Finite Group Databasebeta

← C13×#24469 #15710808

Subgroups — C13×#24469 #15710808

Order 3328.

1402 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3489C211yesmaximal, characteristic, complemented
2C13×#3055C211yesmaximal, characteristic, complemented
3C2×C13×#454C211yesmaximal, characteristic, complemented
4C13×#3006C211yesmaximal, characteristic, complemented
5C2×C13×#421C211yesmaximal, characteristic, complemented
6C13×#2620C211yesmaximal, characteristic, complemented
7C13×#2039C211yesmaximal, characteristic, complemented
8C13×#2038C211yesmaximal, characteristic, complemented
9C13×#2006C211yesmaximal, characteristic, complemented
10C13×#2003C211yesmaximal, characteristic, complemented
11C13×#1901C211yesmaximal, characteristic, complemented
12C13×#1897C211yesmaximal, characteristic, complemented
13C13×#1883C211yesmaximal, characteristic, complemented
14C13×#1859C211yesmaximal, characteristic, complemented
15C13×#1793C211yesmaximal, characteristic, complemented
16C2×C13×2−1+4C2211yescharacteristic
17C22×C13×#41C2211yescharacteristic
18C2×C13×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C13×AGL(1,ℤ/8)C2211yescharacteristic
20C2×C13×AGL(1,ℤ/8)C2211yescharacteristic, complemented
21C22×C13×M16C2211yescharacteristic
22D4×Q8×C13—21no—
23C13×#548—21no—
24C13×#547—21no—
25C13×#547—22no—
26C13×#546—21no—
27C13×#546—22no—
28C13×#537—21no—
29C13×#537C2211yescharacteristic
30C13×#536—21no—
31C13×#536C2211yescharacteristic
32C2×C13×#124C2211yescharacteristic, complemented
33C13×#525—21no—
34C13×#525C2211yescharacteristic
35C2×C13×C22⋊Q8—21no—
36C2×C13×C22⋊Q8C2211yescharacteristic
37C2×C13×#121C2211yescharacteristic
38C13×#520C2211yescharacteristic
39C2×C13×#117C2211yescharacteristic
40C13×#469—21no—
41C13×#468—21no—
42C13×#466—21no—
43C13×#465—21no—
44C13×#454—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
54C2×C13×#104C2211yescharacteristic
55C2×C13×#104C2211yescharacteristic, complemented
56C2×C13×#104C2211yescharacteristic, complemented
57C13×#418C2211yescharacteristic, complemented
58C13×#417C2211yescharacteristic
59C13×#417C2211yescharacteristic
60C13×#417C2211yescharacteristic, complemented
61C2×C13×#101C2211yescharacteristic, complemented
62C2×C13×#101C2211yescharacteristic, complemented
63C13×#407C2211yescharacteristic
64C13×#396—22no—
65C13×#394—22no—
66C13×#391C2211yescharacteristic, complemented
67C13×#390C2211yescharacteristic, complemented
68C13×#384C2211yescharacteristic, complemented
69C13×#343C2211yescharacteristic, complemented
70C13×#343C2211yescharacteristic, complemented
71C13×#339C2211yescharacteristic, complemented
72C13×#339C2211yescharacteristic, complemented
73C13×2−1+4—22no—
74C13×2−1+4—22no—
75C13×2−1+4—41no—
76C13×2−1+4—41no—
77C2×C13×#41—21no—
78C2×C13×#41—21no—
79C2×C13×#41—21no—
80C2×C13×#41—22no—
81C2×C13×#41—21no—
82C2×C13×#41—22no—
83C2×C13×#41—22no—
84C2×C13×#41—41no—
85C2×C13×#41—41no—
86C2×C13×#41D411yescharacteristic
87C2×C13×#41D411yescharacteristic
88C2×C13×#41C2311yescharacteristic
89C2×C13×#41C2311yescharacteristic
90C2×C13×#41C2311yescharacteristic
91C22×Q8×C13—21no—
92C22×Q8×C13—21no—
93C22×Q8×C13D411yescharacteristic
94C22×Q8×C13C2311yescharacteristic
95C22×D4×C13—21no—
96C22×D4×C13—21no—
97C22×D4×C13D411yescharacteristic
98C22×D4×C13C2311yescharacteristic
99C23×C4×C13—21no—
100C23×C4×C13C2311yescharacteristic
101C13×AGL(1,ℤ/8)—22no—
102C13×AGL(1,ℤ/8)—22no—
103C13×AGL(1,ℤ/8)—22no—
104C13×AGL(1,ℤ/8)—41no—
105C13×AGL(1,ℤ/8)—41no—
106C13×AGL(1,ℤ/8)—41no—
107C2×C13×SD16—21no—
108C2×C13×SD16—21no—
109C2×C13×SD16—21no—
110C2×C13×D8—21no—
111C2×C13×D8—21no—
112C2×C13×D8—21no—
113C2×C13×M16—21no—
114C2×C13×M16—22no—
115C2×C13×M16—41no—
116C2×C13×M16C2311yescharacteristic
117C2×C13×M16C2311yescharacteristic
118C2×C13×M16C2311yescharacteristic
119C2×C13×M16C2311yescharacteristic
120C22×C8×C13—21no—
121C13×C4⋊Q8—22no—
122C13×C4⋊Q8—21no—
123C13×#124—22no—
124C13×#124—21no—
125C13×#124—22no—
126C13×#124—41no—
127C13×#123—22no—
128C13×#123—22no—
129C13×#123—22no—
130C13×#123—21no—
131C13×#123—22no—
132C13×C22⋊Q8—22no—
133C13×C22⋊Q8—22no—
134C13×C22⋊Q8—22no—
135C13×C22⋊Q8—21no—
136C13×C22⋊Q8—21no—
137C13×C22⋊Q8—21no—
138C13×C22⋊Q8—21no—
139C13×C22⋊Q8—21no—
140C13×C22⋊Q8—21no—
141C13×C22⋊Q8—21no—
142C13×C22⋊Q8—21no—
143C13×C22⋊Q8D411yescharacteristic
144C13×C22⋊Q8D411yescharacteristic
145C13×#121—22no—
146C13×#121—22no—
147C13×#121—22no—
148C13×#121—21no—
149C13×#121—21no—
150C13×#121—22no—
151C13×#121—21no—
152C13×#121—21no—
153C13×#121—21no—
154C13×#121—21no—
155C13×#121D411yescharacteristic
156C13×#121D411yescharacteristic
157C13×#120—22no—
158C13×#120—21no—
159C4×Q8×C13—21no—
160C4×D4×C13—22no—
161C4×D4×C13—22no—
162C4×D4×C13—21no—
163C4×D4×C13—22no—
164C4×D4×C13—21no—
165C4×D4×C13—21no—
166C13×#117—21no—
167C13×#117—22no—
168C13×#117—41no—
169C13×#117C2311yescharacteristic
170C2×C13×C4⋊C4—22no—
171C2×C13×C4⋊C4—21no—
172C2×C13×C4⋊C4—21no—
173C2×C13×C4⋊C4—22no—
174C2×C13×C4⋊C4D412yes—
175C2×C13×C4⋊C4C2311yescharacteristic
176C2×C13×C4⋊C4C2311yescharacteristic
177C2×C13×C22⋊C4—22no—
178C2×C13×C22⋊C4—21no—
179C2×C13×C22⋊C4—22no—
180C2×C13×C22⋊C4—21no—
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×#101—22no—
202C13×#101—41no—
203C13×C22⋊C8—21no—
204C13×C22⋊C8—21no—
205C13×#95—22no—
206#24469C1311yesmaximal, characteristic, direct product factor, Sylow
207C24×C13—21no—
208C24×C13—21no—
209C24×C13C2×D411yescharacteristic
210C13×#41—21no—
211C13×#41—21no—
212C13×#41—22no—
213C13×#41—22no—
214C13×#41—21no—
215C13×#41—21no—
216C13×#41—21no—
217C13×#41—21no—
218C13×#41—21no—
219C13×#41—21no—
220C13×#41—21no—
221C13×#41—21no—
222C13×#41—42no—
223C13×#41—42no—
224C13×#41—41no—
225C13×#41—41no—
226C13×#41—42no—
227C13×#41—42no—
228C13×#41—42no—
229C13×#41—42no—
230C13×#41—44no—
231C13×#41—44no—
232C13×#41—42no—
233C13×#41—42no—
234C13×#41C2×D412yes—
235C13×#41#4112yes—
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—21no—
244C2×Q8×C13—22no—
245C2×Q8×C13—41no—
246C2×Q8×C13—42no—
247C2×Q8×C13—42no—
248C2×Q8×C13—42no—
249C2×Q8×C13—42no—
250C2×Q8×C13C2×D411yescharacteristic
251C2×Q8×C13C2×D411yescharacteristic
252C2×Q8×C13C2×D411yescharacteristic
253C2×D4×C13—21no—
254C2×D4×C13—22no—
255C2×D4×C13—22no—
256C2×D4×C13—21no—
257C2×D4×C13—21no—
258C2×D4×C13—21no—
259C2×D4×C13—21no—
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—21no—
270C2×D4×C13—41no—
271C2×D4×C13—42no—
272C2×D4×C13—42no—
273C2×D4×C13—41no—
274C2×D4×C13—41no—
275C2×D4×C13—82no—
276C2×D4×C13C2×D411yescharacteristic
277C2×D4×C13C2×D411yescharacteristic
278C2×D4×C13C2×D411yescharacteristic
279C22×C4×C13—21no—
280C22×C4×C13—21no—
281C22×C4×C13—21no—
282C22×C4×C13—21no—
283C22×C4×C13—21no—
284C22×C4×C13—22no—
285C22×C4×C13—22no—
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—21no—
293C22×C4×C13—21no—
294C22×C4×C13—21no—
295C22×C4×C13—42no—
296C22×C4×C13—42no—
297C22×C4×C13C2×D412yes—
298C22×C4×C13C2×D411yescharacteristic
299C22×C4×C13C2×D411yescharacteristic
300C22×C4×C13C2×D411yescharacteristic
301C22×C4×C13C2×D411yescharacteristic
302C22×C4×C13C2×D411yescharacteristic
303C22×C4×C13C2×D412yes—
304C22×C4×C13C2411yescharacteristic
305C13×SD16—42no—
306C13×SD16—42no—
307C13×SD16—42no—
308C13×D8—42no—
309C13×D8—42no—
310C13×D8—42no—
311C13×M16—21no—
312C13×M16—21no—
313C13×M16—21no—
314C13×M16—21no—
315C13×M16—21no—
316C13×M16—21no—
317C13×M16—21no—
318C13×M16—42no—
319C13×M16C2×D412yes—
320C2×C8×C13—21no—
321C2×C8×C13—21no—
322C2×C8×C13—21no—
323C2×C8×C13—21no—
324C2×C8×C13—42no—
325C13×C4⋊C4—22no—
326C13×C4⋊C4—22no—
327C13×C4⋊C4—22no—
328C13×C4⋊C4—22no—
329C13×C4⋊C4—21no—
330C13×C4⋊C4—22no—
331C13×C4⋊C4—22no—
332C13×C4⋊C4—21no—
333C13×C4⋊C4—21no—
334C13×C4⋊C4—21no—
335C13×C4⋊C4—21no—
336C13×C4⋊C4—21no—
337C13×C4⋊C4—42no—
338C13×C4⋊C4—82no—
339C13×C4⋊C4C2×D411yescharacteristic
340C13×C4⋊C4C2×D411yescharacteristic
341C13×C22⋊C4—22no—
342C13×C22⋊C4—22no—
343C13×C22⋊C4—22no—
344C13×C22⋊C4—22no—
345C13×C22⋊C4—22no—
346C13×C22⋊C4—21no—
347C13×C22⋊C4—22no—
348C13×C22⋊C4—22no—
349C13×C22⋊C4—21no—
350C13×C22⋊C4—21no—
351C13×C22⋊C4—21no—
352C13×C22⋊C4—21no—
353C13×C22⋊C4—44no—
354C13×C22⋊C4—42no—
355C13×C22⋊C4—41no—
356C13×C22⋊C4—41no—
357C13×C22⋊C4—82no—
358C42×C13—22no—
359C42×C13—21no—
360C42×C13—21no—
361C42×C13—21no—
362C42×C13—21no—
363C42×C13C2×D412yes—
364#3489C2×C1311yescharacteristic, complemented
365#3055C2×C1311yescharacteristic, complemented
366C2×#454C2×C1311yescharacteristic, complemented
367#3006C2×C1311yescharacteristic, complemented
368C2×#421C2×C1311yescharacteristic, complemented
369#2620C2×C1311yescharacteristic, complemented
370#2039C2×C1311yescharacteristic, complemented
371#2038C2×C1311yescharacteristic, complemented
372#2006C2×C1311yescharacteristic, complemented
373#2003C2×C1311yescharacteristic, complemented
374#1901C2×C1311yescharacteristic, complemented
375#1897C2×C1311yescharacteristic, complemented
376#1883C2×C1311yescharacteristic, complemented
377#1859C2×C1311yescharacteristic, complemented
378#1793C2×C1311yescharacteristic, complemented
379C23×C13—21no—
380C23×C13—21no—
381C23×C13—21no—
382C23×C13—21no—
383C23×C13—21no—
384C23×C13—41no—
385C23×C13—41no—
386C23×C13—42no—
387C23×C13—42no—
388C23×C13—42no—
389C23×C13—42no—
390C23×C13—41no—
391C23×C13—41no—
392C23×C13—41no—
393C23×C13—81no—
394C23×C13#12011yescharacteristic
395C23×C13#12011yescharacteristic
396C23×C13C22×D411yescharacteristic
397Q8×C13—21no—
398Q8×C13—21no—
399Q8×C13—21no—
400Q8×C13—21no—
401Q8×C13—21no—
402Q8×C13—42no—
403Q8×C13—44no—
404Q8×C13—41no—
405Q8×C13—41no—
406Q8×C13—41no—
407Q8×C13—41no—
408Q8×C13#12112yes—
409D4×C13—22no—
410D4×C13—22no—
411D4×C13—21no—
412D4×C13—21no—
413D4×C13—21no—
414D4×C13—21no—
415D4×C13—21no—
416D4×C13—42no—
417D4×C13—42no—
418D4×C13—42no—
419D4×C13—42no—
420D4×C13—44no—
421D4×C13—41no—
422D4×C13—41no—
423D4×C13—41no—
424D4×C13—41no—
425D4×C13—41no—
426D4×C13—41no—
427D4×C13—41no—
428D4×C13—41no—
429D4×C13—81no—
430D4×C13—82no—
431D4×C13—82no—
432D4×C13—82no—
433D4×C13#12112yes—
434C2×C4×C13—21no—
435C2×C4×C13—21no—
436C2×C4×C13—21no—
437C2×C4×C13—21no—
438C2×C4×C13—21no—
439C2×C4×C13—21no—
440C2×C4×C13—21no—
441C2×C4×C13—21no—
442C2×C4×C13—21no—
443C2×C4×C13—22no—
444C2×C4×C13—21no—
445C2×C4×C13—21no—
446C2×C4×C13—22no—
447C2×C4×C13—21no—
448C2×C4×C13—22no—
449C2×C4×C13—21no—
450C2×C4×C13—21no—
451C2×C4×C13—22no—
452C2×C4×C13—21no—
453C2×C4×C13—22no—
454C2×C4×C13—22no—
455C2×C4×C13—22no—
456C2×C4×C13—42no—
457C2×C4×C13—42no—
458C2×C4×C13—42no—
459C2×C4×C13—44no—
460C2×C4×C13—41no—
461C2×C4×C13—41no—
462C2×C4×C13—44no—
463C2×C4×C13—41no—
464C2×C4×C13—41no—
465C2×C4×C13—41no—
466C2×C4×C13—41no—
467C2×C4×C13—42no—
468C2×C4×C13—41no—
469C2×C4×C13—42no—
470C2×C4×C13—41no—
471C2×C4×C13—41no—
472C2×C4×C13—41no—
473C2×C4×C13—82no—
474C2×C4×C13#12011yescharacteristic
475C2×C4×C13#12011yescharacteristic
476C2×C4×C13C22×D411yescharacteristic
477C2×C4×C13C22×D411yescharacteristic
478C2×C4×C13C22×D411yescharacteristic
479C2×C4×C13C2×#4111yescharacteristic
480C2×C4×C13H(5,𝔽2)11yescharacteristic
481C2×C4×C13H(5,𝔽2)11yescharacteristic
482C8×C13—22no—
483C8×C13—41no—
484C8×C13—41no—
485C8×C13—41no—
486C2×2−1+4C22×C1311yescharacteristic
487C22×#41C22×C1311yescharacteristic
488C2×AGL(1,ℤ/8)C22×C1311yescharacteristic
489C2×AGL(1,ℤ/8)C22×C1311yescharacteristic
490C2×AGL(1,ℤ/8)C22×C1311yescharacteristic, complemented
491C22×M16C22×C1311yescharacteristic
492D4×Q8—21no—
493#548—21no—
494#547—21no—
495#547—22no—
496#546—21no—
497#546—22no—
498#537—21no—
499#537C22×C1311yescharacteristic
500#536—21no—
501#536C22×C1311yescharacteristic
502C2×#124C22×C1311yescharacteristic, complemented
503#525—21no—
504#525C22×C1311yescharacteristic
505C2×C22⋊Q8—21no—
506C2×C22⋊Q8C22×C1311yescharacteristic
507C2×#121C22×C1311yescharacteristic
508#520C22×C1311yescharacteristic
509C2×#117C22×C1311yescharacteristic
510#469—21no—
511#468—21no—
512#466—21no—
513#465—21no—
514#454—24no—
515#449—21no—
516#449—21no—
517#448—21no—
518#447—21no—
519#428C22×C1311yescharacteristic, complemented
520#421—24no—
521C2×#104C22×C1311yescharacteristic
522C2×#104C22×C1311yescharacteristic
523C2×#104C22×C1311yescharacteristic
524C2×#104C22×C1311yescharacteristic
525C2×#104C22×C1311yescharacteristic, complemented
526C2×#104C22×C1311yescharacteristic, complemented
527#418C22×C1311yescharacteristic, complemented
528#417C22×C1311yescharacteristic
529#417C22×C1311yescharacteristic
530#417C22×C1311yescharacteristic, complemented
531C2×#101C22×C1311yescharacteristic, complemented
532C2×#101C22×C1311yescharacteristic, complemented
533#407C22×C1311yescharacteristic
534#396—22no—
535#394—22no—
536#391C22×C1311yescharacteristic, complemented
537#390C22×C1311yescharacteristic, complemented
538#384C22×C1311yescharacteristic, complemented
539#343C22×C1311yescharacteristic, complemented
540#343C22×C1311yescharacteristic, complemented
541#339C22×C1311yescharacteristic, complemented
542#339C22×C1311yescharacteristic, complemented
543C22×C13—21no—
544C22×C13—21no—
545C22×C13—21no—
546C22×C13—21no—
547C22×C13—22no—
548C22×C13—21no—
549C22×C13—21no—
550C22×C13—21no—
551C22×C13—21no—
552C22×C13—41no—
553C22×C13—41no—
554C22×C13—41no—
555C22×C13—41no—
556C22×C13—41no—
557C22×C13—41no—
558C22×C13—41no—
559C22×C13—41no—
560C22×C13—81no—
561C22×C13—81no—
562C22×C13—82no—
563C22×C13—82no—
564C22×C13—84no—
565C22×C13—81no—
566C22×C13—81no—
567C22×C13—81no—
568C22×C13C2×#12011yescharacteristic
569C22×C13D4211yescharacteristic
570C22×C13#54611yescharacteristic
571C4×C13—21no—
572C4×C13—21no—
573C4×C13—22no—
574C4×C13—42no—
575C4×C13—42no—
576C4×C13—41no—
577C4×C13—41no—
578C4×C13—41no—
579C4×C13—42no—
580C4×C13—41no—
581C4×C13—81no—
582C4×C13—81no—
583C4×C13C2×#12111yescharacteristic
584C4×C13#53411yescharacteristic
585C4×C13D4211yescharacteristic
586C4×C13#54611yescharacteristic
5872−1+4—22no—
5882−1+4—22no—
5892−1+4—41no—
5902−1+4—41no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—21no—
594C2×#41—22no—
595C2×#41—21no—
596C2×#41—22no—
597C2×#41—22no—
598C2×#41—41no—
599C2×#41—41no—
600C2×#41D4×C1311yescharacteristic
601C2×#41D4×C1311yescharacteristic
602C2×#41C23×C1311yescharacteristic
603C2×#41C23×C1311yescharacteristic
604C2×#41C23×C1311yescharacteristic
605C22×Q8—21no—
606C22×Q8—21no—
607C22×Q8D4×C1311yescharacteristic
608C22×Q8C23×C1311yescharacteristic
609C22×D4—21no—
610C22×D4—21no—
611C22×D4D4×C1311yescharacteristic
612C22×D4C23×C1311yescharacteristic
613C23×C4—21no—
614C23×C4C23×C1311yescharacteristic
615AGL(1,ℤ/8)—22no—
616AGL(1,ℤ/8)—22no—
617AGL(1,ℤ/8)—22no—
618AGL(1,ℤ/8)—41no—
619AGL(1,ℤ/8)—41no—
620AGL(1,ℤ/8)—41no—
621C2×SD16—21no—
622C2×SD16—21no—
623C2×SD16—21no—
624C2×D8—21no—
625C2×D8—21no—
626C2×D8—21no—
627C2×M16—21no—
628C2×M16—22no—
629C2×M16—41no—
630C2×M16C23×C1311yescharacteristic
631C2×M16C23×C1311yescharacteristic
632C2×M16C23×C1311yescharacteristic
633C2×M16C23×C1311yescharacteristic
634C22×C8—21no—
635C4⋊Q8—22no—
636C4⋊Q8—21no—
637#124—22no—
638#124—21no—
639#124—22no—
640#124—41no—
641#123—22no—
642#123—22no—
643#123—22no—
644#123—21no—
645#123—22no—
646C22⋊Q8—22no—
647C22⋊Q8—22no—
648C22⋊Q8—22no—
649C22⋊Q8—21no—
650C22⋊Q8—21no—
651C22⋊Q8—21no—
652C22⋊Q8—21no—
653C22⋊Q8—21no—
654C22⋊Q8—21no—
655C22⋊Q8—21no—
656C22⋊Q8—21no—
657C22⋊Q8D4×C1311yescharacteristic
658C22⋊Q8D4×C1311yescharacteristic
659#121—22no—
660#121—22no—
661#121—22no—
662#121—21no—
663#121—21no—
664#121—22no—
665#121—21no—
666#121—21no—
667#121—21no—
668#121—21no—
669#121D4×C1311yescharacteristic
670#121D4×C1311yescharacteristic
671#120—22no—
672#120—21no—
673C4×Q8—21no—
674C4×D4—22no—
675C4×D4—22no—
676C4×D4—21no—
677C4×D4—22no—
678C4×D4—21no—
679C4×D4—21no—
680#117—21no—
681#117—22no—
682#117—41no—
683#117C23×C1311yescharacteristic
684C2×C4⋊C4—22no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4D4×C1312yes—
689C2×C4⋊C4C23×C1311yescharacteristic
690C2×C4⋊C4C23×C1311yescharacteristic
691C2×C22⋊C4—22no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4D4×C1312yes—
697C2×C42C23×C1311yescharacteristic
698C2×C42C23×C1311yescharacteristic
699#107—21no—
700#106—21no—
701#104—22no—
702#104—22no—
703#104—22no—
704#104—22no—
705#104—41no—
706#104D4×C1314yescomplemented
707#103—21no—
708#103—21no—
709#103—21no—
710#102—21no—
711#102—21no—
712#102—21no—
713#102—21no—
714#102—21no—
715#101—22no—
716#101—41no—
717C22⋊C8—21no—
718C22⋊C8—21no—
719#95—22no—
720C2×C13—21no—
721C2×C13—21no—
722C2×C13—41no—
723C2×C13—41no—
724C2×C13—42no—
725C2×C13—81no—
726C2×C13—81no—
727C2×C13—161no—
728C2×C13#241011yescharacteristic
729C2×C13#302011yescharacteristic
730C2×C13#302111yescharacteristic
731C24—21no—
732C24—21no—
733C24C2×D4×C1311yescharacteristic
734#41—21no—
735#41—21no—
736#41—22no—
737#41—22no—
738#41—21no—
739#41—21no—
740#41—21no—
741#41—21no—
742#41—21no—
743#41—21no—
744#41—21no—
745#41—21no—
746#41—42no—
747#41—42no—
748#41—41no—
749#41—41no—
750#41—42no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—44no—
755#41—44no—
756#41—42no—
757#41—42no—
758#41C2×D4×C1312yes—
759#41C13×#4112yes—
760C2×Q8—22no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—22no—
769C2×Q8—41no—
770C2×Q8—42no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8C2×D4×C1311yescharacteristic
775C2×Q8C2×D4×C1311yescharacteristic
776C2×Q8C2×D4×C1311yescharacteristic
777C2×D4—21no—
778C2×D4—22no—
779C2×D4—22no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—22no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—41no—
795C2×D4—42no—
796C2×D4—42no—
797C2×D4—41no—
798C2×D4—41no—
799C2×D4—82no—
800C2×D4C2×D4×C1311yescharacteristic
801C2×D4C2×D4×C1311yescharacteristic
802C2×D4C2×D4×C1311yescharacteristic
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—22no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4C2×D4×C1312yes—
822C22×C4C2×D4×C1311yescharacteristic
823C22×C4C2×D4×C1311yescharacteristic
824C22×C4C2×D4×C1311yescharacteristic
825C22×C4C2×D4×C1311yescharacteristic
826C22×C4C2×D4×C1311yescharacteristic
827C22×C4C2×D4×C1312yes—
828C22×C4C24×C1311yescharacteristic
829SD16—42no—
830SD16—42no—
831SD16—42no—
832D8—42no—
833D8—42no—
834D8—42no—
835M16—21no—
836M16—21no—
837M16—21no—
838M16—21no—
839M16—21no—
840M16—21no—
841M16—21no—
842M16—42no—
843M16C2×D4×C1312yes—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—42no—
849C4⋊C4—22no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—21no—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—42no—
862C4⋊C4—82no—
863C4⋊C4C2×D4×C1311yescharacteristic
864C4⋊C4C2×D4×C1311yescharacteristic
865C22⋊C4—22no—
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—21no—
871C22⋊C4—22no—
872C22⋊C4—22no—
873C22⋊C4—21no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—44no—
878C22⋊C4—42no—
879C22⋊C4—41no—
880C22⋊C4—41no—
881C22⋊C4—82no—
882C42—22no—
883C42—21no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42C2×D4×C1312yes—
888C13#2446911yescharacteristic, direct product factor, Sylow
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—41no—
895C23—41no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—81no—
904C23C13×#12011yescharacteristic
905C23C13×#12011yescharacteristic
906C23C22×D4×C1311yescharacteristic
907Q8—21no—
908Q8—21no—
909Q8—21no—
910Q8—21no—
911Q8—21no—
912Q8—42no—
913Q8—44no—
914Q8—41no—
915Q8—41no—
916Q8—41no—
917Q8—41no—
918Q8C13×#12112yes—
919D4—22no—
920D4—22no—
921D4—21no—
922D4—21no—
923D4—21no—
924D4—21no—
925D4—21no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—44no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—81no—
940D4—82no—
941D4—82no—
942D4—82no—
943D4C13×#12112yes—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—44no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—44no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—42no—
978C2×C4—41no—
979C2×C4—42no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—82no—
984C2×C4C13×#12011yescharacteristic
985C2×C4C13×#12011yescharacteristic
986C2×C4C22×D4×C1311yescharacteristic
987C2×C4C22×D4×C1311yescharacteristic
988C2×C4C22×D4×C1311yescharacteristic
989C2×C4C2×C13×#4111yescharacteristic
990C2×C4C13×H(5,𝔽2)11yescharacteristic
991C2×C4C13×H(5,𝔽2)11yescharacteristic
992C8—22no—
993C8—41no—
994C8—41no—
995C8—41no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—22no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—81no—
1014C22—81no—
1015C22—82no—
1016C22—82no—
1017C22—84no—
1018C22—81no—
1019C22—81no—
1020C22—81no—
1021C22C2×C13×#12011yescharacteristic
1022C22D42×C1311yescharacteristic
1023C22C13×#54611yescharacteristic
1024C4—21no—
1025C4—21no—
1026C4—22no—
1027C4—42no—
1028C4—41no—
1029C4—42no—
1030C4—41no—
1031C4—42no—
1032C4—41no—
1033C4—41no—
1034C4—81no—
1035C4—81no—
1036C4C2×C13×#12111yescharacteristic
1037C4C13×#53411yescharacteristic
1038C4D42×C1311yescharacteristic
1039C4C13×#54611yescharacteristic
1040C2—21no—
1041C2—21no—
1042C2—41no—
1043C2—41no—
1044C2—42no—
1045C2—81no—
1046C2—81no—
1047C2—161no—
1048C2C13×#241011yescharacteristic
1049C2C13×#302011yescharacteristic
1050C2C13×#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×#3489C2semidirect
2. C13×#3055C2semidirect
3. C2×C13×#454C2semidirect
4. C13×#3006C2semidirect
5. C2×C13×#421C2semidirect
6. C13×#2620C2semidirect
7. C13×#2039C2semidirect
8. C13×#2038C2semidirect
9. C13×#2006C2semidirect
10. C13×#2003C2semidirect
11. C13×#1901C2semidirect
12. C13×#1897C2semidirect
13. C13×#1883C2semidirect
14. C13×#1859C2semidirect
15. C13×#1793C2semidirect
20. C2×C13×AGL(1,ℤ/8)C22semidirect
32. C2×C13×#124C22semidirect
49. C13×#428C22semidirect
55. C2×C13×#104C22semidirect
56. C2×C13×#104C22semidirect
57. C13×#418C22semidirect
60. C13×#417C22semidirect
61. C2×C13×#101C22semidirect
62. C2×C13×#101C22semidirect
66. C13×#391C22semidirect
67. C13×#390C22semidirect
68. C13×#384C22semidirect
69. C13×#343C22semidirect
70. C13×#343C22semidirect
71. C13×#339C22semidirect
72. C13×#339C22semidirect
192. C13×#104D4semidirect
206. #24469C13direct (N × H)
364. #3489C2×C13semidirect
365. #3055C2×C13semidirect
366. C2×#454C2×C13semidirect
367. #3006C2×C13semidirect
368. C2×#421C2×C13semidirect
369. #2620C2×C13semidirect
370. #2039C2×C13semidirect
371. #2038C2×C13semidirect
372. #2006C2×C13semidirect
373. #2003C2×C13semidirect
374. #1901C2×C13semidirect
375. #1897C2×C13semidirect
376. #1883C2×C13semidirect
377. #1859C2×C13semidirect
378. #1793C2×C13semidirect
490. C2×AGL(1,ℤ/8)C22×C13semidirect
502. C2×#124C22×C13semidirect
519. #428C22×C13semidirect
525. C2×#104C22×C13semidirect
526. C2×#104C22×C13semidirect
527. #418C22×C13semidirect
530. #417C22×C13semidirect
531. C2×#101C22×C13semidirect
532. C2×#101C22×C13semidirect
536. #391C22×C13semidirect
537. #390C22×C13semidirect
538. #384C22×C13semidirect
539. #343C22×C13semidirect
540. #343C22×C13semidirect
541. #339C22×C13semidirect
542. #339C22×C13semidirect
706. #104D4×C13semidirect
888. C13#24469direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34892
C13×#30552
C2×C13×#4542
C13×#30062
C2×C13×#4212
C13×#26202
C13×#20392
C13×#20382
C13×#20062
C13×#20032
C13×#19012
C13×#18972
C13×#18832
C13×#18592
C13×#17932
#2446913