Finite Group Databasebeta

← C13×#62609 #15748948

Subgroups — C13×#62609 #15748948

Order 3328.

1702 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3552C211yesmaximal, characteristic, complemented
2C13×#3547C211yesmaximal, characteristic, complemented
3C13×#3372C211yesmaximal, characteristic, complemented
4C13×#3367C211yesmaximal, characteristic, complemented
5C13×#3360C211yesmaximal, characteristic, complemented
6C13×#3359C211yesmaximal, characteristic, complemented
7C13×#3330C211yesmaximal, characteristic, complemented
8C13×#3329C212yesmaximal, complemented
9C13×#3329C211yesmaximal, characteristic, complemented
10C13×#3326C212yesmaximal, complemented
11C13×#3321C212yesmaximal, complemented
12C13×#3320C212yesmaximal, complemented
13C13×#3303C211yesmaximal, characteristic, complemented
14C13×#3298C211yesmaximal, characteristic, complemented
15C13×#3242C212yesmaximal, complemented
16C13×#3233C211yesmaximal, characteristic, complemented
17C13×#3221C212yesmaximal, complemented
18C13×#3206C211yesmaximal, characteristic, complemented
19C13×#3174C212yesmaximal, complemented
20C13×#3171C211yesmaximal, characteristic, complemented
21C13×#3139C211yesmaximal, characteristic, complemented
22C13×#3137C212yesmaximal, complemented
23C13×#2969C211yesmaximal, characteristic, complemented
24C13×#563—22no—
25C13×#562—22no—
26C13×#557C2211yescharacteristic
27C13×#556C2211yescharacteristic
28C13×#555C2211yescharacteristic
29C13×#555C2212yes—
30C13×#554—21no—
31C13×#554C2211yescharacteristic
32C13×#553—21no—
33C13×#553C2212yes—
34C13×#552—21no—
35D4×Q8×C13C2211yescharacteristic
36D4×Q8×C13C2212yes—
37D4×Q8×C13C2211yescharacteristic
38C13×#548—21no—
39C13×#548C2212yes—
40C13×#547C2211yescharacteristic
41C13×#547C2211yescharacteristic
42C13×#544—21no—
43C13×#544C2212yes—
44C13×#542—22no—
45C13×#542—21no—
46C13×#541C2212yes—
47C13×#540C2212yes—
48C13×#539—22no—
49C13×#537—21no—
50C13×#536—21no—
51C13×#536C2212yes—
52C13×#533C2211yescharacteristic
53C13×#532C2211yescharacteristic
54C2×C13×C4⋊Q8C2211yescharacteristic
55C13×#529C2211yescharacteristic
56C13×#529C2211yescharacteristic
57C13×#501C2211yescharacteristic
58C13×#499C2212yes—
59C13×#496C2211yescharacteristic
60C13×#492C2212yes—
61C13×#491C2212yes—
62C13×#491C2212yes—
63C13×#491C2212yes—
64C13×#490C2211yescharacteristic
65C13×#489C2212yes—
66C13×#489C2211yescharacteristic
67C13×#488C2212yes—
68C13×#488C2212yes—
69C13×#487C2211yescharacteristic
70C13×#487C2211yescharacteristic
71C13×#487C2212yes—
72C13×#487C2211yescharacteristic
73C13×#487C2211yescharacteristic
74C13×#487C2212yes—
75C13×#485C2212yes—
76C13×#485C2212yes—
77C13×#485C2212yes—
78C13×#484C2212yes—
79C13×#483C2212yes—
80C13×#482C2212yes—
81C13×#479C2212yes—
82C13×#479C2212yes—
83C13×#477C2212yes—
84C13×#477C2211yescharacteristic
85C13×#476C2211yescharacteristic
86C13×#475C2211yescharacteristic
87C13×#475C2212yes—
88C13×#474C2211yescharacteristic
89C13×#469C2211yescharacteristic
90C13×#469C2211yescharacteristic
91C13×#468C2211yescharacteristic
92C13×#468C2212yes—
93C13×#468C2211yescharacteristic
94C13×#468C2212yes—
95C13×#465C2212yes—
96C13×#465C2212yes—
97C13×#463C2212yes—
98C13×#463C2212yes—
99C13×#461C2211yescharacteristic
100C13×#461C2211yescharacteristic
101C13×#461C2212yes—
102C13×#461C2211yescharacteristic
103C13×#461C2212yes—
104C13×#461C2211yescharacteristic
105C13×#449C2212yes—
106C13×#449C2212yes—
107C13×#448C2212yes—
108C13×#448C2212yes—
109C13×#448C2212yes—
110C13×#448C2212yes—
111C13×#446C2211yescharacteristic
112C8×Q8×C13C2211yescharacteristic
113C13×#440C2212yes—
114C13×#440C2212yes—
115C4×C13×SD16C2211yescharacteristic
116C4×C13×SD16C2212yes—
117C4×C13×SD16C2211yescharacteristic
118C4×C13×SD16C2212yes—
119C4×C13×D8C2211yescharacteristic
120C4×C13×D8C2211yescharacteristic
121C13×#436C2212yes—
122C13×#436C2211yescharacteristic
123C13×#435C2212yes—
124C8×D4×C13C2211yescharacteristic
125C13×#433C2212yes—
126C13×#431C2211yescharacteristic
127C13×#419C2212yes—
128C13×#419C2212yes—
129C13×#419C2212yes—
130C13×#417C2212yes—
131C13×#416C2212yes—
132C2×C13×#103C2212yes—
133C13×#405C2212yes—
134C4×C13×M16C2211yescharacteristic
135C2×C13×#41—21no—
136C2×C13×#41—21no—
137C2×C13×#41C2312yes—
138C22×Q8×C13—21no—
139C22×Q8×C13C2312yes—
140C22×Q8×C13C2312yes—
141C2×C13×SD16C2311yescharacteristic
142C2×C13×SD16C2311yescharacteristic
143C2×C13×SD16C2312yes—
144C2×C13×SD16C2312yes—
145C2×C13×SD16C2312yes—
146C2×C13×SD16C2312yes—
147C2×C13×D8C2311yescharacteristic
148C2×C13×D8C2311yescharacteristic
149C2×C13×M16C2311yescharacteristic
150C2×C13×M16C2311yescharacteristic
151C2×C13×M16C2312yes—
152C22×C8×C13C2312yes—
153C13×C4⋊Q8—22no—
154C13×C4⋊Q8—21no—
155C13×C4⋊Q8—22no—
156C13×C4⋊Q8—21no—
157C13×C4⋊Q8—21no—
158C13×C4⋊Q8C2311yescharacteristic
159C13×C4⋊Q8C2311yescharacteristic
160C13×C4⋊Q8C2312yes—
161C13×C4⋊Q8C2312yes—
162C13×C4⋊Q8C2311yescharacteristic
163C13×C4⋊Q8C2312yes—
164C13×C4⋊Q8C2311yescharacteristic
165C13×C4⋊Q8C2311yescharacteristic
166C13×#127C2311yescharacteristic
167C13×#126—22no—
168C13×#126—22no—
169C13×#126—22no—
170C13×#126—22no—
171C13×#126—21no—
172C13×#126D412yes—
173C13×#125—22no—
174C13×#125—22no—
175C13×#125—22no—
176C13×#125—21no—
177C13×#125—22no—
178C13×#125D411yescharacteristic
179C13×#125C2312yes—
180C13×#125C2312yes—
181C13×#125C2311yescharacteristic
182C13×#124—22no—
183C13×#124—22no—
184C13×#124—22no—
185C13×#124—22no—
186C13×#124—21no—
187C13×#124D411yescharacteristic
188C13×#124C2312yes—
189C13×#124C2311yescharacteristic
190C13×#123—21no—
191C13×#123—22no—
192C13×#123—22no—
193C13×#123—22no—
194C13×#123—22no—
195C13×#123—22no—
196C13×#123—22no—
197C13×#123—22no—
198C13×#123D412yes—
199C13×C22⋊Q8—21no—
200C13×C22⋊Q8—21no—
201C13×C22⋊Q8—21no—
202C13×C22⋊Q8—21no—
203C13×C22⋊Q8—21no—
204C13×C22⋊Q8—22no—
205C13×C22⋊Q8—22no—
206C13×C22⋊Q8—21no—
207C13×C22⋊Q8—22no—
208C13×C22⋊Q8—22no—
209C13×C22⋊Q8—22no—
210C13×C22⋊Q8—22no—
211C13×C22⋊Q8—22no—
212C13×C22⋊Q8—22no—
213C13×C22⋊Q8—22no—
214C13×C22⋊Q8—22no—
215C13×C22⋊Q8D411yescharacteristic
216C13×C22⋊Q8C2312yes—
217C13×C22⋊Q8C2312yes—
218C13×C22⋊Q8C2311yescharacteristic
219C13×#121—21no—
220C13×#121—22no—
221C13×#121—22no—
222C13×#121—22no—
223C13×#121—21no—
224C13×#121—21no—
225C13×#121—22no—
226C13×#121—22no—
227C13×#121D411yescharacteristic
228C13×#121C2311yescharacteristic
229C13×#121C2311yescharacteristic
230C13×#121C2312yes—
231C13×#121C2312yes—
232C13×#121C2311yescharacteristic
233C4×Q8×C13—21no—
234C4×Q8×C13—21no—
235C4×Q8×C13—21no—
236C4×Q8×C13C2311yescharacteristic
237C4×Q8×C13C2312yes—
238C4×Q8×C13C2312yes—
239C4×Q8×C13C2311yescharacteristic
240C4×D4×C13—22no—
241C4×D4×C13—21no—
242C4×D4×C13—21no—
243C4×D4×C13—22no—
244C4×D4×C13—22no—
245C4×D4×C13—21no—
246C4×D4×C13C2311yescharacteristic
247C4×D4×C13C2311yescharacteristic
248C4×D4×C13C2311yescharacteristic
249C4×D4×C13C2312yes—
250C4×D4×C13C2312yes—
251C4×D4×C13C2311yescharacteristic
252C4×D4×C13C2312yes—
253C13×#117—21no—
254C13×#117—22no—
255C13×#117—21no—
256C13×#117—21no—
257C13×#117C2312yes—
258C13×#117C2312yes—
259C13×#117C2312yes—
260C2×C13×C4⋊C4—21no—
261C2×C13×C4⋊C4—21no—
262C2×C13×C4⋊C4—21no—
263C2×C13×C4⋊C4—21no—
264C2×C13×C4⋊C4C2312yes—
265C2×C42×C13C2311yescharacteristic
266C13×#107C2311yescharacteristic
267C13×#107C2311yescharacteristic
268C13×#107C2312yes—
269C13×#107C2312yes—
270C13×#106C2312yes—
271C13×#106C2312yes—
272C13×#106C2311yescharacteristic
273C13×#106C2311yescharacteristic
274C13×C4⋊C8C2311yescharacteristic
275C13×C4⋊C8C2311yescharacteristic
276C13×C4⋊C8C2312yes—
277C13×C4⋊C8C2312yes—
278C13×#103C2311yescharacteristic
279C13×#103C2312yes—
280C13×#103C2312yes—
281C13×#103C2312yes—
282C13×#103C2312yes—
283C13×#103C2312yes—
284C13×#103C2312yes—
285C13×#103C2312yes—
286C13×#103C2311yescharacteristic
287C13×#103C2312yes—
288C13×#103C2312yes—
289C13×#103C2312yes—
290C13×#103C2312yes—
291C13×#103C2312yes—
292C13×#103C2312yes—
293C13×#103C2312yes—
294C13×#102C2311yescharacteristic
295C13×#102C2312yes—
296C13×#102C2311yescharacteristic
297C13×#102C2312yes—
298C13×#102C2311yescharacteristic
299C13×#102C2311yescharacteristic
300C13×#102C2311yescharacteristic
301C13×#102C2311yescharacteristic
302C13×C22⋊C8C2312yes—
303C13×C22⋊C8C2312yes—
304C13×C22⋊C8C2312yes—
305C13×#97C2311yescharacteristic
306C13×#97C2311yescharacteristic
307C13×#97C2312yes—
308C4×C8×C13C2311yescharacteristic
309C4×C8×C13C2311yescharacteristic
310C4×C8×C13C2312yes—
311C4×C8×C13C2312yes—
312#62609C1311yesmaximal, characteristic, direct product factor, Sylow
313C13×#41—42no—
314C13×#41—42no—
315C13×#41—82no—
316C13×#41—82no—
317C2×Q8×C13—21no—
318C2×Q8×C13—21no—
319C2×Q8×C13—22no—
320C2×Q8×C13—22no—
321C2×Q8×C13—22no—
322C2×Q8×C13—21no—
323C2×Q8×C13—42no—
324C2×Q8×C13—42no—
325C2×Q8×C13—42no—
326C2×Q8×C13—42no—
327C2×Q8×C13—82no—
328C2×Q8×C13C2×D411yescharacteristic
329C2×Q8×C13C2411yescharacteristic
330C2×Q8×C13C2412yes—
331C2×Q8×C13C2412yes—
332C2×D4×C13—21no—
333C2×D4×C13—22no—
334C2×D4×C13—21no—
335C2×D4×C13—22no—
336C2×D4×C13—21no—
337C2×D4×C13—22no—
338C2×D4×C13—21no—
339C2×D4×C13—21no—
340C2×D4×C13C2×D411yescharacteristic
341C2×D4×C13C2×D412yes—
342C2×D4×C13C2411yescharacteristic
343C2×D4×C13C2411yescharacteristic
344C2×D4×C13C2411yescharacteristic
345C22×C4×C13—22no—
346C22×C4×C13—22no—
347C22×C4×C13—22no—
348C22×C4×C13—21no—
349C22×C4×C13—21no—
350C22×C4×C13—21no—
351C22×C4×C13—22no—
352C22×C4×C13—22no—
353C22×C4×C13—22no—
354C22×C4×C13C2×D411yescharacteristic
355C22×C4×C13C2×D411yescharacteristic
356C22×C4×C13C2411yescharacteristic
357C22×C4×C13C2412yes—
358C13×SD16—42no—
359C13×SD16—42no—
360C13×SD16—41no—
361C13×SD16—41no—
362C13×SD16—42no—
363C13×SD16—42no—
364C13×D8—41no—
365C13×D8—41no—
366C13×M16—41no—
367C13×M16—41no—
368C13×M16—42no—
369C2×C8×C13—42no—
370C2×C8×C13C2411yescharacteristic
371C2×C8×C13C2412yes—
372C2×C8×C13C2411yescharacteristic
373C2×C8×C13C2412yes—
374C2×C8×C13C2411yescharacteristic
375C2×C8×C13C2411yescharacteristic
376C13×C4⋊C4—21no—
377C13×C4⋊C4—21no—
378C13×C4⋊C4—21no—
379C13×C4⋊C4—22no—
380C13×C4⋊C4—21no—
381C13×C4⋊C4—22no—
382C13×C4⋊C4—22no—
383C13×C4⋊C4—22no—
384C13×C4⋊C4—21no—
385C13×C4⋊C4—22no—
386C13×C4⋊C4—22no—
387C13×C4⋊C4—21no—
388C13×C4⋊C4—21no—
389C13×C4⋊C4—21no—
390C13×C4⋊C4—22no—
391C13×C4⋊C4—22no—
392C13×C4⋊C4—22no—
393C13×C4⋊C4—21no—
394C13×C4⋊C4—22no—
395C13×C4⋊C4—22no—
396C13×C4⋊C4—21no—
397C13×C4⋊C4—22no—
398C13×C4⋊C4—22no—
399C13×C4⋊C4—22no—
400C13×C4⋊C4—21no—
401C13×C4⋊C4C2×D411yescharacteristic
402C13×C4⋊C4C2×D411yescharacteristic
403C13×C4⋊C4C2×D412yes—
404C13×C4⋊C4C2×D412yes—
405C13×C4⋊C4C2×D412yes—
406C13×C4⋊C4C2×D412yes—
407C13×C4⋊C4C2411yescharacteristic
408C13×C4⋊C4C2411yescharacteristic
409C13×C4⋊C4C2411yescharacteristic
410C13×C4⋊C4C2412yes—
411C13×C4⋊C4C2412yes—
412C13×C4⋊C4C2411yescharacteristic
413C13×C22⋊C4—22no—
414C13×C22⋊C4—22no—
415C13×C22⋊C4—21no—
416C13×C22⋊C4—22no—
417C13×C22⋊C4—22no—
418C13×C22⋊C4—21no—
419C13×C22⋊C4—22no—
420C13×C22⋊C4—21no—
421C13×C22⋊C4—22no—
422C13×C22⋊C4—22no—
423C13×C22⋊C4—21no—
424C13×C22⋊C4—21no—
425C13×C22⋊C4—21no—
426C13×C22⋊C4—22no—
427C13×C22⋊C4—22no—
428C13×C22⋊C4—21no—
429C13×C22⋊C4—22no—
430C13×C22⋊C4—21no—
431C13×C22⋊C4—21no—
432C13×C22⋊C4C2×D412yes—
433C13×C22⋊C4C2×D412yes—
434C13×C22⋊C4C2×D412yes—
435C13×C22⋊C4C2×D412yes—
436C13×C22⋊C4C2×D412yes—
437C42×C13—22no—
438C42×C13—22no—
439C42×C13—21no—
440C42×C13—22no—
441C42×C13—22no—
442C42×C13C2×D411yescharacteristic
443C42×C13C2×D411yescharacteristic
444C42×C13C2411yescharacteristic
445C42×C13C2411yescharacteristic
446C42×C13C2412yes—
447#3552C2×C1311yescharacteristic, complemented
448#3547C2×C1311yescharacteristic, complemented
449#3372C2×C1311yescharacteristic, complemented
450#3367C2×C1311yescharacteristic, complemented
451#3360C2×C1311yescharacteristic, complemented
452#3359C2×C1311yescharacteristic, complemented
453#3330C2×C1311yescharacteristic, complemented
454#3329C2×C1311yescharacteristic, complemented
455#3329C2×C1312yescomplemented
456#3326C2×C1312yescomplemented
457#3321C2×C1312yescomplemented
458#3320C2×C1312yescomplemented
459#3303C2×C1311yescharacteristic, complemented
460#3298C2×C1311yescharacteristic, complemented
461#3242C2×C1312yescomplemented
462#3233C2×C1311yescharacteristic, complemented
463#3221C2×C1312yescomplemented
464#3206C2×C1311yescharacteristic, complemented
465#3174C2×C1312yescomplemented
466#3171C2×C1311yescharacteristic, complemented
467#3139C2×C1311yescharacteristic, complemented
468#3137C2×C1312yescomplemented
469#2969C2×C1311yescharacteristic, complemented
470C23×C13—21no—
471C23×C13—21no—
472C23×C13—21no—
473C23×C13C22×D412yes—
474C23×C13C22×D411yescharacteristic
475Q8×C13—22no—
476Q8×C13—22no—
477Q8×C13—21no—
478Q8×C13—21no—
479Q8×C13—22no—
480Q8×C13—22no—
481Q8×C13—22no—
482Q8×C13—42no—
483Q8×C13—81no—
484Q8×C13—82no—
485Q8×C13—82no—
486Q8×C13—82no—
487Q8×C13—81no—
488D4×C13—22no—
489D4×C13—21no—
490D4×C13—21no—
491D4×C13—21no—
492D4×C13—21no—
493D4×C13—21no—
494D4×C13—21no—
495D4×C13—42no—
496D4×C13—42no—
497D4×C13—81no—
498D4×C13—81no—
499D4×C13—82no—
500D4×C13—82no—
501D4×C13—81no—
502D4×C13—81no—
503D4×C13—82no—
504C2×C4×C13—22no—
505C2×C4×C13—22no—
506C2×C4×C13—21no—
507C2×C4×C13—21no—
508C2×C4×C13—22no—
509C2×C4×C13—21no—
510C2×C4×C13—21no—
511C2×C4×C13—22no—
512C2×C4×C13—21no—
513C2×C4×C13—21no—
514C2×C4×C13—22no—
515C2×C4×C13—22no—
516C2×C4×C13—22no—
517C2×C4×C13—21no—
518C2×C4×C13—41no—
519C2×C4×C13—42no—
520C2×C4×C13—42no—
521C2×C4×C13—42no—
522C2×C4×C13—82no—
523C2×C4×C13—82no—
524C2×C4×C13—82no—
525C2×C4×C13—82no—
526C2×C4×C13—82no—
527C2×C4×C13—82no—
528C2×C4×C13C22×D411yescharacteristic
529C2×C4×C13C22×D412yes—
530C2×C4×C13C22×D412yes—
531C2×C4×C13C22×D412yes—
532C2×C4×C13C22×D411yescharacteristic
533C2×C4×C13C22×D411yescharacteristic
534C2×C4×C13C22×D411yescharacteristic
535C2×C4×C13C22×D411yescharacteristic
536C2×C4×C13C2511yescharacteristic
537C8×C13—21no—
538C8×C13—22no—
539C8×C13—21no—
540C8×C13—21no—
541C8×C13—21no—
542C8×C13—22no—
543#563—22no—
544#562—22no—
545#557C22×C1311yescharacteristic
546#556C22×C1311yescharacteristic
547#555C22×C1311yescharacteristic
548#555C22×C1312yes—
549#554—21no—
550#554C22×C1311yescharacteristic
551#553—21no—
552#553C22×C1312yes—
553#552—21no—
554D4×Q8C22×C1311yescharacteristic
555D4×Q8C22×C1312yes—
556D4×Q8C22×C1311yescharacteristic
557#548—21no—
558#548C22×C1312yes—
559#547C22×C1311yescharacteristic
560#547C22×C1311yescharacteristic
561#544—21no—
562#544C22×C1312yes—
563#542—22no—
564#542—21no—
565#541C22×C1312yes—
566#540C22×C1312yes—
567#539—22no—
568#537—21no—
569#536—21no—
570#536C22×C1312yes—
571#533C22×C1311yescharacteristic
572#532C22×C1311yescharacteristic
573C2×C4⋊Q8C22×C1311yescharacteristic
574#529C22×C1311yescharacteristic
575#529C22×C1311yescharacteristic
576#501C22×C1311yescharacteristic
577#499C22×C1312yes—
578#496C22×C1311yescharacteristic
579#492C22×C1312yes—
580#491C22×C1312yes—
581#491C22×C1312yes—
582#491C22×C1312yes—
583#490C22×C1311yescharacteristic
584#489C22×C1312yes—
585#489C22×C1311yescharacteristic
586#488C22×C1312yes—
587#488C22×C1312yes—
588#487C22×C1312yes—
589#487C22×C1311yescharacteristic
590#487C22×C1311yescharacteristic
591#487C22×C1311yescharacteristic
592#487C22×C1311yescharacteristic
593#487C22×C1312yes—
594#485C22×C1312yes—
595#485C22×C1312yes—
596#485C22×C1312yes—
597#484C22×C1312yes—
598#483C22×C1312yes—
599#482C22×C1312yes—
600#479C22×C1312yes—
601#479C22×C1312yes—
602#477C22×C1312yes—
603#477C22×C1311yescharacteristic
604#476C22×C1311yescharacteristic
605#475C22×C1311yescharacteristic
606#475C22×C1312yes—
607#474C22×C1311yescharacteristic
608#469C22×C1311yescharacteristic
609#469C22×C1311yescharacteristic
610#468C22×C1311yescharacteristic
611#468C22×C1312yes—
612#468C22×C1312yes—
613#468C22×C1311yescharacteristic
614#465C22×C1312yes—
615#465C22×C1312yes—
616#463C22×C1312yes—
617#463C22×C1312yes—
618#461C22×C1311yescharacteristic
619#461C22×C1312yes—
620#461C22×C1311yescharacteristic
621#461C22×C1311yescharacteristic
622#461C22×C1312yes—
623#461C22×C1311yescharacteristic
624#449C22×C1312yes—
625#449C22×C1312yes—
626#448C22×C1312yes—
627#448C22×C1312yes—
628#448C22×C1312yes—
629#448C22×C1312yes—
630#446C22×C1311yescharacteristic
631C8×Q8C22×C1311yescharacteristic
632#440C22×C1312yes—
633#440C22×C1312yes—
634C4×SD16C22×C1311yescharacteristic
635C4×SD16C22×C1312yes—
636C4×SD16C22×C1312yes—
637C4×SD16C22×C1311yescharacteristic
638C4×D8C22×C1311yescharacteristic
639C4×D8C22×C1311yescharacteristic
640#436C22×C1311yescharacteristic
641#436C22×C1312yes—
642#435C22×C1312yes—
643C8×D4C22×C1311yescharacteristic
644#433C22×C1312yes—
645#431C22×C1311yescharacteristic
646#419C22×C1312yes—
647#419C22×C1312yes—
648#419C22×C1312yes—
649#417C22×C1312yes—
650#416C22×C1312yes—
651C2×#103C22×C1312yes—
652#405C22×C1312yes—
653C4×M16C22×C1311yescharacteristic
654C22×C13—21no—
655C22×C13—22no—
656C22×C13—21no—
657C22×C13—22no—
658C22×C13—21no—
659C22×C13—22no—
660C22×C13—41no—
661C22×C13—41no—
662C22×C13—41no—
663C22×C13—41no—
664C22×C13—41no—
665C22×C13—41no—
666C22×C13—41no—
667C22×C13—41no—
668C22×C13—41no—
669C22×C13C23×D411yescharacteristic
670C4×C13—21no—
671C4×C13—21no—
672C4×C13—22no—
673C4×C13—22no—
674C4×C13—21no—
675C4×C13—21no—
676C4×C13—22no—
677C4×C13—42no—
678C4×C13—41no—
679C4×C13—42no—
680C4×C13—41no—
681C4×C13—42no—
682C4×C13—41no—
683C4×C13—41no—
684C4×C13—41no—
685C4×C13—42no—
686C4×C13#57712yes—
687C4×C13#58511yescharacteristic
688C4×C13#58511yescharacteristic
689C2×#41—21no—
690C2×#41—21no—
691C2×#41C23×C1312yes—
692C22×Q8—21no—
693C22×Q8C23×C1312yes—
694C22×Q8C23×C1312yes—
695C2×SD16C23×C1311yescharacteristic
696C2×SD16C23×C1311yescharacteristic
697C2×SD16C23×C1312yes—
698C2×SD16C23×C1312yes—
699C2×SD16C23×C1312yes—
700C2×SD16C23×C1312yes—
701C2×D8C23×C1311yescharacteristic
702C2×D8C23×C1311yescharacteristic
703C2×M16C23×C1311yescharacteristic
704C2×M16C23×C1311yescharacteristic
705C2×M16C23×C1312yes—
706C22×C8C23×C1312yes—
707C4⋊Q8—22no—
708C4⋊Q8—21no—
709C4⋊Q8—22no—
710C4⋊Q8—21no—
711C4⋊Q8—21no—
712C4⋊Q8C23×C1312yes—
713C4⋊Q8C23×C1311yescharacteristic
714C4⋊Q8C23×C1311yescharacteristic
715C4⋊Q8C23×C1312yes—
716C4⋊Q8C23×C1311yescharacteristic
717C4⋊Q8C23×C1311yescharacteristic
718C4⋊Q8C23×C1311yescharacteristic
719C4⋊Q8C23×C1312yes—
720#127C23×C1311yescharacteristic
721#126—22no—
722#126—22no—
723#126—22no—
724#126—22no—
725#126—21no—
726#126D4×C1312yes—
727#125—22no—
728#125—22no—
729#125—22no—
730#125—21no—
731#125—22no—
732#125D4×C1311yescharacteristic
733#125C23×C1311yescharacteristic
734#125C23×C1312yes—
735#125C23×C1312yes—
736#124—22no—
737#124—22no—
738#124—22no—
739#124—22no—
740#124—21no—
741#124D4×C1311yescharacteristic
742#124C23×C1311yescharacteristic
743#124C23×C1312yes—
744#123—21no—
745#123—22no—
746#123—22no—
747#123—22no—
748#123—22no—
749#123—22no—
750#123—22no—
751#123—22no—
752#123D4×C1312yes—
753C22⋊Q8—21no—
754C22⋊Q8—21no—
755C22⋊Q8—21no—
756C22⋊Q8—21no—
757C22⋊Q8—21no—
758C22⋊Q8—22no—
759C22⋊Q8—22no—
760C22⋊Q8—21no—
761C22⋊Q8—22no—
762C22⋊Q8—22no—
763C22⋊Q8—22no—
764C22⋊Q8—22no—
765C22⋊Q8—22no—
766C22⋊Q8—22no—
767C22⋊Q8—22no—
768C22⋊Q8—22no—
769C22⋊Q8D4×C1311yescharacteristic
770C22⋊Q8C23×C1311yescharacteristic
771C22⋊Q8C23×C1312yes—
772C22⋊Q8C23×C1312yes—
773#121—21no—
774#121—22no—
775#121—22no—
776#121—22no—
777#121—21no—
778#121—21no—
779#121—22no—
780#121—22no—
781#121D4×C1311yescharacteristic
782#121C23×C1311yescharacteristic
783#121C23×C1311yescharacteristic
784#121C23×C1311yescharacteristic
785#121C23×C1312yes—
786#121C23×C1312yes—
787C4×Q8—21no—
788C4×Q8—21no—
789C4×Q8—21no—
790C4×Q8C23×C1311yescharacteristic
791C4×Q8C23×C1312yes—
792C4×Q8C23×C1312yes—
793C4×Q8C23×C1311yescharacteristic
794C4×D4—22no—
795C4×D4—21no—
796C4×D4—21no—
797C4×D4—22no—
798C4×D4—22no—
799C4×D4—21no—
800C4×D4C23×C1311yescharacteristic
801C4×D4C23×C1311yescharacteristic
802C4×D4C23×C1311yescharacteristic
803C4×D4C23×C1312yes—
804C4×D4C23×C1312yes—
805C4×D4C23×C1311yescharacteristic
806C4×D4C23×C1312yes—
807#117—21no—
808#117—22no—
809#117—21no—
810#117—21no—
811#117C23×C1312yes—
812#117C23×C1312yes—
813#117C23×C1312yes—
814C2×C4⋊C4—21no—
815C2×C4⋊C4—21no—
816C2×C4⋊C4—21no—
817C2×C4⋊C4—21no—
818C2×C4⋊C4C23×C1312yes—
819C2×C42C23×C1311yescharacteristic
820#107C23×C1311yescharacteristic
821#107C23×C1311yescharacteristic
822#107C23×C1312yes—
823#107C23×C1312yes—
824#106C23×C1312yes—
825#106C23×C1312yes—
826#106C23×C1311yescharacteristic
827#106C23×C1311yescharacteristic
828C4⋊C8C23×C1311yescharacteristic
829C4⋊C8C23×C1311yescharacteristic
830C4⋊C8C23×C1312yes—
831C4⋊C8C23×C1312yes—
832#103C23×C1311yescharacteristic
833#103C23×C1312yes—
834#103C23×C1312yes—
835#103C23×C1312yes—
836#103C23×C1312yes—
837#103C23×C1312yes—
838#103C23×C1312yes—
839#103C23×C1312yes—
840#103C23×C1311yescharacteristic
841#103C23×C1312yes—
842#103C23×C1312yes—
843#103C23×C1312yes—
844#103C23×C1312yes—
845#103C23×C1312yes—
846#103C23×C1312yes—
847#103C23×C1312yes—
848#102C23×C1311yescharacteristic
849#102C23×C1312yes—
850#102C23×C1311yescharacteristic
851#102C23×C1312yes—
852#102C23×C1311yescharacteristic
853#102C23×C1311yescharacteristic
854#102C23×C1311yescharacteristic
855#102C23×C1311yescharacteristic
856C22⋊C8C23×C1312yes—
857C22⋊C8C23×C1312yes—
858C22⋊C8C23×C1312yes—
859#97C23×C1311yescharacteristic
860#97C23×C1311yescharacteristic
861#97C23×C1312yes—
862C4×C8C23×C1311yescharacteristic
863C4×C8C23×C1311yescharacteristic
864C4×C8C23×C1312yes—
865C4×C8C23×C1312yes—
866C2×C13—41no—
867C2×C13—42no—
868C2×C13—81no—
869C2×C13—81no—
870C2×C13—81no—
871C2×C13#350011yescharacteristic
872C2×C13C2×#57711yescharacteristic
873C2×C13#358611yescharacteristic
874#41—42no—
875#41—42no—
876#41—82no—
877#41—82no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—22no—
881C2×Q8—22no—
882C2×Q8—22no—
883C2×Q8—21no—
884C2×Q8—42no—
885C2×Q8—42no—
886C2×Q8—42no—
887C2×Q8—42no—
888C2×Q8—82no—
889C2×Q8C2×D4×C1311yescharacteristic
890C2×Q8C24×C1311yescharacteristic
891C2×Q8C24×C1312yes—
892C2×Q8C24×C1312yes—
893C2×D4—21no—
894C2×D4—22no—
895C2×D4—21no—
896C2×D4—22no—
897C2×D4—21no—
898C2×D4—22no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4C2×D4×C1311yescharacteristic
902C2×D4C2×D4×C1312yes—
903C2×D4C24×C1311yescharacteristic
904C2×D4C24×C1311yescharacteristic
905C2×D4C24×C1311yescharacteristic
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4C2×D4×C1311yescharacteristic
916C22×C4C2×D4×C1311yescharacteristic
917C22×C4C24×C1311yescharacteristic
918C22×C4C24×C1312yes—
919SD16—42no—
920SD16—42no—
921SD16—41no—
922SD16—41no—
923SD16—42no—
924SD16—42no—
925D8—41no—
926D8—41no—
927M16—41no—
928M16—41no—
929M16—42no—
930C2×C8—42no—
931C2×C8C24×C1311yescharacteristic
932C2×C8C24×C1312yes—
933C2×C8C24×C1311yescharacteristic
934C2×C8C24×C1312yes—
935C2×C8C24×C1311yescharacteristic
936C2×C8C24×C1311yescharacteristic
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—22no—
941C4⋊C4—21no—
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—22no—
945C4⋊C4—21no—
946C4⋊C4—22no—
947C4⋊C4—22no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—21no—
955C4⋊C4—22no—
956C4⋊C4—22no—
957C4⋊C4—21no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—21no—
962C4⋊C4C2×D4×C1311yescharacteristic
963C4⋊C4C2×D4×C1311yescharacteristic
964C4⋊C4C2×D4×C1312yes—
965C4⋊C4C2×D4×C1312yes—
966C4⋊C4C2×D4×C1312yes—
967C4⋊C4C2×D4×C1312yes—
968C4⋊C4C24×C1311yescharacteristic
969C4⋊C4C24×C1311yescharacteristic
970C4⋊C4C24×C1311yescharacteristic
971C4⋊C4C24×C1312yes—
972C4⋊C4C24×C1312yes—
973C4⋊C4C24×C1311yescharacteristic
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—21no—
977C22⋊C4—22no—
978C22⋊C4—22no—
979C22⋊C4—21no—
980C22⋊C4—22no—
981C22⋊C4—21no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—21no—
985C22⋊C4—21no—
986C22⋊C4—21no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—21no—
990C22⋊C4—22no—
991C22⋊C4—21no—
992C22⋊C4—21no—
993C22⋊C4C2×D4×C1312yes—
994C22⋊C4C2×D4×C1312yes—
995C22⋊C4C2×D4×C1312yes—
996C22⋊C4C2×D4×C1312yes—
997C22⋊C4C2×D4×C1312yes—
998C42—22no—
999C42—22no—
1000C42—21no—
1001C42—22no—
1002C42—22no—
1003C42C2×D4×C1311yescharacteristic
1004C42C2×D4×C1311yescharacteristic
1005C42C24×C1311yescharacteristic
1006C42C24×C1311yescharacteristic
1007C42C24×C1312yes—
1008C13#6260911yescharacteristic, direct product factor, Sylow
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23C22×D4×C1312yes—
1013C23C22×D4×C1311yescharacteristic
1014Q8—22no—
1015Q8—22no—
1016Q8—21no—
1017Q8—21no—
1018Q8—22no—
1019Q8—22no—
1020Q8—22no—
1021Q8—42no—
1022Q8—82no—
1023Q8—82no—
1024Q8—82no—
1025Q8—81no—
1026Q8—81no—
1027D4—22no—
1028D4—21no—
1029D4—21no—
1030D4—21no—
1031D4—21no—
1032D4—21no—
1033D4—21no—
1034D4—42no—
1035D4—42no—
1036D4—81no—
1037D4—81no—
1038D4—82no—
1039D4—82no—
1040D4—81no—
1041D4—81no—
1042D4—82no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—21no—
1057C2×C4—41no—
1058C2×C4—42no—
1059C2×C4—42no—
1060C2×C4—42no—
1061C2×C4—82no—
1062C2×C4—82no—
1063C2×C4—82no—
1064C2×C4—82no—
1065C2×C4—82no—
1066C2×C4—82no—
1067C2×C4C22×D4×C1311yescharacteristic
1068C2×C4C22×D4×C1312yes—
1069C2×C4C22×D4×C1312yes—
1070C2×C4C22×D4×C1312yes—
1071C2×C4C22×D4×C1311yescharacteristic
1072C2×C4C22×D4×C1311yescharacteristic
1073C2×C4C22×D4×C1311yescharacteristic
1074C2×C4C22×D4×C1311yescharacteristic
1075C2×C4C25×C1311yescharacteristic
1076C8—21no—
1077C8—22no—
1078C8—21no—
1079C8—21no—
1080C8—21no—
1081C8—22no—
1082C22—21no—
1083C22—22no—
1084C22—21no—
1085C22—22no—
1086C22—21no—
1087C22—22no—
1088C22—41no—
1089C22—41no—
1090C22—41no—
1091C22—41no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—41no—
1096C22—41no—
1097C22C23×D4×C1311yescharacteristic
1098C4—21no—
1099C4—22no—
1100C4—21no—
1101C4—21no—
1102C4—22no—
1103C4—22no—
1104C4—21no—
1105C4—41no—
1106C4—41no—
1107C4—41no—
1108C4—42no—
1109C4—42no—
1110C4—41no—
1111C4—42no—
1112C4—41no—
1113C4—42no—
1114C4C13×#57712yes—
1115C4C13×#58511yescharacteristic
1116C4C13×#58511yescharacteristic
1117C2—41no—
1118C2—42no—
1119C2—81no—
1120C2—81no—
1121C2—81no—
1122C2C13×#350011yescharacteristic
1123C2C2×C13×#57711yescharacteristic
1124C2C13×#358611yescharacteristic
subgroupG/H
center, socleC22×C13C23×D4
commutator, Frattini, cosocleC2×C4C25×C13
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×#3552C2semidirect
2. C13×#3547C2semidirect
3. C13×#3372C2semidirect
4. C13×#3367C2semidirect
5. C13×#3360C2semidirect
6. C13×#3359C2semidirect
7. C13×#3330C2semidirect
8. C13×#3329C2semidirect
9. C13×#3329C2semidirect
10. C13×#3326C2semidirect
11. C13×#3321C2semidirect
12. C13×#3320C2semidirect
13. C13×#3303C2semidirect
14. C13×#3298C2semidirect
15. C13×#3242C2semidirect
16. C13×#3233C2semidirect
17. C13×#3221C2semidirect
18. C13×#3206C2semidirect
19. C13×#3174C2semidirect
20. C13×#3171C2semidirect
21. C13×#3139C2semidirect
22. C13×#3137C2semidirect
23. C13×#2969C2semidirect
312. #62609C13direct (N × H)
447. #3552C2×C13semidirect
448. #3547C2×C13semidirect
449. #3372C2×C13semidirect
450. #3367C2×C13semidirect
451. #3360C2×C13semidirect
452. #3359C2×C13semidirect
453. #3330C2×C13semidirect
454. #3329C2×C13semidirect
455. #3329C2×C13semidirect
456. #3326C2×C13semidirect
457. #3321C2×C13semidirect
458. #3320C2×C13semidirect
459. #3303C2×C13semidirect
460. #3298C2×C13semidirect
461. #3242C2×C13semidirect
462. #3233C2×C13semidirect
463. #3221C2×C13semidirect
464. #3206C2×C13semidirect
465. #3174C2×C13semidirect
466. #3171C2×C13semidirect
467. #3139C2×C13semidirect
468. #3137C2×C13semidirect
469. #2969C2×C13semidirect
1008. C13#62609direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35522
C13×#35472
C13×#33722
C13×#33672
C13×#33602
C13×#33592
C13×#33302
C13×#33292
C13×#33262
C13×#33212
C13×#33202
C13×#33032
C13×#32982
C13×#32422
C13×#32332
C13×#32212
C13×#32062
C13×#31742
C13×#31712
C13×#31392
C13×#31372
C13×#29692
#6260913