Finite Group Databasebeta

← C13×#25107 #15711446

Subgroups — C13×#25107 #15711446

Order 3328.

1074 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#468C211yesmaximal, characteristic
2C2×C13×#464C211yesmaximal, characteristic, complemented
3C2×C13×#451C211yesmaximal, characteristic, complemented
4C2×C13×#419C211yesmaximal, characteristic, complemented
5C13×#2436C211yesmaximal, characteristic
6C13×#2362C211yesmaximal, characteristic, complemented
7C13×#2068C211yesmaximal, characteristic, complemented
8C13×#2056C211yesmaximal, characteristic, complemented
9C13×#2042C211yesmaximal, characteristic, complemented
10C13×#2015C211yesmaximal, characteristic, complemented
11C13×#1983C211yesmaximal, characteristic, complemented
12C13×#1928C211yesmaximal, characteristic, complemented
13C13×#1878C211yesmaximal, characteristic, complemented
14C13×#1875C211yesmaximal, characteristic
15C13×#1851C211yesmaximal, characteristic, complemented
16C23×Q8×C13C2211yescharacteristic
17C22×C13×Q16C2211yescharacteristic
18C22×C13×Q16C2211yescharacteristic
19C22×C13×SD16C2211yescharacteristic
20C22×C13×M16C2211yescharacteristic
21C2×C13×#124C2211yescharacteristic
22C2×C13×#124C2211yescharacteristic
23C2×C13×C22⋊Q8C2211yescharacteristic
24C2×C13×#121C2211yescharacteristic
25C2×C4×Q8×C13C2211yescharacteristic
26C2×C13×#117C2211yescharacteristic
27C13×#468—24no—
28C13×#464—24no—
29C13×#451—24no—
30C2×C13×#107C2211yescharacteristic
31C2×C13×C4⋊C8C2211yescharacteristic
32C2×C13×C4⋊C8C2211yescharacteristic
33C13×#419—24no—
34C2×C13×#103C2211yescharacteristic
35C2×C13×#103C2211yescharacteristic
36C2×C13×#103C2211yescharacteristic
37C2×C13×#103C2211yescharacteristic
38C2×C13×#103C2211yescharacteristic
39C2×C13×#103C2211yescharacteristic
40C2×C13×#103C2211yescharacteristic
41C2×C13×#102C2211yescharacteristic
42C2×C13×#102C2211yescharacteristic
43C2×C13×#102C2211yescharacteristic
44C2×C13×C22⋊C8C2211yescharacteristic
45C13×#393—21no—
46C13×#393—21no—
47C13×#391C2211yescharacteristic
48C13×#391C2211yescharacteristic
49C13×#391C2211yescharacteristic
50C13×#389C2211yescharacteristic
51C13×#388—21no—
52C13×#388—21no—
53C13×#387—21no—
54C13×#386—21no—
55C13×#386—21no—
56C4×C13×C4⋊C4—21no—
57C4×C13×C4⋊C4C2211yescharacteristic
58C4×C13×C22⋊C4C2211yescharacteristic
59C13×#340C2211yescharacteristic
60C13×#340C2211yescharacteristic
61C13×#336C2211yescharacteristic
62C13×#336C2211yescharacteristic
63C22×Q8×C13—21no—
64C22×Q8×C13—22no—
65C22×Q8×C13—22no—
66C22×Q8×C13—22no—
67C22×Q8×C13—22no—
68C22×Q8×C13—41no—
69C22×Q8×C13—41no—
70C22×Q8×C13C2311yescharacteristic
71C22×Q8×C13C2311yescharacteristic
72C22×Q8×C13C2311yescharacteristic
73C22×D4×C13—21no—
74C22×D4×C13C2311yescharacteristic
75C23×C4×C13—21no—
76C23×C4×C13C2311yescharacteristic
77C2×C13×Q16—22no—
78C2×C13×Q16—22no—
79C2×C13×Q16—22no—
80C2×C13×Q16—22no—
81C2×C13×Q16—41no—
82C2×C13×Q16—41no—
83C2×C13×SD16—22no—
84C2×C13×SD16—22no—
85C2×C13×SD16—41no—
86C2×C13×M16—22no—
87C2×C13×M16—22no—
88C2×C13×M16—41no—
89C22×C8×C13C2311yescharacteristic
90C22×C8×C13C2311yescharacteristic
91C22×C8×C13C2311yescharacteristic
92C22×C8×C13C2311yescharacteristic
93C13×#124—22no—
94C13×#124—22no—
95C13×#124—41no—
96C13×#124—41no—
97C13×C22⋊Q8—22no—
98C13×C22⋊Q8D414yes—
99C13×#121—22no—
100C13×#121—22no—
101C4×Q8×C13—22no—
102C4×Q8×C13—41no—
103C13×#117—22no—
104C13×#117—41no—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4C2311yescharacteristic
109C2×C13×C4⋊C4C2311yescharacteristic
110C2×C13×C4⋊C4C2311yescharacteristic
111C2×C13×C4⋊C4C2311yescharacteristic
112C2×C13×C22⋊C4—21no—
113C2×C13×C22⋊C4—21no—
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4—21no—
116C2×C13×C22⋊C4—21no—
117C2×C13×C22⋊C4—21no—
118C2×C13×C22⋊C4—21no—
119C2×C13×C22⋊C4D411yescharacteristic
120C2×C13×C22⋊C4D411yescharacteristic
121C2×C42×C13—21no—
122C2×C42×C13—21no—
123C2×C42×C13—21no—
124C2×C42×C13C2311yescharacteristic
125C2×C42×C13C2311yescharacteristic
126C13×#107—22no—
127C13×C4⋊C8—22no—
128C13×C4⋊C8—41no—
129C13×#103—22no—
130C13×#103—22no—
131C13×#103—22no—
132C13×#103—22no—
133C13×#103—22no—
134C13×#103—22no—
135C13×#103D414yescomplemented
136C13×#102—22no—
137C13×#102—22no—
138C13×#102—41no—
139C13×C22⋊C8—22no—
140C13×#95—21no—
141C13×#95—21no—
142C13×#95—21no—
143C13×#95—21no—
144C13×#95—21no—
145C13×#95—21no—
146C13×#95—21no—
147C13×#95—21no—
148C13×#95D411yescharacteristic
149C13×#95D411yescharacteristic
150#25107C1311yesmaximal, characteristic, direct product factor, Sylow
151C24×C13—21no—
152C24×C13C2×D411yescharacteristic
153C2×Q8×C13—21no—
154C2×Q8×C13—21no—
155C2×Q8×C13—21no—
156C2×Q8×C13—28no—
157C2×Q8×C13—21no—
158C2×Q8×C13—21no—
159C2×Q8×C13—21no—
160C2×Q8×C13—21no—
161C2×Q8×C13—21no—
162C2×Q8×C13—21no—
163C2×Q8×C13—21no—
164C2×Q8×C13—21no—
165C2×Q8×C13—21no—
166C2×Q8×C13—21no—
167C2×Q8×C13—21no—
168C2×Q8×C13—21no—
169C2×Q8×C13—42no—
170C2×Q8×C13—42no—
171C2×Q8×C13—44no—
172C2×Q8×C13—44no—
173C2×Q8×C13—44no—
174C2×Q8×C13—42no—
175C2×Q8×C13C2×D412yes—
176C2×Q8×C13C2×D412yes—
177C2×Q8×C13#4112yes—
178C2×D4×C13—21no—
179C2×D4×C13—21no—
180C2×D4×C13—21no—
181C2×D4×C13—21no—
182C2×D4×C13—21no—
183C2×D4×C13—21no—
184C2×D4×C13—42no—
185C2×D4×C13—42no—
186C2×D4×C13—42no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—42no—
199C22×C4×C13—42no—
200C22×C4×C13—42no—
201C22×C4×C13C2×D411yescharacteristic
202C22×C4×C13C2×D411yescharacteristic
203C22×C4×C13C2×D411yescharacteristic
204C22×C4×C13C2×D411yescharacteristic
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13C2×D412yes—
207C22×C4×C13#4112yes—
208C22×C4×C13C2411yescharacteristic
209C13×Q16—44no—
210C13×Q16—44no—
211C13×SD16—44no—
212C13×M16—44no—
213C2×C8×C13—21no—
214C2×C8×C13—21no—
215C2×C8×C13—21no—
216C2×C8×C13—21no—
217C2×C8×C13—21no—
218C2×C8×C13—21no—
219C2×C8×C13—21no—
220C2×C8×C13—21no—
221C2×C8×C13—21no—
222C2×C8×C13—21no—
223C2×C8×C13—21no—
224C2×C8×C13C2×D412yes—
225C13×C4⋊C4—24no—
226C13×C4⋊C4—21no—
227C13×C4⋊C4—21no—
228C13×C4⋊C4—21no—
229C13×C4⋊C4—21no—
230C13×C4⋊C4—21no—
231C13×C4⋊C4—21no—
232C13×C4⋊C4—42no—
233C13×C4⋊C4—42no—
234C13×C4⋊C4C2×D412yes—
235C13×C4⋊C4C2×D412yes—
236C13×C22⋊C4—24no—
237C13×C22⋊C4—41no—
238C13×C22⋊C4—41no—
239C13×C22⋊C4—42no—
240C13×C22⋊C4—42no—
241C13×C22⋊C4—42no—
242C13×C22⋊C4—42no—
243C13×C22⋊C4—42no—
244C13×C22⋊C4—42no—
245C42×C13—21no—
246C42×C13—21no—
247C42×C13—21no—
248C42×C13—21no—
249C42×C13—42no—
250C42×C13—42no—
251C42×C13—42no—
252C2×#468C2×C1311yescharacteristic
253C2×#464C2×C1311yescharacteristic, complemented
254C2×#451C2×C1311yescharacteristic, complemented
255C2×#419C2×C1311yescharacteristic, complemented
256#2436C2×C1311yescharacteristic
257#2362C2×C1311yescharacteristic, complemented
258#2068C2×C1311yescharacteristic, complemented
259#2056C2×C1311yescharacteristic, complemented
260#2042C2×C1311yescharacteristic, complemented
261#2015C2×C1311yescharacteristic, complemented
262#1983C2×C1311yescharacteristic, complemented
263#1928C2×C1311yescharacteristic, complemented
264#1878C2×C1311yescharacteristic, complemented
265#1875C2×C1311yescharacteristic
266#1851C2×C1311yescharacteristic, complemented
267C23×C13—21no—
268C23×C13—21no—
269C23×C13—21no—
270C23×C13—21no—
271C23×C13—21no—
272C23×C13—21no—
273C23×C13—41no—
274C23×C13—41no—
275C23×C13—41no—
276C23×C13—41no—
277C23×C13—41no—
278C23×C13—41no—
279C23×C13—41no—
280C23×C13#12112yes—
281C23×C13C22×D411yescharacteristic
282Q8×C13—22no—
283Q8×C13—22no—
284Q8×C13—22no—
285Q8×C13—22no—
286Q8×C13—22no—
287Q8×C13—22no—
288Q8×C13—48no—
289Q8×C13—41no—
290Q8×C13—41no—
291Q8×C13—41no—
292Q8×C13—41no—
293Q8×C13—41no—
294Q8×C13—41no—
295D4×C13—41no—
296D4×C13—41no—
297D4×C13—41no—
298D4×C13—41no—
299D4×C13—84no—
300C2×C4×C13—21no—
301C2×C4×C13—21no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—21no—
309C2×C4×C13—21no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—21no—
313C2×C4×C13—21no—
314C2×C4×C13—22no—
315C2×C4×C13—21no—
316C2×C4×C13—21no—
317C2×C4×C13—21no—
318C2×C4×C13—21no—
319C2×C4×C13—21no—
320C2×C4×C13—21no—
321C2×C4×C13—21no—
322C2×C4×C13—21no—
323C2×C4×C13—48no—
324C2×C4×C13—41no—
325C2×C4×C13—41no—
326C2×C4×C13—41no—
327C2×C4×C13—41no—
328C2×C4×C13—41no—
329C2×C4×C13—41no—
330C2×C4×C13—41no—
331C2×C4×C13—41no—
332C2×C4×C13—41no—
333C2×C4×C13—41no—
334C2×C4×C13—41no—
335C2×C4×C13—41no—
336C2×C4×C13—41no—
337C2×C4×C13—41no—
338C2×C4×C13—41no—
339C2×C4×C13—41no—
340C2×C4×C13#12112yes—
341C2×C4×C13C22×D411yescharacteristic
342C2×C4×C13C22×D411yescharacteristic
343C2×C4×C13C2×#4111yescharacteristic
344C2×C4×C13C2×#4111yescharacteristic
345C2×C4×C13H(5,𝔽2)11yescharacteristic
346C2×C4×C13H(5,𝔽2)11yescharacteristic
347C8×C13—22no—
348C8×C13—41no—
349C8×C13—41no—
350C8×C13—41no—
351C23×Q8C22×C1311yescharacteristic
352C22×Q16C22×C1311yescharacteristic
353C22×Q16C22×C1311yescharacteristic
354C22×SD16C22×C1311yescharacteristic
355C22×M16C22×C1311yescharacteristic
356C2×#124C22×C1311yescharacteristic
357C2×#124C22×C1311yescharacteristic
358C2×C22⋊Q8C22×C1311yescharacteristic
359C2×#121C22×C1311yescharacteristic
360C2×C4×Q8C22×C1311yescharacteristic
361C2×#117C22×C1311yescharacteristic
362#468—24no—
363#464—24no—
364#451—24no—
365C2×#107C22×C1311yescharacteristic
366C2×C4⋊C8C22×C1311yescharacteristic
367C2×C4⋊C8C22×C1311yescharacteristic
368#419—24no—
369C2×#103C22×C1311yescharacteristic
370C2×#103C22×C1311yescharacteristic
371C2×#103C22×C1311yescharacteristic
372C2×#103C22×C1311yescharacteristic
373C2×#103C22×C1311yescharacteristic
374C2×#103C22×C1311yescharacteristic
375C2×#103C22×C1311yescharacteristic
376C2×#102C22×C1311yescharacteristic
377C2×#102C22×C1311yescharacteristic
378C2×#102C22×C1311yescharacteristic
379C2×C22⋊C8C22×C1311yescharacteristic
380#393—21no—
381#393—21no—
382#391C22×C1311yescharacteristic
383#391C22×C1311yescharacteristic
384#391C22×C1311yescharacteristic
385#389C22×C1311yescharacteristic
386#388—21no—
387#388—21no—
388#387—21no—
389#386—21no—
390#386—21no—
391C4×C4⋊C4—21no—
392C4×C4⋊C4C22×C1311yescharacteristic
393C4×C22⋊C4C22×C1311yescharacteristic
394#340C22×C1311yescharacteristic
395#340C22×C1311yescharacteristic
396#336C22×C1311yescharacteristic
397#336C22×C1311yescharacteristic
398C22×C13—22no—
399C22×C13—22no—
400C22×C13—22no—
401C22×C13—41no—
402C22×C13—41no—
403C22×C13—41no—
404C22×C13—41no—
405C22×C13—81no—
406C22×C13—81no—
407C22×C13—81no—
408C22×C13—81no—
409C22×C13—81no—
410C22×C13—81no—
411C22×C13—81no—
412C22×C13C2×#12111yescharacteristic
413C22×C13D4211yescharacteristic
414C22×C13#54611yescharacteristic
415C22×C13#57511yescharacteristic
416C22×C13#57511yescharacteristic
417C22×C13#57811yescharacteristic
418C22×C13#57811yescharacteristic
419C4×C13—22no—
420C4×C13—42no—
421C4×C13—42no—
422C4×C13—42no—
423C4×C13—41no—
424C4×C13—42no—
425C4×C13—41no—
426C4×C13—42no—
427C4×C13—41no—
428C4×C13—41no—
429C4×C13—81no—
430C4×C13—81no—
431C4×C13#52511yescharacteristic
432C4×C13#53811yescharacteristic
433C4×C13D4211yescharacteristic
434C4×C13#54611yescharacteristic
435C22×Q8—21no—
436C22×Q8—22no—
437C22×Q8—22no—
438C22×Q8—22no—
439C22×Q8—22no—
440C22×Q8—41no—
441C22×Q8—41no—
442C22×Q8C23×C1311yescharacteristic
443C22×Q8C23×C1311yescharacteristic
444C22×Q8C23×C1311yescharacteristic
445C22×D4—21no—
446C22×D4C23×C1311yescharacteristic
447C23×C4—21no—
448C23×C4C23×C1311yescharacteristic
449C2×Q16—22no—
450C2×Q16—22no—
451C2×Q16—22no—
452C2×Q16—22no—
453C2×Q16—41no—
454C2×Q16—41no—
455C2×SD16—22no—
456C2×SD16—22no—
457C2×SD16—41no—
458C2×M16—22no—
459C2×M16—22no—
460C2×M16—41no—
461C22×C8C23×C1311yescharacteristic
462C22×C8C23×C1311yescharacteristic
463C22×C8C23×C1311yescharacteristic
464C22×C8C23×C1311yescharacteristic
465#124—22no—
466#124—22no—
467#124—41no—
468#124—41no—
469C22⋊Q8—22no—
470C22⋊Q8D4×C1314yes—
471#121—22no—
472#121—22no—
473C4×Q8—22no—
474C4×Q8—41no—
475#117—22no—
476#117—41no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4C23×C1311yescharacteristic
481C2×C4⋊C4C23×C1311yescharacteristic
482C2×C4⋊C4C23×C1311yescharacteristic
483C2×C4⋊C4C23×C1311yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4D4×C1311yescharacteristic
492C2×C22⋊C4D4×C1311yescharacteristic
493C2×C42—21no—
494C2×C42—21no—
495C2×C42—21no—
496C2×C42C23×C1311yescharacteristic
497C2×C42C23×C1311yescharacteristic
498#107—22no—
499C4⋊C8—22no—
500C4⋊C8—41no—
501#103—22no—
502#103—22no—
503#103—22no—
504#103—22no—
505#103—22no—
506#103—22no—
507#103D4×C1314yescomplemented
508#102—22no—
509#102—22no—
510#102—41no—
511C22⋊C8—22no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95D4×C1311yescharacteristic
521#95D4×C1311yescharacteristic
522C2×C13—42no—
523C2×C13—161no—
524C2×C13#242411yescharacteristic
525C2×C13#304011yescharacteristic
526C2×C13#304411yescharacteristic
527C2×C13#326911yescharacteristic
528C2×C13#327711yescharacteristic
529C2×C13#331311yescharacteristic
530C2×C13#332711yescharacteristic
531C24—21no—
532C24C2×D4×C1311yescharacteristic
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—28no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—42no—
550C2×Q8—42no—
551C2×Q8—44no—
552C2×Q8—44no—
553C2×Q8—44no—
554C2×Q8—42no—
555C2×Q8C2×D4×C1312yes—
556C2×Q8C2×D4×C1312yes—
557C2×Q8C13×#4112yes—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4C2×D4×C1311yescharacteristic
582C22×C4C2×D4×C1311yescharacteristic
583C22×C4C2×D4×C1311yescharacteristic
584C22×C4C2×D4×C1311yescharacteristic
585C22×C4C2×D4×C1311yescharacteristic
586C22×C4C2×D4×C1312yes—
587C22×C4C13×#4112yes—
588C22×C4C24×C1311yescharacteristic
589Q16—44no—
590Q16—44no—
591SD16—44no—
592M16—44no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8C2×D4×C1312yes—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4C2×D4×C1312yes—
615C4⋊C4C2×D4×C1312yes—
616C22⋊C4—24no—
617C22⋊C4—41no—
618C22⋊C4—41no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—42no—
630C42—42no—
631C42—42no—
632C13#2510711yescharacteristic, direct product factor, Sylow
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23C13×#12112yes—
647C23C22×D4×C1311yescharacteristic
648Q8—22no—
649Q8—22no—
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—48no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—84no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—48no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4C13×#12112yes—
707C2×C4C22×D4×C1311yescharacteristic
708C2×C4C22×D4×C1311yescharacteristic
709C2×C4C2×C13×#4111yescharacteristic
710C2×C4C2×C13×#4111yescharacteristic
711C2×C4C13×H(5,𝔽2)11yescharacteristic
712C2×C4C13×H(5,𝔽2)11yescharacteristic
713C8—22no—
714C8—41no—
715C8—41no—
716C8—41no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22C2×C13×#12111yescharacteristic
732C22D42×C1311yescharacteristic
733C22C13×#54611yescharacteristic
734C22C13×#57511yescharacteristic
735C22C13×#57511yescharacteristic
736C22C13×#57811yescharacteristic
737C22C13×#57811yescharacteristic
738C4—22no—
739C4—41no—
740C4—42no—
741C4—41no—
742C4—42no—
743C4—41no—
744C4—41no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4—81no—
749C4—81no—
750C4C13×#52511yescharacteristic
751C4C13×#53811yescharacteristic
752C4D42×C1311yescharacteristic
753C4C13×#54611yescharacteristic
754C2—42no—
755C2—161no—
756C2C13×#242411yescharacteristic
757C2C13×#304011yescharacteristic
758C2C13×#304411yescharacteristic
759C2C13×#326911yescharacteristic
760C2C13×#327711yescharacteristic
761C2C13×#331311yescharacteristic
762C2C13×#332711yescharacteristic
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC2×C13×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C4×C13×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#464C2semidirect
3. C2×C13×#451C2semidirect
4. C2×C13×#419C2semidirect
6. C13×#2362C2semidirect
7. C13×#2068C2semidirect
8. C13×#2056C2semidirect
9. C13×#2042C2semidirect
10. C13×#2015C2semidirect
11. C13×#1983C2semidirect
12. C13×#1928C2semidirect
13. C13×#1878C2semidirect
15. C13×#1851C2semidirect
135. C13×#103D4semidirect
150. #25107C13direct (N × H)
253. C2×#464C2×C13semidirect
254. C2×#451C2×C13semidirect
255. C2×#419C2×C13semidirect
257. #2362C2×C13semidirect
258. #2068C2×C13semidirect
259. #2056C2×C13semidirect
260. #2042C2×C13semidirect
261. #2015C2×C13semidirect
262. #1983C2×C13semidirect
263. #1928C2×C13semidirect
264. #1878C2×C13semidirect
266. #1851C2×C13semidirect
507. #103D4×C13semidirect
632. C13#25107direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4682
C2×C13×#4642
C2×C13×#4512
C2×C13×#4192
C13×#24362
C13×#23622
C13×#20682
C13×#20562
C13×#20422
C13×#20152
C13×#19832
C13×#19282
C13×#18782
C13×#18752
C13×#18512
#2510713