Finite Group Databasebeta

← C13×#24899 #15711238

Subgroups — C13×#24899 #15711238

Order 3328.

1070 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×#449C211yesmaximal, characteristic
2C2×C4×C13×D8C211yesmaximal, characteristic, complemented
3C13×#2422C211yesmaximal, characteristic, complemented
4C13×#2339C211yesmaximal, characteristic, complemented
5C13×#2095C211yesmaximal, characteristic, complemented
6C13×#2076C211yesmaximal, characteristic, complemented
7C13×#2055C211yesmaximal, characteristic, complemented
8C13×#2033C211yesmaximal, characteristic, complemented
9C13×#1933C211yesmaximal, characteristic, complemented
10C13×#1923C211yesmaximal, characteristic, complemented
11C13×#1879C211yesmaximal, characteristic, complemented
12C13×#1877C211yesmaximal, characteristic, complemented
13C13×#1862C211yesmaximal, characteristic, complemented
14C13×#1802C211yesmaximal, characteristic, complemented
15C13×#1788C211yesmaximal, characteristic, complemented
16C22×C13×#41C2211yescharacteristic
17C22×C13×SD16C2211yescharacteristic
18C22×C13×D8C2211yescharacteristic
19C2×C13×#123—21no—
20C2×C13×#121C2211yescharacteristic
21C2×C4×D4×C13C2211yescharacteristic
22C2×C4×D4×C13C2211yescharacteristic
23C2×C4×D4×C13C2211yescharacteristic
24C13×#449—24no—
25C4×C13×D8—24no—
26C2×C13×#107C2211yescharacteristic
27C2×C13×#107C2211yescharacteristic
28C2×C13×C4⋊C8C2211yescharacteristic
29C2×C13×#103C2211yescharacteristic
30C2×C13×#103C2211yescharacteristic
31C2×C13×#103C2211yescharacteristic
32C2×C13×#102C2211yescharacteristic
33C2×C13×#102C2211yescharacteristic
34C2×C13×#102C2211yescharacteristic
35C2×C13×#102C2211yescharacteristic
36C2×C13×#102C2211yescharacteristic
37C2×C13×C22⋊C8C2211yescharacteristic
38C2×C13×C22⋊C8C2211yescharacteristic
39C2×C4×C8×C13C2211yescharacteristic
40C13×#397—21no—
41C13×#394—21no—
42C13×#391C2211yescharacteristic
43C13×#391C2211yescharacteristic
44C13×#390C2211yescharacteristic
45C13×#389C2211yescharacteristic
46C13×#386—21no—
47C13×#386—21no—
48C13×#385—21no—
49C13×#384C2211yescharacteristic
50C13×#381—21no—
51C13×#380C2211yescharacteristic
52C13×#380C2211yescharacteristic
53C4×C13×C22⋊C4C2211yescharacteristic
54C2×C13×#95—21no—
55C13×#340C2211yescharacteristic
56C13×#340C2211yescharacteristic
57C13×#340C2211yescharacteristic
58C13×#340C2211yescharacteristic
59C13×#336C2211yescharacteristic
60C13×#336C2211yescharacteristic
61C2×C13×#41—22no—
62C2×C13×#41—22no—
63C2×C13×#41—22no—
64C2×C13×#41—22no—
65C2×C13×#41—41no—
66C2×C13×#41—41no—
67C22×Q8×C13C2311yescharacteristic
68C22×D4×C13—21no—
69C22×D4×C13—21no—
70C22×D4×C13C2311yescharacteristic
71C22×D4×C13C2311yescharacteristic
72C23×C4×C13—21no—
73C23×C4×C13—21no—
74C23×C4×C13—21no—
75C23×C4×C13—21no—
76C23×C4×C13C2311yescharacteristic
77C2×C13×SD16—22no—
78C2×C13×SD16—22no—
79C2×C13×SD16—41no—
80C2×C13×D8—22no—
81C2×C13×D8—22no—
82C2×C13×D8D414yes—
83C22×C8×C13C2311yescharacteristic
84C22×C8×C13C2311yescharacteristic
85C22×C8×C13C2311yescharacteristic
86C22×C8×C13C2311yescharacteristic
87C13×#123—44no—
88C13×#121—22no—
89C13×#121—41no—
90C4×D4×C13—22no—
91C4×D4×C13—22no—
92C4×D4×C13—22no—
93C4×D4×C13—41no—
94C4×D4×C13—41no—
95C4×D4×C13—41no—
96C2×C13×C4⋊C4—21no—
97C2×C13×C4⋊C4—21no—
98C2×C13×C4⋊C4—21no—
99C2×C13×C4⋊C4C2311yescharacteristic
100C2×C13×C4⋊C4C2311yescharacteristic
101C2×C13×C4⋊C4C2311yescharacteristic
102C2×C13×C4⋊C4C2311yescharacteristic
103C2×C13×C4⋊C4C2311yescharacteristic
104C2×C13×C22⋊C4—21no—
105C2×C13×C22⋊C4—21no—
106C2×C13×C22⋊C4—21no—
107C2×C13×C22⋊C4—21no—
108C2×C13×C22⋊C4—21no—
109C2×C13×C22⋊C4—21no—
110C2×C13×C22⋊C4—21no—
111C2×C13×C22⋊C4—21no—
112C2×C13×C22⋊C4D411yescharacteristic
113C2×C13×C22⋊C4D411yescharacteristic
114C2×C42×C13C2311yescharacteristic
115C2×C42×C13C2311yescharacteristic
116C13×#107—22no—
117C13×#107—41no—
118C13×C4⋊C8—41no—
119C13×#103—22no—
120C13×#103—22no—
121C13×#103—41no—
122C13×#102—22no—
123C13×#102—22no—
124C13×#102—22no—
125C13×#102—22no—
126C13×#102—41no—
127C13×C22⋊C8—22no—
128C13×C22⋊C8—41no—
129C4×C8×C13—22no—
130C13×#95—21no—
131C13×#95—21no—
132C13×#95—21no—
133C13×#95—21no—
134C13×#95—21no—
135C13×#95—21no—
136C13×#95—21no—
137C13×#95D411yescharacteristic
138C13×#95D411yescharacteristic
139#24899C1311yesmaximal, characteristic, direct product factor, Sylow
140C24×C13—21no—
141C24×C13—21no—
142C24×C13C2×D411yescharacteristic
143C13×#41—44no—
144C13×#41—44no—
145C13×#41—44no—
146C13×#41—44no—
147C2×Q8×C13—21no—
148C2×Q8×C13—21no—
149C2×Q8×C13—21no—
150C2×Q8×C13—21no—
151C2×Q8×C13—21no—
152C2×Q8×C13#4112yes—
153C2×D4×C13—24no—
154C2×D4×C13—21no—
155C2×D4×C13—21no—
156C2×D4×C13—21no—
157C2×D4×C13—21no—
158C2×D4×C13—21no—
159C2×D4×C13—21no—
160C2×D4×C13—21no—
161C2×D4×C13—21no—
162C2×D4×C13—42no—
163C2×D4×C13—42no—
164C2×D4×C13—42no—
165C2×D4×C13—42no—
166C2×D4×C13—81no—
167C2×D4×C13C2×D412yes—
168C2×D4×C13C2×D412yes—
169C2×D4×C13#4112yes—
170C2×D4×C13#4112yes—
171C22×C4×C13—24no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—42no—
185C22×C4×C13—42no—
186C22×C4×C13—42no—
187C22×C4×C13—42no—
188C22×C4×C13—42no—
189C22×C4×C13—42no—
190C22×C4×C13—42no—
191C22×C4×C13—42no—
192C22×C4×C13—81no—
193C22×C4×C13—81no—
194C22×C4×C13—81no—
195C22×C4×C13C2×D411yescharacteristic
196C22×C4×C13C2×D411yescharacteristic
197C22×C4×C13C2×D411yescharacteristic
198C22×C4×C13C2×D411yescharacteristic
199C22×C4×C13C2×D411yescharacteristic
200C22×C4×C13C2411yescharacteristic
201C13×SD16—44no—
202C13×D8—28no—
203C2×C8×C13—21no—
204C2×C8×C13—21no—
205C2×C8×C13—21no—
206C2×C8×C13—21no—
207C2×C8×C13—21no—
208C2×C8×C13—21no—
209C2×C8×C13—21no—
210C2×C8×C13—21no—
211C2×C8×C13—21no—
212C2×C8×C13—21no—
213C2×C8×C13—21no—
214C2×C8×C13C2×D412yes—
215C13×C4⋊C4—21no—
216C13×C4⋊C4—21no—
217C13×C4⋊C4—21no—
218C13×C4⋊C4—21no—
219C13×C4⋊C4—21no—
220C13×C4⋊C4—21no—
221C13×C4⋊C4—21no—
222C13×C4⋊C4—21no—
223C13×C4⋊C4—21no—
224C13×C4⋊C4—21no—
225C13×C4⋊C4—42no—
226C13×C4⋊C4—42no—
227C13×C4⋊C4—81no—
228C13×C22⋊C4—22no—
229C13×C22⋊C4—22no—
230C13×C22⋊C4—42no—
231C13×C22⋊C4—42no—
232C13×C22⋊C4—42no—
233C13×C22⋊C4—42no—
234C13×C22⋊C4—42no—
235C13×C22⋊C4—42no—
236C13×C22⋊C4—42no—
237C13×C22⋊C4—81no—
238C42×C13—21no—
239C42×C13—21no—
240C42×C13—21no—
241C42×C13—21no—
242C2×#449C2×C1311yescharacteristic
243C2×C4×D8C2×C1311yescharacteristic, complemented
244#2422C2×C1311yescharacteristic, complemented
245#2339C2×C1311yescharacteristic, complemented
246#2095C2×C1311yescharacteristic, complemented
247#2076C2×C1311yescharacteristic, complemented
248#2055C2×C1311yescharacteristic, complemented
249#2033C2×C1311yescharacteristic, complemented
250#1933C2×C1311yescharacteristic, complemented
251#1923C2×C1311yescharacteristic, complemented
252#1879C2×C1311yescharacteristic, complemented
253#1877C2×C1311yescharacteristic, complemented
254#1862C2×C1311yescharacteristic, complemented
255#1802C2×C1311yescharacteristic, complemented
256#1788C2×C1311yescharacteristic, complemented
257C23×C13—22no—
258C23×C13—22no—
259C23×C13—22no—
260C23×C13—21no—
261C23×C13—22no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13—21no—
266C23×C13—21no—
267C23×C13—21no—
268C23×C13—41no—
269C23×C13—41no—
270C23×C13—41no—
271C23×C13—41no—
272C23×C13—41no—
273C23×C13—41no—
274C23×C13—41no—
275C23×C13—41no—
276C23×C13—41no—
277C23×C13—41no—
278C23×C13C22×D411yescharacteristic
279Q8×C13—22no—
280Q8×C13—22no—
281Q8×C13—41no—
282Q8×C13—41no—
283D4×C13—22no—
284D4×C13—22no—
285D4×C13—22no—
286D4×C13—22no—
287D4×C13—22no—
288D4×C13—48no—
289D4×C13—41no—
290D4×C13—41no—
291D4×C13—84no—
292D4×C13#12314yescomplemented
293C2×C4×C13—21no—
294C2×C4×C13—21no—
295C2×C4×C13—21no—
296C2×C4×C13—21no—
297C2×C4×C13—21no—
298C2×C4×C13—22no—
299C2×C4×C13—21no—
300C2×C4×C13—21no—
301C2×C4×C13—21no—
302C2×C4×C13—21no—
303C2×C4×C13—21no—
304C2×C4×C13—21no—
305C2×C4×C13—21no—
306C2×C4×C13—21no—
307C2×C4×C13—48no—
308C2×C4×C13—41no—
309C2×C4×C13—41no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—41no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13—41no—
316C2×C4×C13—41no—
317C2×C4×C13—41no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×C4×C13—41no—
322C2×C4×C13—41no—
323C2×C4×C13—41no—
324C2×C4×C13—41no—
325C2×C4×C13—41no—
326C2×C4×C13—41no—
327C2×C4×C13—41no—
328C2×C4×C13—41no—
329C2×C4×C13—84no—
330C2×C4×C13—84no—
331C2×C4×C13—84no—
332C2×C4×C13#13512yes—
333C2×C4×C13AGL(1,ℤ/8)12yes—
334C2×C4×C13C22×D411yescharacteristic
335C2×C4×C13C2×#4111yescharacteristic
336C2×C4×C13C2×#4111yescharacteristic
337C2×C4×C13C2×#4111yescharacteristic
338C2×C4×C13H(5,𝔽2)11yescharacteristic
339C2×C4×C13H(5,𝔽2)11yescharacteristic
340C8×C13—22no—
341C8×C13—41no—
342C8×C13—41no—
343C8×C13—41no—
344C22×#41C22×C1311yescharacteristic
345C22×SD16C22×C1311yescharacteristic
346C22×D8C22×C1311yescharacteristic
347C2×#123—21no—
348C2×#121C22×C1311yescharacteristic
349C2×C4×D4C22×C1311yescharacteristic
350C2×C4×D4C22×C1311yescharacteristic
351C2×C4×D4C22×C1311yescharacteristic
352#449—24no—
353C4×D8—24no—
354C2×#107C22×C1311yescharacteristic
355C2×#107C22×C1311yescharacteristic
356C2×C4⋊C8C22×C1311yescharacteristic
357C2×#103C22×C1311yescharacteristic
358C2×#103C22×C1311yescharacteristic
359C2×#103C22×C1311yescharacteristic
360C2×#102C22×C1311yescharacteristic
361C2×#102C22×C1311yescharacteristic
362C2×#102C22×C1311yescharacteristic
363C2×#102C22×C1311yescharacteristic
364C2×#102C22×C1311yescharacteristic
365C2×C22⋊C8C22×C1311yescharacteristic
366C2×C22⋊C8C22×C1311yescharacteristic
367C2×C4×C8C22×C1311yescharacteristic
368#397—21no—
369#394—21no—
370#391C22×C1311yescharacteristic
371#391C22×C1311yescharacteristic
372#390C22×C1311yescharacteristic
373#389C22×C1311yescharacteristic
374#386—21no—
375#386—21no—
376#385—21no—
377#384C22×C1311yescharacteristic
378#381—21no—
379#380C22×C1311yescharacteristic
380#380C22×C1311yescharacteristic
381C4×C22⋊C4C22×C1311yescharacteristic
382C2×#95—21no—
383#340C22×C1311yescharacteristic
384#340C22×C1311yescharacteristic
385#340C22×C1311yescharacteristic
386#340C22×C1311yescharacteristic
387#336C22×C1311yescharacteristic
388#336C22×C1311yescharacteristic
389C22×C13—24no—
390C22×C13—42no—
391C22×C13—42no—
392C22×C13—42no—
393C22×C13—42no—
394C22×C13—42no—
395C22×C13—42no—
396C22×C13—41no—
397C22×C13—41no—
398C22×C13—41no—
399C22×C13—41no—
400C22×C13—42no—
401C22×C13—42no—
402C22×C13—41no—
403C22×C13—41no—
404C22×C13—42no—
405C22×C13—41no—
406C22×C13—81no—
407C22×C13—81no—
408C22×C13—81no—
409C22×C13—81no—
410C22×C13#52511yescharacteristic
411C22×C13D4211yescharacteristic
412C22×C13#54611yescharacteristic
413C22×C13C2×#13511yescharacteristic
414C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
415C22×C13#57611yescharacteristic
416C22×C13#57811yescharacteristic
417C4×C13—22no—
418C4×C13—22no—
419C4×C13—41no—
420C4×C13—41no—
421C4×C13—42no—
422C4×C13—41no—
423C4×C13—81no—
424C4×C13—81no—
425C4×C13—81no—
426C4×C13—81no—
427C4×C13—81no—
428C4×C13C2×#12311yescharacteristic
429C4×C13#53811yescharacteristic
430C4×C13#54611yescharacteristic
431C4×C13#55111yescharacteristic
432C2×#41—22no—
433C2×#41—22no—
434C2×#41—22no—
435C2×#41—22no—
436C2×#41—41no—
437C2×#41—41no—
438C22×Q8C23×C1311yescharacteristic
439C22×D4—21no—
440C22×D4—21no—
441C22×D4C23×C1311yescharacteristic
442C22×D4C23×C1311yescharacteristic
443C23×C4—21no—
444C23×C4—21no—
445C23×C4—21no—
446C23×C4—21no—
447C23×C4C23×C1311yescharacteristic
448C2×SD16—22no—
449C2×SD16—22no—
450C2×SD16—41no—
451C2×D8—22no—
452C2×D8—22no—
453C2×D8D4×C1314yes—
454C22×C8C23×C1311yescharacteristic
455C22×C8C23×C1311yescharacteristic
456C22×C8C23×C1311yescharacteristic
457C22×C8C23×C1311yescharacteristic
458#123—44no—
459#121—22no—
460#121—41no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—22no—
464C4×D4—41no—
465C4×D4—41no—
466C4×D4—41no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4C23×C1311yescharacteristic
471C2×C4⋊C4C23×C1311yescharacteristic
472C2×C4⋊C4C23×C1311yescharacteristic
473C2×C4⋊C4C23×C1311yescharacteristic
474C2×C4⋊C4C23×C1311yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4D4×C1311yescharacteristic
484C2×C22⋊C4D4×C1311yescharacteristic
485C2×C42C23×C1311yescharacteristic
486C2×C42C23×C1311yescharacteristic
487#107—22no—
488#107—41no—
489C4⋊C8—41no—
490#103—22no—
491#103—22no—
492#103—41no—
493#102—22no—
494#102—22no—
495#102—22no—
496#102—22no—
497#102—41no—
498C22⋊C8—22no—
499C22⋊C8—41no—
500C4×C8—22no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95D4×C1311yescharacteristic
509#95D4×C1311yescharacteristic
510C2×C13—44no—
511C2×C13—81no—
512C2×C13—82no—
513C2×C13#241811yescharacteristic
514C2×C13#310611yescharacteristic
515C2×C13#312411yescharacteristic
516C2×C13#326411yescharacteristic
517C2×C13#328311yescharacteristic
518C2×C13#329711yescharacteristic
519C2×C13#333011yescharacteristic
520C24—21no—
521C24—21no—
522C24C2×D4×C1311yescharacteristic
523#41—44no—
524#41—44no—
525#41—44no—
526#41—44no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8C13×#4112yes—
533C2×D4—24no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—81no—
547C2×D4C2×D4×C1312yes—
548C2×D4C2×D4×C1312yes—
549C2×D4C13×#4112yes—
550C2×D4C13×#4112yes—
551C22×C4—24no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—81no—
573C22×C4—81no—
574C22×C4—81no—
575C22×C4C2×D4×C1311yescharacteristic
576C22×C4C2×D4×C1311yescharacteristic
577C22×C4C2×D4×C1311yescharacteristic
578C22×C4C2×D4×C1311yescharacteristic
579C22×C4C2×D4×C1311yescharacteristic
580C22×C4C24×C1311yescharacteristic
581SD16—44no—
582D8—28no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8C2×D4×C1312yes—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—81no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—81no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—21no—
622C13#2489911yescharacteristic, direct product factor, Sylow
623C23—22no—
624C23—22no—
625C23—22no—
626C23—21no—
627C23—22no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23C22×D4×C1311yescharacteristic
645Q8—22no—
646Q8—22no—
647Q8—41no—
648Q8—41no—
649D4—22no—
650D4—22no—
651D4—22no—
652D4—22no—
653D4—22no—
654D4—48no—
655D4—41no—
656D4—41no—
657D4—84no—
658D4C13×#12314yescomplemented
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—48no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—84no—
696C2×C4—84no—
697C2×C4—84no—
698C2×C4C13×#13512yes—
699C2×C4C13×AGL(1,ℤ/8)12yes—
700C2×C4C22×D4×C1311yescharacteristic
701C2×C4C2×C13×#4111yescharacteristic
702C2×C4C2×C13×#4111yescharacteristic
703C2×C4C2×C13×#4111yescharacteristic
704C2×C4C13×H(5,𝔽2)11yescharacteristic
705C2×C4C13×H(5,𝔽2)11yescharacteristic
706C8—22no—
707C8—41no—
708C8—41no—
709C8—41no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—41no—
719C22—41no—
720C22—42no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—42no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22C13×#52511yescharacteristic
732C22D42×C1311yescharacteristic
733C22C13×#54611yescharacteristic
734C22C2×C13×#13511yescharacteristic
735C22C2×C13×AGL(1,ℤ/8)11yescharacteristic
736C22C13×#57611yescharacteristic
737C22C13×#57811yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—42no—
744C4—81no—
745C4—81no—
746C4—81no—
747C4—81no—
748C4—81no—
749C4C2×C13×#12311yescharacteristic
750C4C13×#53811yescharacteristic
751C4C13×#54611yescharacteristic
752C4C13×#55111yescharacteristic
753C2—44no—
754C2—81no—
755C2—82no—
756C2C13×#241811yescharacteristic
757C2C13×#310611yescharacteristic
758C2C13×#312411yescharacteristic
759C2C13×#326411yescharacteristic
760C2C13×#328311yescharacteristic
761C2C13×#329711yescharacteristic
762C2C13×#333011yescharacteristic
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC2×C13×#449C2
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×C4×C13×D8C2semidirect
3. C13×#2422C2semidirect
4. C13×#2339C2semidirect
5. C13×#2095C2semidirect
6. C13×#2076C2semidirect
7. C13×#2055C2semidirect
8. C13×#2033C2semidirect
9. C13×#1933C2semidirect
10. C13×#1923C2semidirect
11. C13×#1879C2semidirect
12. C13×#1877C2semidirect
13. C13×#1862C2semidirect
14. C13×#1802C2semidirect
15. C13×#1788C2semidirect
139. #24899C13direct (N × H)
243. C2×C4×D8C2×C13semidirect
244. #2422C2×C13semidirect
245. #2339C2×C13semidirect
246. #2095C2×C13semidirect
247. #2076C2×C13semidirect
248. #2055C2×C13semidirect
249. #2033C2×C13semidirect
250. #1933C2×C13semidirect
251. #1923C2×C13semidirect
252. #1879C2×C13semidirect
253. #1877C2×C13semidirect
254. #1862C2×C13semidirect
255. #1802C2×C13semidirect
256. #1788C2×C13semidirect
292. D4×C13#123semidirect
622. C13#24899direct (N × H)
658. D4C13×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#4492
C2×C4×C13×D82
C13×#24222
C13×#23392
C13×#20952
C13×#20762
C13×#20552
C13×#20332
C13×#19332
C13×#19232
C13×#18792
C13×#18772
C13×#18622
C13×#18022
C13×#17882
#2489913