharacteristic
509C2×#124C22×C1311yescharacteristic, complemented
510#525—21no—
511#525C22×C1311yescharacteristic
512C2×C22⋊Q8C22×C1311yescharacteristic, complemented
513C2×#121—21no—
514C2×#121C22×C1311yescharacteristic
515#520C22×C1311yescharacteristic
516C22×C42C22×C1311yescharacteristic, complemented
517#470—21no—
518#468—21no—
519#467—21no—
520#465—21no—
521#455—24no—
522#452—21no—
523#452—21no—
524#451—21no—
525#450—21no—
526#428C22×C1311yescharacteristic, complemented
527C2×#104—24no—
528C2×#104C22×C1311yescharacteristic
529C2×#104C22×C1311yescharacteristic
530C2×#104C22×C1311yescharacteristic, complemented
531C2×#104C22×C1311yescharacteristic, complemented
532C2×#104C22×C1311yescharacteristic, complemented
533C2×#104C22×C1311yescharacteristic, complemented
534#419C22×C1311yescharacteristic, complemented
535#417C22×C1311yescharacteristic
536#417C22×C1311yescharacteristic, complemented
537#417C22×C1311yescharacteristic, complemented
538C2×#100C22×C1311yescharacteristic, complemented
539C2×#100C22×C1311yescharacteristic, complemented
540#407C22×C1311yescharacteristic, complemented
541#391C22×C1311yescharacteristic, complemented
542#390C22×C1311yescharacteristic, complemented
543#388—22no—
544#386—22no—
545#382C22×C1311yescharacteristic, complemented
546#343C22×C1311yescharacteristic, complemented
547#343C22×C1311yescharacteristic, complemented
548#339C22×C1311yescharacteristic, complemented
549#339C22×C1311yescharacteristic, complemented
550C22×C13—21no—
551C22×C13—21no—
552C22×C13—21no—
553C22×C13—21no—
554C22×C13—21no—
555C22×C13—22no—
556C22×C13—21no—
557C22×C13—21no—
558C22×C13—42no—
559C22×C13—42no—
560C22×C13—41no—
561C22×C13—41no—
562C22×C13—41no—
563C22×C13—41no—
564C22×C13—42no—
565C22×C13—42no—
566C22×C13—41no—
567C22×C13—41no—
568C22×C13—41no—
569C22×C13—42no—
570C22×C13—41no—
571C22×C13—84no—
572C22×C13—82no—
573C22×C13—82no—
574C22×C13—164no—
575C22×C13#45512yescomplemented
576C22×C13C2×#12011yescharacteristic
577C22×C13D4211yescharacteristic
578C22×C13#54611yescharacteristic
579C4×C13—21no—
580C4×C13—21no—
581C4×C13—22no—
582C4×C13—42no—
583C4×C13—42no—
584C4×C13—41no—
585C4×C13—41no—
586C4×C13—42no—
587C4×C13—41no—
588C4×C13—41no—
589C4×C13—81no—
590C4×C13—81no—
591C4×C13C2×#12111yescharacteristic
592C4×C13#53411yescharacteristic
593C4×C13D4211yescharacteristic
594C4×C13#54611yescharacteristic
595H(5,𝔽2)—22no—
596H(5,𝔽2)—22no—
597H(5,𝔽2)—41no—
598H(5,𝔽2)—41no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—21no—
602C2×#41—21no—
603C2×#41—22no—
604C2×#41—22no—
605C2×#41—41no—
606C2×#41—41no—
607C2×#41D4×C1311yescharacteristic
608C2×#41D4×C1311yescharacteristic
609C2×#41C23×C1311yescharacteristic
610C2×#41C23×C1311yescharacteristic
611C2×#41C23×C1311yescharacteristic
612C22×Q8D4×C1311yescharacteristic
613C22×Q8C23×C1311yescharacteristic
614C22×D4—21no—
615C22×D4—22no—
616C22×D4—22no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4D4×C1311yescharacteristic
620C22×D4D4×C1312yes—
621C22×D4C23×C1311yescharacteristic
622C23×C4—21no—
623C23×C4—21no—
624C23×C4C23×C1311yescharacteristic
625#137—22no—
626#137—22no—
627#137—22no—
628#137—41no—
629#137—41no—
630#137—41no—
631C2×Q16—21no—
632C2×Q16—21no—
633C2×Q16—21no—
634C2×SD16—21no—
635C2×SD16—21no—
636C2×SD16—21no—
637C2×M16—21no—
638C2×M16—22no—
639C2×M16—41no—
640C2×M16C23×C1311yescharacteristic
641C2×M16C23×C1311yescharacteristic
642C2×M16C23×C1311yescharacteristic
643C2×M16C23×C1311yescharacteristic
644C22×C8—21no—
645#127—22no—
646#127—21no—
647#124—22no—
648#124—21no—
649#124—22no—
650#124—41no—
651#123—22no—
652#123—21no—
653C22⋊Q8—22no—
654C22⋊Q8—21no—
655C22⋊Q8—21no—
656C22⋊Q8—21no—
657C22⋊Q8—21no—
658C22⋊Q8—21no—
659C22⋊Q8—21no—
660C22⋊Q8D4×C1311yescharacteristic
661C22⋊Q8D4×C1311yescharacteristic
662#121—22no—
663#121—22no—
664#121—22no—
665#121—22no—
666#121—22no—
667#121—21no—
668#121—21no—
669#121—21no—
670#121—21no—
671#121—21no—
672#121—21no—
673#121—22no—
674#121—21no—
675#121—21no—
676#121D4×C1311yescharacteristic
677#121D4×C1311yescharacteristic
678#120—22no—
679#120—22no—
680#120—22no—
681#120—21no—
682#120—22no—
683C4×Q8—21no—
684C4×D4—22no—
685C4×D4—22no—
686C4×D4—21no—
687C4×D4—22no—
688C4×D4—21no—
689C4×D4—21no—
690#117—21no—
691#117C23×C1311yescharacteristic
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4C23×C1311yescharacteristic
695C2×C4⋊C4C23×C1311yescharacteristic
696C2×C22⋊C4—22no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4D4×C1312yes—
701C2×C42—22no—
702C2×C42—21no—
703C2×C42—41no—
704C2×C42C23×C1311yescharacteristic
705C2×C42C23×C1311yescharacteristic
706#107—21no—
707#106—21no—
708#104—22no—
709#104—22no—
710#104—22no—
711#104—22no—
712#104—41no—
713#104D4×C1314yescomplemented
714#103—21no—
715#103—21no—
716#103—21no—
717#103—21no—
718#103—21no—
719#102—21no—
720#102—21no—
721#102—21no—
722#100—22no—
723#100—41no—
724C22⋊C8—21no—
725C22⋊C8—21no—
726#95—22no—
727#95—22no—
728C2×C13—21no—
729C2×C13—21no—
730C2×C13—22no—
731C2×C13—41no—
732C2×C13—42no—
733C2×C13—81no—
734C2×C13—82no—
735C2×C13—81no—
736C2×C13#241011yescharacteristic
737C2×C13C2×#45511yescharacteristic
738C2×C13#301811yescharacteristic
739C24—22no—
740C24—21no—
741C24C2×D4×C1311yescharacteristic
742C24C2×D4×C1312yes—
743#41—21no—
744#41—21no—
745#41—22no—
746#41—22no—
747#41—21no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—21no—
755#41—42no—
756#41—42no—
757#41—41no—
758#41—41no—
759#41—42no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41—42no—
765#41C2×D4×C1312yes—
766#41C13×#4112yes—
767C2×Q8—21no—
768C2×Q8—22no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—41no—
776C2×Q8C2×D4×C1311yescharacteristic
777C2×Q8C2×D4×C1311yescharacteristic
778C2×Q8C2×D4×C1311yescharacteristic
779C2×D4—21no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—21no—
793C2×D4—22no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—41no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—42no—
809C2×D4—42no—
810C2×D4—44no—
811C2×D4—84no—
812C2×D4C2×D4×C1311yescharacteristic
813C2×D4C2×D4×C1311yescharacteristic
814C2×D4C2×D4×C1311yescharacteristic
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4C2×D4×C1311yescharacteristic
837C22×C4C2×D4×C1311yescharacteristic
838C22×C4C2×D4×C1311yescharacteristic
839C22×C4C2×D4×C1311yescharacteristic
840C22×C4C2×D4×C1311yescharacteristic
841C22×C4C2×D4×C1312yes—
842C22×C4C24×C1311yescharacteristic
843Q16—42no—
844Q16—42no—
845Q16—42no—
846SD16—42no—
847SD16—42no—
848SD16—42no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16—42no—
857M16C2×D4×C1312yescomplemented
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—42no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—41no—
872C4⋊C4—41no—
873C4⋊C4C2×D4×C1311yescharacteristic
874C4⋊C4C2×D4×C1311yescharacteristic
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—22no—
885C22⋊C4—22no—
886C22⋊C4—21no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—41no—
890C22⋊C4—41no—
891C42—22no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—42no—
897C42C2×D4×C1312yescomplemented
898C13#2446711yescharacteristic, direct product factor, Sylow
899C23—22no—
900C23—21no—
901C23—21no—
902C23—21no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—42no—
910C23—44no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—81no—
915C23—82no—
916C23—82no—
917C23C13×#12011yescharacteristic
918C23C13×#12011yescharacteristic
919C23C22×D4×C1311yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—21no—
923Q8—21no—
924Q8—21no—
925Q8—42no—
926Q8—41no—
927Q8—41no—
928Q8—41no—
929Q8—41no—
930Q8C13×#12112yes—
931D4—22no—
932D4—22no—
933D4—21no—
934D4—21no—
935D4—21no—
936D4—21no—
937D4—21no—
938D4—42no—
939D4—42no—
940D4—44no—
941D4—42no—
942D4—44no—
943D4—44no—
944D4—42no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—82no—
954D4—81no—
955D4—82no—
956D4—82no—
957D4—82no—
958D4C13×#12112yes—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—44no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—48no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—82no—
999C2×C4C13×#12011yescharacteristic
1000C2×C4C13×#12011yescharacteristic
1001C2×C4C22×D4×C1311yescharacteristic
1002C2×C4C22×D4×C1311yescharacteristic
1003C2×C4C22×D4×C1311yescharacteristic
1004C2×C4C2×C13×#4111yescharacteristic
1005C2×C4C13×H(5,𝔽2)11yescharacteristic
1006C2×C4C13×H(5,𝔽2)11yescharacteristic
1007C8—22no—
1008C8—41no—
1009C8—41no—
1010C8—41no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—21no—
1017C22—21no—
1018C22—22no—
1019C22—42no—
1020C22—42no—
1021C22—41no—
1022C22—41no—
1023C22—42no—
1024C22—41no—
1025C22—41no—
1026C22—41no—
1027C22—42no—
1028C22—41no—
1029C22—41no—
1030C22—41no—
1031C22—42no—
1032C22—84no—
1033C22—82no—
1034C22—82no—
1035C22—164no—
1036C22C13×#45512yescomplemented
1037C22C2×C13×#12011yescharacteristic
1038C22D42×C1311yescharacteristic
1039C22C13×#54611yescharacteristic
1040C4—21no—
1041C4—21no—
1042C4—22no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—41no—
1047C4—41no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C4—81no—
1052C4C2×C13×#12111yescharacteristic
1053C4C13×#53411yescharacteristic
1054C4D42×C1311yescharacteristic
1055C4C13×#54611yescharacteristic
1056C2—21no—
1057C2—22no—
1058C2—21no—
1059C2—41no—
1060C2—42no—
1061C2—81no—
1062C2—82no—
1063C2—81no—
1064C2C13×#241011yescharacteristic
1065C2C2×C13×#45511yescharacteristic
1066C2C13×#301811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3488C2
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
2. C13×#3056C2semidirect
3. C2×C13×#455C2semidirect
4. C13×#3007C2semidirect
5. C22×C13×#104C2semidirect
6. C13×#2850C2semidirect
7. C13×#2040C2semidirect
8. C13×#2037C2semidirect
9. C13×#2007C2semidirect
10. C13×#2004C2semidirect
11. C13×#1900C2semidirect
12. C13×#1896C2semidirect
13. C13×#1882C2semidirect
14. C13×#1860C2semidirect
15. C13×#1792C2semidirect
19. C2×C13×#137C22semidirect
20. C2×C13×#137C22semidirect
21. C22×C13×M16C22semidirect
32. C2×C13×#124C22semidirect
35. C2×C13×C22⋊Q8C22semidirect
39. C22×C42×C13C22semidirect
49. C13×#428C22semidirect
53. C2×C13×#104C22semidirect
54. C2×C13×#104C22semidirect
55. C2×C13×#104C22semidirect
56. C2×C13×#104C22semidirect
57. C13×#419C22semidirect
59. C13×#417C22semidirect
60. C13×#417C22semidirect
61. C2×C13×#100C22semidirect
62. C2×C13×#100C22semidirect
63. C13×#407C22semidirect
64. C13×#391C22semidirect
65. C13×#390C22semidirect
68. C13×#382C22semidirect
69. C13×#343C22semidirect
70. C13×#343C22semidirect
71. C13×#339C22semidirect
72. C13×#339C22semidirect
191. C13×#104D4semidirect
206. #24467C13direct (N × H)
325. C13×M16C2×D4semidirect
365. C42×C13C2×D4semidirect
367. #3056C2×C13semidirect
368. C2×#455C2×C13semidirect
369. #3007C2×C13semidirect
370. C22×#104C2×C13semidirect
371. #2850C2×C13semidirect
372. #2040C2×C13semidirect
373. #2037C2×C13semidirect
374. #2007C2×C13semidirect
375. #2004C2×C13semidirect
376. #1900C2×C13semidirect
377. #1896C2×C13semidirect
378. #1882C2×C13semidirect
379. #1860C2×C13semidirect
380. #1792C2×C13semidirect
496. C2×#137C22×C13semidirect
497. C2×#137C22×C13semidirect
498. C22×M16C22×C13semidirect
509. C2×#124C22×C13semidirect
512. C2×C22⋊Q8C22×C13semidirect
516. C22×C42C22×C13semidirect
526. #428C22×C13semidirect
530. C2×#104C22×C13semidirect
531. C2×#104C22×C13semidirect
532. C2×#104C22×C13semidirect
533. C2×#104C22×C13semidirect
534. #419C22×C13semidirect
536. #417C22×C13semidirect
537. #417C22×C13semidirect
538. C2×#100C22×C13semidirect
539. C2×#100C22×C13semidirect
540. #407C22×C13semidirect
541. #391C22×C13semidirect
542. #390C22×C13semidirect
545. #382C22×C13semidirect
546. #343C22×C13semidirect
547. #343C22×C13semidirect
548. #339C22×C13semidirect
549. #339C22×C13semidirect
575. C22×C13#455semidirect
713. #104D4×C13semidirect
857. M16C2×D4×C13semidirect
897. C42C2×D4×C13semidirect
898. C13#24467direct (N × H)
1036. C22C13×#455semidirect

Maximal subgroups

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

subgroupindex
C13×#34882
C13×#30562
C2×C13×#4552
C13×#30072
C22×C13×#1042
C13×#28502
C13×#20402
C13×#20372
C13×#20072
C13×#20042
C13×#19002
C13×#18962
C13×#18822
C13×#18602
C13×#17922
#2446713