Finite Group Databasebeta

← C13×#61544 #15747883

Subgroups — C13×#61544 #15747883

Order 3328.

1754 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3523C211yesmaximal, characteristic, complemented
2C13×#3518C211yesmaximal, characteristic
3C13×#3398C211yesmaximal, characteristic, complemented
4C13×#3387C211yesmaximal, characteristic, complemented
5C13×#3364C211yesmaximal, characteristic, complemented
6C13×#3363C211yesmaximal, characteristic, complemented
7C13×#3349C212yesmaximal, complemented
8C13×#3340C211yesmaximal, characteristic, complemented
9C13×#3329C211yesmaximal, characteristic, complemented
10C13×#3328C211yesmaximal, characteristic, complemented
11C13×#3328C212yesmaximal, complemented
12C13×#3327C212yesmaximal, complemented
13D4×C13×Q16C211yesmaximal, characteristic, complemented
14C13×#3270C212yesmaximal, complemented
15C13×#3185C211yesmaximal, characteristic, complemented
16C13×#3178C212yesmaximal, complemented
17C13×#3127C212yesmaximal, complemented
18C13×#3121C212yesmaximal, complemented
19C13×#3107C211yesmaximal, characteristic, complemented
20C13×#3104C211yesmaximal, characteristic, complemented
21C13×#2969C211yesmaximal, characteristic, complemented
22C13×#2950C212yesmaximal, complemented
23C4×C13×#137C211yesmaximal, characteristic, complemented
24C2×C13×#137C2211yescharacteristic
25C22×C13×Q16C2212yes—
26Q82×C13C2211yescharacteristic
27C13×#557—21no—
28C13×#557C2211yescharacteristic
29C13×#557C2211yescharacteristic
30C13×#556—22no—
31C13×#556—21no—
32C13×#556—21no—
33C13×#556C2211yescharacteristic
34C13×#556C2212yes—
35C13×#556C2211yescharacteristic
36C13×#555—21no—
37C13×#555C2211yescharacteristic
38C13×#552—22no—
39C13×#552C2212yes—
40D4×Q8×C13C2211yescharacteristic
41D4×Q8×C13C2212yes—
42D4×Q8×C13C2211yescharacteristic
43C13×#548C2212yes—
44C13×#542—22no—
45C13×#542C2212yes—
46C13×#541—22no—
47C13×#541C2212yes—
48C13×#533—21no—
49C13×#533—21no—
50C13×#533C2211yescharacteristic
51C13×#533C2211yescharacteristic
52C13×#529—21no—
53C13×#529—21no—
54C13×#529C2211yescharacteristic
55C13×#519C2212yes—
56C13×#519C2212yes—
57C4×C13×#41C2211yescharacteristic
58C2×C4×Q8×C13C2211yescharacteristic
59C13×#501C2212yes—
60C13×#498C2211yescharacteristic
61C13×#497C2212yes—
62C13×#494C2211yescharacteristic
63C13×#488C2212yes—
64C13×#487C2212yes—
65C13×#487C2211yescharacteristic
66C13×#487C2211yescharacteristic
67C13×#485C2212yes—
68C13×#485C2212yes—
69C13×#485C2212yes—
70C13×#485C2212yes—
71C13×#484C2212yes—
72C13×#482C2212yes—
73C13×#479C2212yes—
74C13×#479C2212yes—
75C13×#477C2211yescharacteristic
76C13×#477C2211yescharacteristic
77C13×#477C2212yes—
78C13×#475C2211yescharacteristic
79C13×#475C2212yes—
80C13×#474C2211yescharacteristic
81C13×#470C2212yes—
82C13×#470C2212yes—
83C13×#470C2212yes—
84C13×#468C2212yes—
85C13×#467C2212yes—
86C13×#465C2212yes—
87C13×#464C2212yes—
88C13×#464C2212yes—
89C13×#462C2212yes—
90C13×#462C2211yescharacteristic
91C13×#462C2211yescharacteristic
92C13×#462C2211yescharacteristic
93C13×#462C2212yes—
94C13×#461C2211yescharacteristic
95C13×#452C2212yes—
96C13×#451C2212yes—
97C13×#451C2212yes—
98C13×#451C2212yes—
99C13×#451C2212yes—
100C13×#448C2212yes—
101C13×#446C2211yescharacteristic
102C8×Q8×C13C2211yescharacteristic
103C13×#441C2212yes—
104C13×#441C2212yes—
105C13×#441C2212yes—
106C13×#441C2211yescharacteristic
107C13×#441C2212yes—
108C13×#441C2211yescharacteristic
109C13×#440C2211yescharacteristic
110C13×#440C2211yescharacteristic
111C4×C13×Q16C2211yescharacteristic
112C4×C13×Q16C2212yes—
113C4×C13×Q16C2211yescharacteristic
114C4×C13×Q16C2212yes—
115C4×C13×Q16C2212yes—
116C4×C13×Q16C2212yes—
117C4×C13×Q16C2212yes—
118C4×C13×SD16C2211yescharacteristic
119C4×C13×SD16C2211yescharacteristic
120C4×C13×SD16C2212yes—
121C13×#436C2212yes—
122C13×#436C2211yescharacteristic
123C13×#435C2212yes—
124C8×D4×C13C2211yescharacteristic
125C13×#433C2212yes—
126C13×#431C2211yescharacteristic
127C13×#428C2211yescharacteristic
128C13×#427C2212yes—
129C13×#419C2212yes—
130C13×#419C2211yescharacteristic
131C13×#419C2212yes—
132C13×#417C2211yescharacteristic
133C13×#405C2212yes—
134C4×C13×M16C2211yescharacteristic
135C2×C13×#41C2311yescharacteristic
136C22×Q8×C13C2312yes—
137C22×Q8×C13C2311yescharacteristic
138C22×Q8×C13C2312yes—
139C13×#137—24no—
140C2×C13×Q16—28no—
141C2×C13×Q16C2312yes—
142C2×C13×Q16C2312yes—
143C2×C13×Q16C2311yescharacteristic
144C2×C13×Q16C2312yes—
145C2×C13×Q16C2312yes—
146C2×C13×Q16C2312yes—
147C2×C13×Q16C2311yescharacteristic
148C2×C13×SD16C2311yescharacteristic
149C2×C13×SD16C2311yescharacteristic
150C2×C13×SD16C2312yes—
151C2×C13×M16C2311yescharacteristic
152C2×C13×M16C2311yescharacteristic
153C2×C13×M16C2312yes—
154C22×C8×C13C2312yes—
155C13×C4⋊Q8—21no—
156C13×C4⋊Q8—21no—
157C13×C4⋊Q8—21no—
158C13×C4⋊Q8—21no—
159C13×C4⋊Q8—22no—
160C13×C4⋊Q8—22no—
161C13×C4⋊Q8C2311yescharacteristic
162C13×C4⋊Q8C2311yescharacteristic
163C13×C4⋊Q8C2312yes—
164C13×C4⋊Q8C2311yescharacteristic
165C13×C4⋊Q8C2312yes—
166C13×C4⋊Q8C2311yescharacteristic
167C13×#126—22no—
168C13×#126—22no—
169C13×#126—22no—
170C13×#126—22no—
171C13×#126—22no—
172C13×#126—22no—
173C13×#126—22no—
174C13×#126—22no—
175C13×#126D412yes—
176C13×#125—21no—
177C13×#125—22no—
178C13×#125—22no—
179C13×#125—22no—
180C13×#125—22no—
181C13×#125—22no—
182C13×#125—21no—
183C13×#125—21no—
184C13×#125D411yescharacteristic
185C13×#125C2312yes—
186C13×#124—21no—
187C13×#124—22no—
188C13×#124—22no—
189C13×#124—22no—
190C13×#124—22no—
191C13×#124D411yescharacteristic
192C13×#124C2312yes—
193C13×#123—22no—
194C13×#123—22no—
195C13×#123D412yes—
196C13×C22⋊Q8—21no—
197C13×C22⋊Q8—21no—
198C13×C22⋊Q8—21no—
199C13×C22⋊Q8—22no—
200C13×C22⋊Q8—22no—
201C13×C22⋊Q8—22no—
202C13×C22⋊Q8—22no—
203C13×C22⋊Q8—22no—
204C13×C22⋊Q8—22no—
205C13×C22⋊Q8D411yescharacteristic
206C13×C22⋊Q8C2312yes—
207C13×C22⋊Q8C2312yes—
208C13×C22⋊Q8C2312yes—
209C13×C22⋊Q8C2312yes—
210C13×C22⋊Q8C2312yes—
211C13×#121—21no—
212C13×#121—22no—
213C13×#121D411yescharacteristic
214C13×#121C2312yes—
215C4×Q8×C13—21no—
216C4×Q8×C13—21no—
217C4×Q8×C13—22no—
218C4×Q8×C13—22no—
219C4×Q8×C13—22no—
220C4×Q8×C13—22no—
221C4×Q8×C13—21no—
222C4×Q8×C13—22no—
223C4×Q8×C13—21no—
224C4×Q8×C13—21no—
225C4×Q8×C13—21no—
226C4×Q8×C13—21no—
227C4×Q8×C13—21no—
228C4×Q8×C13C2312yes—
229C4×Q8×C13C2311yescharacteristic
230C4×Q8×C13C2311yescharacteristic
231C4×Q8×C13C2311yescharacteristic
232C4×Q8×C13C2311yescharacteristic
233C4×Q8×C13C2311yescharacteristic
234C4×Q8×C13C2312yes—
235C4×Q8×C13C2311yescharacteristic
236C4×Q8×C13C2312yes—
237C4×Q8×C13C2312yes—
238C4×Q8×C13C2312yes—
239C4×Q8×C13C2312yes—
240C4×Q8×C13C2311yescharacteristic
241C4×D4×C13—22no—
242C4×D4×C13—21no—
243C4×D4×C13—21no—
244C4×D4×C13—21no—
245C4×D4×C13—21no—
246C4×D4×C13—22no—
247C4×D4×C13C2311yescharacteristic
248C4×D4×C13C2311yescharacteristic
249C4×D4×C13C2311yescharacteristic
250C4×D4×C13C2312yes—
251C13×#117—21no—
252C13×#117—21no—
253C13×#117—21no—
254C13×#117—21no—
255C13×#117—22no—
256C13×#117—22no—
257C13×#117—22no—
258C13×#117—22no—
259C13×#117—22no—
260C13×#117—21no—
261C13×#117C2312yes—
262C13×#117C2312yes—
263C13×#117C2311yescharacteristic
264C13×#117C2312yes—
265C2×C13×C4⋊C4—21no—
266C2×C13×C4⋊C4C2311yescharacteristic
267C2×C42×C13—21no—
268C2×C42×C13—21no—
269C2×C42×C13C2311yescharacteristic
270C13×#107C2312yes—
271C13×#107C2312yes—
272C13×#107C2311yescharacteristic
273C13×#107C2311yescharacteristic
274C13×#107C2312yes—
275C13×#106C2311yescharacteristic
276C13×#106C2312yes—
277C13×#106C2311yescharacteristic
278C13×#106C2312yes—
279C13×#106C2312yes—
280C13×C4⋊C8C2311yescharacteristic
281C13×C4⋊C8C2311yescharacteristic
282C13×C4⋊C8C2312yes—
283C13×C4⋊C8C2312yes—
284C13×#103C2311yescharacteristic
285C13×#103C2311yescharacteristic
286C13×#103C2311yescharacteristic
287C13×#103C2311yescharacteristic
288C13×#103C2311yescharacteristic
289C13×#103C2311yescharacteristic
290C13×#103C2312yes—
291C13×#103C2312yes—
292C13×#103C2312yes—
293C13×#103C2312yes—
294C13×#103C2312yes—
295C13×#103C2312yes—
296C13×#103C2312yes—
297C13×#103C2312yes—
298C13×#103C2312yes—
299C13×#103C2312yes—
300C13×#103C2312yes—
301C13×#102C2311yescharacteristic
302C13×#102C2311yescharacteristic
303C13×#102C2312yes—
304C13×C22⋊C8C2312yes—
305C13×C22⋊C8C2312yes—
306C13×C22⋊C8C2312yes—
307C13×#97C2311yescharacteristic
308C13×#97C2311yescharacteristic
309C13×#97C2312yes—
310C4×C8×C13C2311yescharacteristic
311C4×C8×C13C2311yescharacteristic
312C4×C8×C13C2312yes—
313C4×C8×C13C2312yes—
314#61544C1311yesmaximal, characteristic, direct product factor, Sylow
315C13×#41—22no—
316C13×#41—41no—
317C2×Q8×C13—21no—
318C2×Q8×C13—22no—
319C2×Q8×C13—22no—
320C2×Q8×C13—21no—
321C2×Q8×C13—21no—
322C2×Q8×C13—22no—
323C2×Q8×C13—24no—
324C2×Q8×C13—24no—
325C2×Q8×C13—22no—
326C2×Q8×C13—42no—
327C2×Q8×C13—42no—
328C2×Q8×C13—41no—
329C2×Q8×C13C2×D411yescharacteristic
330C2×Q8×C13C2412yes—
331C2×Q8×C13C2411yescharacteristic
332C2×Q8×C13C2412yes—
333C2×Q8×C13C2411yescharacteristic
334C2×Q8×C13C2411yescharacteristic
335C2×D4×C13—21no—
336C2×D4×C13—22no—
337C2×D4×C13C2×D411yescharacteristic
338C2×D4×C13C2×D412yes—
339C2×D4×C13C2411yescharacteristic
340C22×C4×C13—21no—
341C22×C4×C13—21no—
342C22×C4×C13—22no—
343C22×C4×C13—22no—
344C22×C4×C13—21no—
345C22×C4×C13—21no—
346C22×C4×C13—21no—
347C22×C4×C13C2×D411yescharacteristic
348C22×C4×C13C2×D411yescharacteristic
349C22×C4×C13C2411yescharacteristic
350C22×C4×C13C2412yes—
351C13×Q16—24no—
352C13×Q16—24no—
353C13×Q16—22no—
354C13×Q16—24no—
355C13×Q16—42no—
356C13×Q16—42no—
357C13×Q16#4114yes—
358C13×SD16—22no—
359C13×SD16—22no—
360C13×SD16—42no—
361C13×M16—22no—
362C13×M16—42no—
363C13×M16—41no—
364C2×C8×C13—24no—
365C2×C8×C13C2411yescharacteristic
366C2×C8×C13C2412yes—
367C2×C8×C13C2411yescharacteristic
368C2×C8×C13C2411yescharacteristic
369C2×C8×C13C2412yes—
370C2×C8×C13C2411yescharacteristic
371C13×C4⋊C4—21no—
372C13×C4⋊C4—21no—
373C13×C4⋊C4—21no—
374C13×C4⋊C4—21no—
375C13×C4⋊C4—21no—
376C13×C4⋊C4—21no—
377C13×C4⋊C4—21no—
378C13×C4⋊C4—21no—
379C13×C4⋊C4—21no—
380C13×C4⋊C4—22no—
381C13×C4⋊C4—22no—
382C13×C4⋊C4—22no—
383C13×C4⋊C4—22no—
384C13×C4⋊C4—22no—
385C13×C4⋊C4—22no—
386C13×C4⋊C4—21no—
387C13×C4⋊C4—22no—
388C13×C4⋊C4—21no—
389C13×C4⋊C4—22no—
390C13×C4⋊C4—22no—
391C13×C4⋊C4—21no—
392C13×C4⋊C4—22no—
393C13×C4⋊C4—21no—
394C13×C4⋊C4—22no—
395C13×C4⋊C4—22no—
396C13×C4⋊C4—22no—
397C13×C4⋊C4—22no—
398C13×C4⋊C4—22no—
399C13×C4⋊C4—22no—
400C13×C4⋊C4C2×D411yescharacteristic
401C13×C4⋊C4C2×D411yescharacteristic
402C13×C4⋊C4C2×D412yes—
403C13×C4⋊C4C2×D412yes—
404C13×C4⋊C4C2×D412yes—
405C13×C4⋊C4C2×D412yes—
406C13×C4⋊C4C2412yes—
407C13×C4⋊C4C2411yescharacteristic
408C13×C4⋊C4C2411yescharacteristic
409C13×C4⋊C4C2411yescharacteristic
410C13×C4⋊C4C2411yescharacteristic
411C13×C4⋊C4C2412yes—
412C13×C22⋊C4—22no—
413C13×C22⋊C4—22no—
414C13×C22⋊C4—22no—
415C13×C22⋊C4—22no—
416C13×C22⋊C4—21no—
417C13×C22⋊C4—22no—
418C13×C22⋊C4—22no—
419C13×C22⋊C4—22no—
420C13×C22⋊C4—21no—
421C13×C22⋊C4—21no—
422C13×C22⋊C4—22no—
423C13×C22⋊C4—22no—
424C13×C22⋊C4—22no—
425C13×C22⋊C4C2×D412yes—
426C13×C22⋊C4C2×D412yes—
427C13×C22⋊C4C2×D412yes—
428C13×C22⋊C4C2×D412yes—
429C13×C22⋊C4C2×D412yes—
430C42×C13—21no—
431C42×C13—21no—
432C42×C13—21no—
433C42×C13—21no—
434C42×C13—21no—
435C42×C13—21no—
436C42×C13—21no—
437C42×C13—22no—
438C42×C13—22no—
439C42×C13—22no—
440C42×C13—22no—
441C42×C13—22no—
442C42×C13—22no—
443C42×C13—22no—
444C42×C13—22no—
445C42×C13C2×D411yescharacteristic
446C42×C13C2×D411yescharacteristic
447C42×C13C2411yescharacteristic
448C42×C13C2411yescharacteristic
449C42×C13C2412yes—
450#3523C2×C1311yescharacteristic, complemented
451#3518C2×C1311yescharacteristic
452#3398C2×C1311yescharacteristic, complemented
453#3387C2×C1311yescharacteristic, complemented
454#3364C2×C1311yescharacteristic, complemented
455#3363C2×C1311yescharacteristic, complemented
456#3349C2×C1312yescomplemented
457#3340C2×C1311yescharacteristic, complemented
458#3329C2×C1311yescharacteristic, complemented
459#3328C2×C1311yescharacteristic, complemented
460#3328C2×C1312yescomplemented
461#3327C2×C1312yescomplemented
462D4×Q16C2×C1311yescharacteristic, complemented
463#3270C2×C1312yescomplemented
464#3185C2×C1311yescharacteristic, complemented
465#3178C2×C1312yescomplemented
466#3127C2×C1312yescomplemented
467#3121C2×C1312yescomplemented
468#3107C2×C1311yescharacteristic, complemented
469#3104C2×C1311yescharacteristic, complemented
470#2969C2×C1311yescharacteristic, complemented
471#2950C2×C1312yescomplemented
472C4×#137C2×C1311yescharacteristic, complemented
473C23×C13—21no—
474C23×C13C22×D412yes—
475C23×C13C22×D411yescharacteristic
476Q8×C13—22no—
477Q8×C13—21no—
478Q8×C13—21no—
479Q8×C13—21no—
480Q8×C13—22no—
481Q8×C13—22no—
482Q8×C13—22no—
483Q8×C13—22no—
484Q8×C13—21no—
485Q8×C13—42no—
486Q8×C13—44no—
487Q8×C13—44no—
488Q8×C13—42no—
489Q8×C13—81no—
490Q8×C13—82no—
491Q8×C13C2×#4112yes—
492Q8×C13C2×#4112yes—
493D4×C13—22no—
494D4×C13—21no—
495D4×C13—21no—
496D4×C13—42no—
497D4×C13—42no—
498D4×C13—82no—
499C2×C4×C13—21no—
500C2×C4×C13—21no—
501C2×C4×C13—22no—
502C2×C4×C13—22no—
503C2×C4×C13—21no—
504C2×C4×C13—22no—
505C2×C4×C13—21no—
506C2×C4×C13—21no—
507C2×C4×C13—21no—
508C2×C4×C13—22no—
509C2×C4×C13—22no—
510C2×C4×C13—22no—
511C2×C4×C13—21no—
512C2×C4×C13—21no—
513C2×C4×C13—21no—
514C2×C4×C13—22no—
515C2×C4×C13—41no—
516C2×C4×C13—42no—
517C2×C4×C13—44no—
518C2×C4×C13—44no—
519C2×C4×C13—42no—
520C2×C4×C13—42no—
521C2×C4×C13—42no—
522C2×C4×C13—81no—
523C2×C4×C13C22×D411yescharacteristic
524C2×C4×C13C22×D411yescharacteristic
525C2×C4×C13C22×D412yes—
526C2×C4×C13C22×D412yes—
527C2×C4×C13C22×D412yes—
528C2×C4×C13C22×D411yescharacteristic
529C2×C4×C13C22×D411yescharacteristic
530C2×C4×C13C22×D411yescharacteristic
531C2×C4×C13C2511yescharacteristic
532C8×C13—22no—
533C8×C13—21no—
534C8×C13—21no—
535C8×C13—22no—
536C8×C13—21no—
537C8×C13C2×#4112yes—
538C2×#137C22×C1311yescharacteristic
539C22×Q16C22×C1312yes—
540Q82C22×C1311yescharacteristic
541#557—21no—
542#557C22×C1311yescharacteristic
543#557C22×C1311yescharacteristic
544#556—22no—
545#556—21no—
546#556—21no—
547#556C22×C1311yescharacteristic
548#556C22×C1311yescharacteristic
549#556C22×C1312yes—
550#555—21no—
551#555C22×C1311yescharacteristic
552#552—22no—
553#552C22×C1312yes—
554D4×Q8C22×C1311yescharacteristic
555D4×Q8C22×C1312yes—
556D4×Q8C22×C1311yescharacteristic
557#548C22×C1312yes—
558#542—22no—
559#542C22×C1312yes—
560#541—22no—
561#541C22×C1312yes—
562#533—21no—
563#533—21no—
564#533C22×C1311yescharacteristic
565#533C22×C1311yescharacteristic
566#529—21no—
567#529—21no—
568#529C22×C1311yescharacteristic
569#519C22×C1312yes—
570#519C22×C1312yes—
571C4×#41C22×C1311yescharacteristic
572C2×C4×Q8C22×C1311yescharacteristic
573#501C22×C1312yes—
574#498C22×C1311yescharacteristic
575#497C22×C1312yes—
576#494C22×C1311yescharacteristic
577#488C22×C1312yes—
578#487C22×C1312yes—
579#487C22×C1311yescharacteristic
580#487C22×C1311yescharacteristic
581#485C22×C1312yes—
582#485C22×C1312yes—
583#485C22×C1312yes—
584#485C22×C1312yes—
585#484C22×C1312yes—
586#482C22×C1312yes—
587#479C22×C1312yes—
588#479C22×C1312yes—
589#477C22×C1311yescharacteristic
590#477C22×C1311yescharacteristic
591#477C22×C1312yes—
592#475C22×C1311yescharacteristic
593#475C22×C1312yes—
594#474C22×C1311yescharacteristic
595#470C22×C1312yes—
596#470C22×C1312yes—
597#470C22×C1312yes—
598#468C22×C1312yes—
599#467C22×C1312yes—
600#465C22×C1312yes—
601#464C22×C1312yes—
602#464C22×C1312yes—
603#462C22×C1311yescharacteristic
604#462C22×C1312yes—
605#462C22×C1311yescharacteristic
606#462C22×C1311yescharacteristic
607#462C22×C1312yes—
608#461C22×C1311yescharacteristic
609#452C22×C1312yes—
610#451C22×C1312yes—
611#451C22×C1312yes—
612#451C22×C1312yes—
613#451C22×C1312yes—
614#448C22×C1312yes—
615#446C22×C1311yescharacteristic
616C8×Q8C22×C1311yescharacteristic
617#441C22×C1312yes—
618#441C22×C1312yes—
619#441C22×C1311yescharacteristic
620#441C22×C1312yes—
621#441C22×C1312yes—
622#441C22×C1311yescharacteristic
623#440C22×C1311yescharacteristic
624#440C22×C1311yescharacteristic
625C4×Q16C22×C1311yescharacteristic
626C4×Q16C22×C1312yes—
627C4×Q16C22×C1312yes—
628C4×Q16C22×C1312yes—
629C4×Q16C22×C1312yes—
630C4×Q16C22×C1312yes—
631C4×Q16C22×C1311yescharacteristic
632C4×SD16C22×C1311yescharacteristic
633C4×SD16C22×C1311yescharacteristic
634C4×SD16C22×C1312yes—
635#436C22×C1311yescharacteristic
636#436C22×C1312yes—
637#435C22×C1312yes—
638C8×D4C22×C1311yescharacteristic
639#433C22×C1312yes—
640#431C22×C1311yescharacteristic
641#428C22×C1311yescharacteristic
642#427C22×C1312yes—
643#419C22×C1311yescharacteristic
644#419C22×C1312yes—
645#419C22×C1312yes—
646#417C22×C1311yescharacteristic
647#405C22×C1312yes—
648C4×M16C22×C1311yescharacteristic
649C22×C13—21no—
650C22×C13—22no—
651C22×C13—22no—
652C22×C13—21no—
653C22×C13—21no—
654C22×C13—22no—
655C22×C13—41no—
656C22×C13—41no—
657C22×C13—41no—
658C22×C13C23×D411yescharacteristic
659C4×C13—21no—
660C4×C13—21no—
661C4×C13—22no—
662C4×C13—21no—
663C4×C13—22no—
664C4×C13—22no—
665C4×C13—22no—
666C4×C13—21no—
667C4×C13—22no—
668C4×C13—41no—
669C4×C13—41no—
670C4×C13—41no—
671C4×C13—42no—
672C4×C13—42no—
673C4×C13—41no—
674C4×C13—42no—
675C4×C13—41no—
676C4×C13—42no—
677C4×C13#57812yes—
678C4×C13C22×#4111yescharacteristic
679C4×C13#58511yescharacteristic
680C2×#41C23×C1311yescharacteristic
681C22×Q8C23×C1311yescharacteristic
682C22×Q8C23×C1312yes—
683C22×Q8C23×C1312yes—
684#137—24no—
685C2×Q16—28no—
686C2×Q16C23×C1312yes—
687C2×Q16C23×C1312yes—
688C2×Q16C23×C1312yes—
689C2×Q16C23×C1311yescharacteristic
690C2×Q16C23×C1312yes—
691C2×Q16C23×C1312yes—
692C2×Q16C23×C1311yescharacteristic
693C2×SD16C23×C1311yescharacteristic
694C2×SD16C23×C1311yescharacteristic
695C2×SD16C23×C1312yes—
696C2×M16C23×C1311yescharacteristic
697C2×M16C23×C1311yescharacteristic
698C2×M16C23×C1312yes—
699C22×C8C23×C1312yes—
700C4⋊Q8—21no—
701C4⋊Q8—21no—
702C4⋊Q8—21no—
703C4⋊Q8—21no—
704C4⋊Q8—22no—
705C4⋊Q8—22no—
706C4⋊Q8C23×C1311yescharacteristic
707C4⋊Q8C23×C1311yescharacteristic
708C4⋊Q8C23×C1312yes—
709C4⋊Q8C23×C1311yescharacteristic
710C4⋊Q8C23×C1311yescharacteristic
711C4⋊Q8C23×C1312yes—
712#126—22no—
713#126—22no—
714#126—22no—
715#126—22no—
716#126—22no—
717#126—22no—
718#126—22no—
719#126—22no—
720#126D4×C1312yes—
721#125—21no—
722#125—22no—
723#125—22no—
724#125—22no—
725#125—22no—
726#125—22no—
727#125—21no—
728#125—21no—
729#125D4×C1311yescharacteristic
730#125C23×C1312yes—
731#124—21no—
732#124—22no—
733#124—22no—
734#124—22no—
735#124—22no—
736#124D4×C1311yescharacteristic
737#124C23×C1312yes—
738#123—22no—
739#123—22no—
740#123D4×C1312yes—
741C22⋊Q8—21no—
742C22⋊Q8—21no—
743C22⋊Q8—21no—
744C22⋊Q8—22no—
745C22⋊Q8—22no—
746C22⋊Q8—22no—
747C22⋊Q8—22no—
748C22⋊Q8—22no—
749C22⋊Q8—22no—
750C22⋊Q8D4×C1311yescharacteristic
751C22⋊Q8C23×C1312yes—
752C22⋊Q8C23×C1312yes—
753C22⋊Q8C23×C1312yes—
754C22⋊Q8C23×C1312yes—
755C22⋊Q8C23×C1312yes—
756#121—21no—
757#121—22no—
758#121D4×C1311yescharacteristic
759#121C23×C1312yes—
760C4×Q8—21no—
761C4×Q8—21no—
762C4×Q8—22no—
763C4×Q8—22no—
764C4×Q8—22no—
765C4×Q8—22no—
766C4×Q8—21no—
767C4×Q8—22no—
768C4×Q8—21no—
769C4×Q8—21no—
770C4×Q8—21no—
771C4×Q8—21no—
772C4×Q8—21no—
773C4×Q8C23×C1311yescharacteristic
774C4×Q8C23×C1311yescharacteristic
775C4×Q8C23×C1311yescharacteristic
776C4×Q8C23×C1311yescharacteristic
777C4×Q8C23×C1311yescharacteristic
778C4×Q8C23×C1311yescharacteristic
779C4×Q8C23×C1312yes—
780C4×Q8C23×C1312yes—
781C4×Q8C23×C1312yes—
782C4×Q8C23×C1312yes—
783C4×Q8C23×C1312yes—
784C4×Q8C23×C1312yes—
785C4×Q8C23×C1311yescharacteristic
786C4×D4—22no—
787C4×D4—21no—
788C4×D4—21no—
789C4×D4—21no—
790C4×D4—21no—
791C4×D4—22no—
792C4×D4C23×C1311yescharacteristic
793C4×D4C23×C1311yescharacteristic
794C4×D4C23×C1312yes—
795C4×D4C23×C1311yescharacteristic
796#117—21no—
797#117—21no—
798#117—21no—
799#117—21no—
800#117—22no—
801#117—22no—
802#117—22no—
803#117—22no—
804#117—22no—
805#117—21no—
806#117C23×C1311yescharacteristic
807#117C23×C1312yes—
808#117C23×C1312yes—
809#117C23×C1312yes—
810C2×C4⋊C4—21no—
811C2×C4⋊C4C23×C1311yescharacteristic
812C2×C42—21no—
813C2×C42—21no—
814C2×C42C23×C1311yescharacteristic
815#107C23×C1312yes—
816#107C23×C1312yes—
817#107C23×C1311yescharacteristic
818#107C23×C1311yescharacteristic
819#107C23×C1312yes—
820#106C23×C1311yescharacteristic
821#106C23×C1312yes—
822#106C23×C1311yescharacteristic
823#106C23×C1312yes—
824#106C23×C1312yes—
825C4⋊C8C23×C1311yescharacteristic
826C4⋊C8C23×C1311yescharacteristic
827C4⋊C8C23×C1312yes—
828C4⋊C8C23×C1312yes—
829#103C23×C1311yescharacteristic
830#103C23×C1311yescharacteristic
831#103C23×C1311yescharacteristic
832#103C23×C1311yescharacteristic
833#103C23×C1311yescharacteristic
834#103C23×C1311yescharacteristic
835#103C23×C1312yes—
836#103C23×C1312yes—
837#103C23×C1312yes—
838#103C23×C1312yes—
839#103C23×C1312yes—
840#103C23×C1312yes—
841#103C23×C1312yes—
842#103C23×C1312yes—
843#103C23×C1312yes—
844#103C23×C1312yes—
845#103C23×C1312yes—
846#102C23×C1311yescharacteristic
847#102C23×C1311yescharacteristic
848#102C23×C1312yes—
849C22⋊C8C23×C1312yes—
850C22⋊C8C23×C1312yes—
851C22⋊C8C23×C1312yes—
852#97C23×C1311yescharacteristic
853#97C23×C1311yescharacteristic
854#97C23×C1312yes—
855C4×C8C23×C1311yescharacteristic
856C4×C8C23×C1311yescharacteristic
857C4×C8C23×C1312yes—
858C4×C8C23×C1312yes—
859C2×C13—41no—
860C2×C13—42no—
861C2×C13—81no—
862C2×C13D4×#4111yescharacteristic
863C2×C13C2×#57811yescharacteristic
864C2×C13#358611yescharacteristic
865#41—22no—
866#41—41no—
867C2×Q8—21no—
868C2×Q8—22no—
869C2×Q8—22no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—22no—
873C2×Q8—24no—
874C2×Q8—24no—
875C2×Q8—22no—
876C2×Q8—42no—
877C2×Q8—42no—
878C2×Q8—41no—
879C2×Q8C2×D4×C1311yescharacteristic
880C2×Q8C24×C1312yes—
881C2×Q8C24×C1311yescharacteristic
882C2×Q8C24×C1312yes—
883C2×Q8C24×C1311yescharacteristic
884C2×Q8C24×C1311yescharacteristic
885C2×D4—21no—
886C2×D4—22no—
887C2×D4C2×D4×C1311yescharacteristic
888C2×D4C2×D4×C1312yes—
889C2×D4C24×C1311yescharacteristic
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4C2×D4×C1311yescharacteristic
898C22×C4C2×D4×C1311yescharacteristic
899C22×C4C24×C1311yescharacteristic
900C22×C4C24×C1312yes—
901Q16—24no—
902Q16—24no—
903Q16—22no—
904Q16—24no—
905Q16—42no—
906Q16—42no—
907Q16C13×#4114yes—
908SD16—22no—
909SD16—22no—
910SD16—42no—
911M16—22no—
912M16—42no—
913M16—41no—
914C2×C8—24no—
915C2×C8C24×C1311yescharacteristic
916C2×C8C24×C1312yes—
917C2×C8C24×C1311yescharacteristic
918C2×C8C24×C1311yescharacteristic
919C2×C8C24×C1312yes—
920C2×C8C24×C1311yescharacteristic
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—22no—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—21no—
937C4⋊C4—22no—
938C4⋊C4—21no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—21no—
942C4⋊C4—22no—
943C4⋊C4—21no—
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—22no—
950C4⋊C4C2×D4×C1311yescharacteristic
951C4⋊C4C2×D4×C1311yescharacteristic
952C4⋊C4C2×D4×C1312yes—
953C4⋊C4C2×D4×C1312yes—
954C4⋊C4C2×D4×C1312yes—
955C4⋊C4C2×D4×C1312yes—
956C4⋊C4C24×C1312yes—
957C4⋊C4C24×C1311yescharacteristic
958C4⋊C4C24×C1311yescharacteristic
959C4⋊C4C24×C1311yescharacteristic
960C4⋊C4C24×C1311yescharacteristic
961C4⋊C4C24×C1312yes—
962C22⋊C4—22no—
963C22⋊C4—22no—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—21no—
967C22⋊C4—22no—
968C22⋊C4—22no—
969C22⋊C4—22no—
970C22⋊C4—21no—
971C22⋊C4—21no—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4C2×D4×C1312yes—
976C22⋊C4C2×D4×C1312yes—
977C22⋊C4C2×D4×C1312yes—
978C22⋊C4C2×D4×C1312yes—
979C22⋊C4C2×D4×C1312yes—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—22no—
988C42—22no—
989C42—22no—
990C42—22no—
991C42—22no—
992C42—22no—
993C42—22no—
994C42—22no—
995C42C2×D4×C1311yescharacteristic
996C42C2×D4×C1311yescharacteristic
997C42C24×C1311yescharacteristic
998C42C24×C1311yescharacteristic
999C42C24×C1312yes—
1000C13#6154411yescharacteristic, direct product factor, Sylow
1001C23—21no—
1002C23C22×D4×C1312yes—
1003C23C22×D4×C1311yescharacteristic
1004Q8—22no—
1005Q8—21no—
1006Q8—21no—
1007Q8—21no—
1008Q8—22no—
1009Q8—22no—
1010Q8—22no—
1011Q8—22no—
1012Q8—21no—
1013Q8—42no—
1014Q8—44no—
1015Q8—44no—
1016Q8—42no—
1017Q8—81no—
1018Q8—82no—
1019Q8C2×C13×#4112yes—
1020Q8C2×C13×#4112yes—
1021D4—22no—
1022D4—21no—
1023D4—21no—
1024D4—42no—
1025D4—42no—
1026D4—82no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—41no—
1044C2×C4—42no—
1045C2×C4—44no—
1046C2×C4—44no—
1047C2×C4—42no—
1048C2×C4—42no—
1049C2×C4—42no—
1050C2×C4—81no—
1051C2×C4C22×D4×C1311yescharacteristic
1052C2×C4C22×D4×C1311yescharacteristic
1053C2×C4C22×D4×C1312yes—
1054C2×C4C22×D4×C1312yes—
1055C2×C4C22×D4×C1312yes—
1056C2×C4C22×D4×C1311yescharacteristic
1057C2×C4C22×D4×C1311yescharacteristic
1058C2×C4C22×D4×C1311yescharacteristic
1059C2×C4C25×C1311yescharacteristic
1060C8—22no—
1061C8—21no—
1062C8—21no—
1063C8—22no—
1064C8—21no—
1065C8C2×C13×#4112yes—
1066C22—21no—
1067C22—22no—
1068C22—21no—
1069C22—22no—
1070C22—22no—
1071C22—21no—
1072C22—41no—
1073C22—41no—
1074C22—41no—
1075C22C23×D4×C1311yescharacteristic
1076C4—21no—
1077C4—22no—
1078C4—21no—
1079C4—21no—
1080C4—22no—
1081C4—21no—
1082C4—22no—
1083C4—22no—
1084C4—22no—
1085C4—41no—
1086C4—42no—
1087C4—41no—
1088C4—41no—
1089C4—41no—
1090C4—42no—
1091C4—42no—
1092C4—41no—
1093C4—42no—
1094C4C13×#57812yes—
1095C4C22×C13×#4111yescharacteristic
1096C4C13×#58511yescharacteristic
1097C2—41no—
1098C2—42no—
1099C2—81no—
1100C2D4×C13×#4111yescharacteristic
1101C2C2×C13×#57811yescharacteristic
1102C2C13×#358611yescharacteristic
subgroupG/H
center, socleC22×C13C23×D4
commutator, Frattini, cosocleC2×C4C25×C13
prime radicalC13×#3518C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C13×#529 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3523C2semidirect
3. C13×#3398C2semidirect
4. C13×#3387C2semidirect
5. C13×#3364C2semidirect
6. C13×#3363C2semidirect
7. C13×#3349C2semidirect
8. C13×#3340C2semidirect
9. C13×#3329C2semidirect
10. C13×#3328C2semidirect
11. C13×#3328C2semidirect
12. C13×#3327C2semidirect
13. D4×C13×Q16C2semidirect
14. C13×#3270C2semidirect
15. C13×#3185C2semidirect
16. C13×#3178C2semidirect
17. C13×#3127C2semidirect
18. C13×#3121C2semidirect
19. C13×#3107C2semidirect
20. C13×#3104C2semidirect
21. C13×#2969C2semidirect
22. C13×#2950C2semidirect
23. C4×C13×#137C2semidirect
314. #61544C13direct (N × H)
450. #3523C2×C13semidirect
452. #3398C2×C13semidirect
453. #3387C2×C13semidirect
454. #3364C2×C13semidirect
455. #3363C2×C13semidirect
456. #3349C2×C13semidirect
457. #3340C2×C13semidirect
458. #3329C2×C13semidirect
459. #3328C2×C13semidirect
460. #3328C2×C13semidirect
461. #3327C2×C13semidirect
462. D4×Q16C2×C13semidirect
463. #3270C2×C13semidirect
464. #3185C2×C13semidirect
465. #3178C2×C13semidirect
466. #3127C2×C13semidirect
467. #3121C2×C13semidirect
468. #3107C2×C13semidirect
469. #3104C2×C13semidirect
470. #2969C2×C13semidirect
471. #2950C2×C13semidirect
472. C4×#137C2×C13semidirect
1000. C13#61544direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35232
C13×#35182
C13×#33982
C13×#33872
C13×#33642
C13×#33632
C13×#33492
C13×#33402
C13×#33292
C13×#33282
C13×#33272
D4×C13×Q162
C13×#32702
C13×#31852
C13×#31782
C13×#31272
C13×#31212
C13×#31072
C13×#31042
C13×#29692
C13×#29502
C4×C13×#1372
#6154413