Finite Group Databasebeta

← C13×#24916 #15711255

Subgroups — C13×#24916 #15711255

Order 3328.

1036 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#449C211yesmaximal, characteristic
2C2×C13×#440C211yesmaximal, characteristic, complemented
3C13×#2422C211yesmaximal, characteristic, complemented
4C13×#2341C211yesmaximal, characteristic, complemented
5C13×#2093C211yesmaximal, characteristic, complemented
6C13×#2076C211yesmaximal, characteristic, complemented
7C13×#2054C211yesmaximal, characteristic, complemented
8C13×#2033C211yesmaximal, characteristic, complemented
9C13×#1936C211yesmaximal, characteristic, complemented
10C13×#1924C211yesmaximal, characteristic, complemented
11C13×#1880C211yesmaximal, characteristic, complemented
12C13×#1879C211yesmaximal, characteristic, complemented
13C13×#1863C211yesmaximal, characteristic, complemented
14C13×#1803C211yesmaximal, characteristic, complemented
15C13×#1788C211yesmaximal, characteristic, complemented
16C22×C13×#41C2211yescharacteristic
17C22×C13×SD16C2211yescharacteristic
18C22×C13×D8C2211yescharacteristic
19C2×C13×#123—21no—
20C2×C13×#121C2211yescharacteristic
21C2×C4×Q8×C13C2211yescharacteristic
22C2×C4×Q8×C13C2211yescharacteristic
23C2×C4×D4×C13C2211yescharacteristic
24C13×#449—24no—
25C13×#440—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×C13×#97C2211yescharacteristic
40C13×#397—21no—
41C13×#394—21no—
42C13×#390—21no—
43C13×#390—21no—
44C13×#390C2211yescharacteristic
45C13×#390C2211yescharacteristic
46C13×#390C2211yescharacteristic
47C13×#389C2211yescharacteristic
48C13×#385—21no—
49C13×#384C2211yescharacteristic
50C13×#380—21no—
51C13×#380C2211yescharacteristic
52C13×#380C2211yescharacteristic
53C4×C13×C22⋊C4—21no—
54C4×C13×C22⋊C4C2211yescharacteristic
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×C13C2311yescharacteristic
75C2×C13×SD16—22no—
76C2×C13×SD16—22no—
77C2×C13×SD16D414yes—
78C2×C13×D8—22no—
79C2×C13×D8—22no—
80C2×C13×D8—41no—
81C22×C8×C13C2311yescharacteristic
82C22×C8×C13C2311yescharacteristic
83C22×C8×C13C2311yescharacteristic
84C22×C8×C13C2311yescharacteristic
85C13×#123—44no—
86C13×#121—22no—
87C13×#121—41no—
88C4×Q8×C13—22no—
89C4×Q8×C13—22no—
90C4×Q8×C13—41no—
91C4×Q8×C13—41no—
92C4×D4×C13—22no—
93C4×D4×C13—41no—
94C2×C13×C4⋊C4—21no—
95C2×C13×C4⋊C4—21no—
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⋊C4—21no—
113C2×C13×C22⋊C4—21no—
114C2×C13×C22⋊C4D411yescharacteristic
115C2×C13×C22⋊C4D411yescharacteristic
116C2×C42×C13—21no—
117C2×C42×C13—21no—
118C2×C42×C13C2311yescharacteristic
119C2×C42×C13C2311yescharacteristic
120C13×#107—22no—
121C13×#107—41no—
122C13×C4⋊C8—41no—
123C13×#103—22no—
124C13×#103—22no—
125C13×#103—22no—
126C13×#102—22no—
127C13×#102—22no—
128C13×#102—22no—
129C13×#102—41no—
130C13×#102—41no—
131C13×C22⋊C8—22no—
132C13×C22⋊C8—41no—
133C13×#97—22no—
134C13×#95—21no—
135C13×#95—21no—
136C13×#95—21no—
137C13×#95D411yescharacteristic
138C13×#95D411yescharacteristic
139#24916C1311yesmaximal, 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×C13C2×D412yes—
151C2×Q8×C13#4112yes—
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—21no—
163C2×D4×C13—21no—
164C2×D4×C13—42no—
165C2×D4×C13—42no—
166C2×D4×C13—42no—
167C2×D4×C13—42no—
168C2×D4×C13—81no—
169C2×D4×C13C2×D412yes—
170C2×D4×C13#4112yes—
171C22×C4×C13—21no—
172C22×C4×C13—24no—
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—81no—
189C22×C4×C13C2×D411yescharacteristic
190C22×C4×C13C2×D411yescharacteristic
191C22×C4×C13C2×D411yescharacteristic
192C22×C4×C13C2×D411yescharacteristic
193C22×C4×C13C2×D411yescharacteristic
194C22×C4×C13C2411yescharacteristic
195C13×SD16—28no—
196C13×D8—44no—
197C2×C8×C13—21no—
198C2×C8×C13—21no—
199C2×C8×C13—21no—
200C2×C8×C13—21no—
201C2×C8×C13—21no—
202C2×C8×C13—21no—
203C2×C8×C13—21no—
204C2×C8×C13—21no—
205C2×C8×C13—21no—
206C2×C8×C13—21no—
207C2×C8×C13—21no—
208C2×C8×C13C2×D412yes—
209C13×C4⋊C4—21no—
210C13×C4⋊C4—21no—
211C13×C4⋊C4—21no—
212C13×C4⋊C4—21no—
213C13×C4⋊C4—21no—
214C13×C4⋊C4—21no—
215C13×C4⋊C4—21no—
216C13×C4⋊C4—21no—
217C13×C4⋊C4—21no—
218C13×C4⋊C4—21no—
219C13×C4⋊C4—42no—
220C13×C4⋊C4—42no—
221C13×C4⋊C4—42no—
222C13×C4⋊C4—42no—
223C13×C4⋊C4—81no—
224C13×C22⋊C4—22no—
225C13×C22⋊C4—41no—
226C13×C22⋊C4—42no—
227C13×C22⋊C4—42no—
228C13×C22⋊C4—42no—
229C13×C22⋊C4—42no—
230C13×C22⋊C4—42no—
231C13×C22⋊C4—42no—
232C13×C22⋊C4—42no—
233C13×C22⋊C4—81no—
234C13×C22⋊C4—81no—
235C13×C22⋊C4—81no—
236C42×C13—21no—
237C42×C13—21no—
238C42×C13—21no—
239C42×C13—21no—
240C42×C13—42no—
241C42×C13—42no—
242C2×#449C2×C1311yescharacteristic
243C2×#440C2×C1311yescharacteristic, complemented
244#2422C2×C1311yescharacteristic, complemented
245#2341C2×C1311yescharacteristic, complemented
246#2093C2×C1311yescharacteristic, complemented
247#2076C2×C1311yescharacteristic, complemented
248#2054C2×C1311yescharacteristic, complemented
249#2033C2×C1311yescharacteristic, complemented
250#1936C2×C1311yescharacteristic, complemented
251#1924C2×C1311yescharacteristic, complemented
252#1880C2×C1311yescharacteristic, complemented
253#1879C2×C1311yescharacteristic, complemented
254#1863C2×C1311yescharacteristic, complemented
255#1803C2×C1311yescharacteristic, complemented
256#1788C2×C1311yescharacteristic, complemented
257C23×C13—21no—
258C23×C13—22no—
259C23×C13—22no—
260C23×C13—21no—
261C23×C13—21no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13—21no—
266C23×C13—41no—
267C23×C13—41no—
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—22no—
282Q8×C13#12314yescomplemented
283D4×C13—22no—
284D4×C13—22no—
285D4×C13—22no—
286D4×C13—22no—
287D4×C13—48no—
288D4×C13—41no—
289D4×C13—41no—
290D4×C13—41no—
291D4×C13—41no—
292D4×C13—84no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—21no—
296C2×C4×C13—22no—
297C2×C4×C13—21no—
298C2×C4×C13—21no—
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—21no—
308C2×C4×C13—21no—
309C2×C4×C13—21no—
310C2×C4×C13—48no—
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—41no—
330C2×C4×C13—84no—
331C2×C4×C13AGL(1,ℤ/8)12yes—
332C2×C4×C13C22×D411yescharacteristic
333C2×C4×C13C2×#4111yescharacteristic
334C2×C4×C13C2×#4111yescharacteristic
335C2×C4×C13C2×#4111yescharacteristic
336C2×C4×C13H(5,𝔽2)11yescharacteristic
337C2×C4×C13H(5,𝔽2)11yescharacteristic
338C8×C13—22no—
339C8×C13—41no—
340C8×C13—41no—
341C8×C13—41no—
342C22×#41C22×C1311yescharacteristic
343C22×SD16C22×C1311yescharacteristic
344C22×D8C22×C1311yescharacteristic
345C2×#123—21no—
346C2×#121C22×C1311yescharacteristic
347C2×C4×Q8C22×C1311yescharacteristic
348C2×C4×Q8C22×C1311yescharacteristic
349C2×C4×D4C22×C1311yescharacteristic
350#449—24no—
351#440—24no—
352C2×#107C22×C1311yescharacteristic
353C2×#107C22×C1311yescharacteristic
354C2×C4⋊C8C22×C1311yescharacteristic
355C2×#103C22×C1311yescharacteristic
356C2×#103C22×C1311yescharacteristic
357C2×#103C22×C1311yescharacteristic
358C2×#102C22×C1311yescharacteristic
359C2×#102C22×C1311yescharacteristic
360C2×#102C22×C1311yescharacteristic
361C2×#102C22×C1311yescharacteristic
362C2×#102C22×C1311yescharacteristic
363C2×C22⋊C8C22×C1311yescharacteristic
364C2×C22⋊C8C22×C1311yescharacteristic
365C2×#97C22×C1311yescharacteristic
366#397—21no—
367#394—21no—
368#390—21no—
369#390—21no—
370#390C22×C1311yescharacteristic
371#390C22×C1311yescharacteristic
372#390C22×C1311yescharacteristic
373#389C22×C1311yescharacteristic
374#385—21no—
375#384C22×C1311yescharacteristic
376#380—21no—
377#380C22×C1311yescharacteristic
378#380C22×C1311yescharacteristic
379C4×C22⋊C4—21no—
380C4×C22⋊C4C22×C1311yescharacteristic
381#340C22×C1311yescharacteristic
382#340C22×C1311yescharacteristic
383#340C22×C1311yescharacteristic
384#340C22×C1311yescharacteristic
385#336C22×C1311yescharacteristic
386#336C22×C1311yescharacteristic
387C22×C13—41no—
388C22×C13—42no—
389C22×C13—41no—
390C22×C13—42no—
391C22×C13—42no—
392C22×C13—41no—
393C22×C13—42no—
394C22×C13—41no—
395C22×C13—42no—
396C22×C13—42no—
397C22×C13—41no—
398C22×C13—41no—
399C22×C13—41no—
400C22×C13—81no—
401C22×C13—81no—
402C22×C13—81no—
403C22×C13—81no—
404C22×C13—81no—
405C22×C13—81no—
406C22×C13—81no—
407C22×C13—81no—
408C22×C13#52511yescharacteristic
409C22×C13D4211yescharacteristic
410C22×C13#54611yescharacteristic
411C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
412C22×C13#57511yescharacteristic
413C22×C13#57611yescharacteristic
414C22×C13#57811yescharacteristic
415C4×C13—24no—
416C4×C13—22no—
417C4×C13—41no—
418C4×C13—41no—
419C4×C13—41no—
420C4×C13—41no—
421C4×C13—81no—
422C4×C13—81no—
423C4×C13—81no—
424C4×C13—81no—
425C4×C13—81no—
426C4×C13C2×#12311yescharacteristic
427C4×C13#53811yescharacteristic
428C4×C13#54611yescharacteristic
429C4×C13#55111yescharacteristic
430C2×#41—22no—
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—22no—
434C2×#41—41no—
435C2×#41—41no—
436C22×Q8C23×C1311yescharacteristic
437C22×D4—21no—
438C22×D4—21no—
439C22×D4C23×C1311yescharacteristic
440C22×D4C23×C1311yescharacteristic
441C23×C4—21no—
442C23×C4—21no—
443C23×C4C23×C1311yescharacteristic
444C2×SD16—22no—
445C2×SD16—22no—
446C2×SD16D4×C1314yes—
447C2×D8—22no—
448C2×D8—22no—
449C2×D8—41no—
450C22×C8C23×C1311yescharacteristic
451C22×C8C23×C1311yescharacteristic
452C22×C8C23×C1311yescharacteristic
453C22×C8C23×C1311yescharacteristic
454#123—44no—
455#121—22no—
456#121—41no—
457C4×Q8—22no—
458C4×Q8—22no—
459C4×Q8—41no—
460C4×Q8—41no—
461C4×D4—22no—
462C4×D4—41no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4C23×C1311yescharacteristic
469C2×C4⋊C4C23×C1311yescharacteristic
470C2×C4⋊C4C23×C1311yescharacteristic
471C2×C4⋊C4C23×C1311yescharacteristic
472C2×C4⋊C4C23×C1311yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
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×C42—21no—
486C2×C42—21no—
487C2×C42C23×C1311yescharacteristic
488C2×C42C23×C1311yescharacteristic
489#107—22no—
490#107—41no—
491C4⋊C8—41no—
492#103—22no—
493#103—22no—
494#103—22no—
495#102—22no—
496#102—22no—
497#102—22no—
498#102—41no—
499#102—41no—
500C22⋊C8—22no—
501C22⋊C8—41no—
502#97—22no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95D4×C1311yescharacteristic
507#95D4×C1311yescharacteristic
508C2×C13—81no—
509C2×C13—82no—
510C2×C13—82no—
511C2×C13#241811yescharacteristic
512C2×C13#311511yescharacteristic
513C2×C13#312411yescharacteristic
514C2×C13#326911yescharacteristic
515C2×C13#327411yescharacteristic
516C2×C13#330811yescharacteristic
517C2×C13#330911yescharacteristic
518C24—21no—
519C24—21no—
520C24C2×D4×C1311yescharacteristic
521#41—44no—
522#41—44no—
523#41—44no—
524#41—44no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8C2×D4×C1312yes—
529C2×Q8C13×#4112yes—
530C2×Q8C13×#4112yes—
531C2×D4—24no—
532C2×D4—21no—
533C2×D4—21no—
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×D4C13×#4112yes—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—21no—
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—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—81no—
567C22×C4C2×D4×C1311yescharacteristic
568C22×C4C2×D4×C1311yescharacteristic
569C22×C4C2×D4×C1311yescharacteristic
570C22×C4C2×D4×C1311yescharacteristic
571C22×C4C2×D4×C1311yescharacteristic
572C22×C4C24×C1311yescharacteristic
573SD16—28no—
574D8—44no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8C2×D4×C1312yes—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—81no—
602C22⋊C4—22no—
603C22⋊C4—41no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—81no—
612C22⋊C4—81no—
613C22⋊C4—81no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—42no—
619C42—42no—
620C13#2491611yescharacteristic, direct product factor, Sylow
621C23—21no—
622C23—22no—
623C23—22no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23C22×D4×C1311yescharacteristic
643Q8—22no—
644Q8—22no—
645Q8—22no—
646Q8C13×#12314yescomplemented
647D4—22no—
648D4—22no—
649D4—22no—
650D4—22no—
651D4—48no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—84no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
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—21no—
674C2×C4—48no—
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—84no—
695C2×C4C13×AGL(1,ℤ/8)12yes—
696C2×C4C22×D4×C1311yescharacteristic
697C2×C4C2×C13×#4111yescharacteristic
698C2×C4C2×C13×#4111yescharacteristic
699C2×C4C2×C13×#4111yescharacteristic
700C2×C4C13×H(5,𝔽2)11yescharacteristic
701C2×C4C13×H(5,𝔽2)11yescharacteristic
702C8—22no—
703C8—41no—
704C8—41no—
705C8—41no—
706C22—41no—
707C22—42no—
708C22—42no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—42no—
714C22—41no—
715C22—42no—
716C22—42no—
717C22—41no—
718C22—42no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22C13×#52511yescharacteristic
728C22D42×C1311yescharacteristic
729C22C13×#54611yescharacteristic
730C22C2×C13×AGL(1,ℤ/8)11yescharacteristic
731C22C13×#57511yescharacteristic
732C22C13×#57611yescharacteristic
733C22C13×#57811yescharacteristic
734C4—22no—
735C4—24no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—81no—
741C4—81no—
742C4—81no—
743C4—81no—
744C4—81no—
745C4C2×C13×#12311yescharacteristic
746C4C13×#53811yescharacteristic
747C4C13×#54611yescharacteristic
748C4C13×#55111yescharacteristic
749C2—81no—
750C2—82no—
751C2—82no—
752C2C13×#241811yescharacteristic
753C2C13×#311511yescharacteristic
754C2C13×#312411yescharacteristic
755C2C13×#326911yescharacteristic
756C2C13×#327411yescharacteristic
757C2C13×#330811yescharacteristic
758C2C13×#330911yescharacteristic
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×C13×#440C2semidirect
3. C13×#2422C2semidirect
4. C13×#2341C2semidirect
5. C13×#2093C2semidirect
6. C13×#2076C2semidirect
7. C13×#2054C2semidirect
8. C13×#2033C2semidirect
9. C13×#1936C2semidirect
10. C13×#1924C2semidirect
11. C13×#1880C2semidirect
12. C13×#1879C2semidirect
13. C13×#1863C2semidirect
14. C13×#1803C2semidirect
15. C13×#1788C2semidirect
139. #24916C13direct (N × H)
243. C2×#440C2×C13semidirect
244. #2422C2×C13semidirect
245. #2341C2×C13semidirect
246. #2093C2×C13semidirect
247. #2076C2×C13semidirect
248. #2054C2×C13semidirect
249. #2033C2×C13semidirect
250. #1936C2×C13semidirect
251. #1924C2×C13semidirect
252. #1880C2×C13semidirect
253. #1879C2×C13semidirect
254. #1863C2×C13semidirect
255. #1803C2×C13semidirect
256. #1788C2×C13semidirect
282. Q8×C13#123semidirect
620. C13#24916direct (N × H)
646. Q8C13×#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×C13×#4402
C13×#24222
C13×#23412
C13×#20932
C13×#20762
C13×#20542
C13×#20332
C13×#19362
C13×#19242
C13×#18802
C13×#18792
C13×#18632
C13×#18032
C13×#17882
#2491613