Finite Group Databasebeta

← C13×#18262 #15704601

Subgroups — C13×#18262 #15704601

Order 3328.

1012 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3534C211yesmaximal, characteristic
2C13×#3094C211yesmaximal, characteristic, complemented
3C13×#3091C211yesmaximal, characteristic, complemented
4C13×#2498C211yesmaximal, characteristic, complemented
5C13×#1618C211yesmaximal, characteristic, complemented
6C13×#1616C211yesmaximal, characteristic, complemented
7C13×#1615C211yesmaximal, characteristic, complemented
8C13×#1613C211yesmaximal, characteristic, complemented
9C13×#1612C211yesmaximal, characteristic, complemented
10C13×#1610C211yesmaximal, characteristic, complemented
11C13×#1609C211yesmaximal, characteristic, complemented
12C13×#1607C211yesmaximal, characteristic, complemented
13C13×#1504C211yesmaximal, characteristic, complemented
14C2×C13×#327C211yesmaximal, characteristic, complemented
15C13×#1468C211yesmaximal, characteristic, complemented
16C13×#562—21no—
17C13×#560—21no—
18C13×#553—21no—
19C13×#551—21no—
20C13×#546—21no—
21C13×#546—21no—
22C13×#546—21no—
23D42×C13—21no—
24C13×#540—21no—
25C13×#539—21no—
26C13×#539C2211yescharacteristic
27C13×#538—21no—
28C13×#538C2211yescharacteristic
29C13×#537C2211yescharacteristic
30C13×#534—21no—
31C13×#534C2211yescharacteristic
32C13×#525C2211yescharacteristic
33C2×C13×#123C2211yescharacteristic
34C2×C13×#121C2211yescharacteristic
35C2×C13×#117C2211yescharacteristic, complemented
36C13×#485—21no—
37C13×#484C2211yescharacteristic, complemented
38C13×#483C2211yescharacteristic, complemented
39C13×#482—21no—
40C13×#482—21no—
41C13×#482—21no—
42C13×#481C2211yescharacteristic
43C13×#481C2211yescharacteristic, complemented
44C13×#481C2211yescharacteristic, complemented
45C13×#480C2211yescharacteristic
46C13×#480C2211yescharacteristic, complemented
47C13×#480C2211yescharacteristic, complemented
48C13×#428—21no—
49C13×#427—21no—
50C13×#418—21no—
51C13×#416—21no—
52C13×#407C2211yescharacteristic, complemented
53C2×C13×C22⋊C8C2211yescharacteristic, complemented
54C13×#400C2211yescharacteristic, complemented
55C13×#399C2211yescharacteristic, complemented
56C13×#398C2211yescharacteristic, complemented
57C13×#397C2211yescharacteristic, complemented
58C13×#388—21no—
59C13×#387—21no—
60C13×#386—21no—
61C13×#380—21no—
62C2×C13×#95C2211yescharacteristic, complemented
63C13×#328C2211yescharacteristic, complemented
64C13×#328C2211yescharacteristic, complemented
65C13×#327C2211yescharacteristic
66C13×#327C2211yescharacteristic
67C13×#327C2211yescharacteristic, complemented
68C13×#327C2211yescharacteristic, complemented
69C13×#327C2211yescharacteristic, complemented
70C13×#327C2211yescharacteristic, complemented
71C13×#324C2211yescharacteristic, complemented
72C13×#324C2211yescharacteristic, complemented
73C13×#323C2211yescharacteristic, complemented
74C13×#323C2211yescharacteristic, complemented
75C2×C13×#41—21no—
76C2×C13×#41D411yescharacteristic
77C22×D4×C13—21no—
78C22×D4×C13—21no—
79C22×D4×C13—21no—
80C22×D4×C13D411yescharacteristic
81C22×D4×C13D411yescharacteristic
82C23×C4×C13—21no—
83C23×C4×C13C2311yescharacteristic
84C2×C13×M16—21no—
85C22×C8×C13—21no—
86C13×#127—21no—
87C13×#126—21no—
88C13×#126—21no—
89C13×#126—21no—
90C13×#126—21no—
91C13×#125—21no—
92C13×#125—21no—
93C13×#124—21no—
94C13×#124—21no—
95C13×#124—21no—
96C13×#123—21no—
97C13×#123—21no—
98C13×#123—21no—
99C13×#123—21no—
100C13×#123—21no—
101C13×#123—21no—
102C13×#123—21no—
103C13×#123—21no—
104C13×#123—21no—
105C13×#123—21no—
106C13×#123—21no—
107C13×#123—21no—
108C13×#123—21no—
109C13×#123—21no—
110C13×C22⋊Q8—21no—
111C13×C22⋊Q8—21no—
112C13×C22⋊Q8—21no—
113C13×C22⋊Q8—21no—
114C13×C22⋊Q8—21no—
115C13×C22⋊Q8D411yescharacteristic
116C13×C22⋊Q8C2311yescharacteristic
117C13×#121—21no—
118C13×#121—21no—
119C13×#121—21no—
120C13×#121—21no—
121C13×#121—21no—
122C13×#121—21no—
123C13×#121—21no—
124C13×#121—21no—
125C13×#121—21no—
126C13×#121—21no—
127C13×#121—21no—
128C13×#121—21no—
129C13×#121—21no—
130C13×#121—21no—
131C13×#121—21no—
132C13×#121D411yescharacteristic
133C13×#121D411yescharacteristic
134C13×#121D411yescharacteristic
135C13×#121C2311yescharacteristic
136C13×#121C2311yescharacteristic
137C13×#121C2311yescharacteristic
138C13×#120—21no—
139C13×#120—21no—
140C13×#120—21no—
141C13×#120—21no—
142C13×#120—21no—
143C13×#120—21no—
144C13×#120—21no—
145C13×#120—21no—
146C4×D4×C13—21no—
147C4×D4×C13—21no—
148C4×D4×C13—21no—
149C4×D4×C13—21no—
150C4×D4×C13—21no—
151C4×D4×C13—21no—
152C4×D4×C13—21no—
153C4×D4×C13—21no—
154C13×#117—21no—
155C13×#117—21no—
156C13×#117—21no—
157C13×#117—21no—
158C13×#117—21no—
159C13×#117D411yescharacteristic
160C2×C13×C4⋊C4—21no—
161C2×C13×C4⋊C4—21no—
162C2×C13×C4⋊C4D411yescharacteristic
163C2×C13×C4⋊C4D411yescharacteristic
164C2×C13×C4⋊C4C2311yescharacteristic
165C2×C13×C4⋊C4C2311yescharacteristic
166C2×C13×C4⋊C4C2311yescharacteristic
167C2×C13×C22⋊C4—21no—
168C2×C13×C22⋊C4—21no—
169C2×C13×C22⋊C4—21no—
170C2×C13×C22⋊C4—21no—
171C2×C13×C22⋊C4—21no—
172C2×C13×C22⋊C4—21no—
173C2×C13×C22⋊C4D411yescharacteristic
174C2×C13×C22⋊C4D411yescharacteristic
175C2×C13×C22⋊C4C2311yescharacteristic
176C2×C42×C13—21no—
177C13×#107—21no—
178C13×#107—21no—
179C13×#107—21no—
180C13×#107—21no—
181C13×#106—21no—
182C13×#106—21no—
183C13×#106—21no—
184C13×#106—21no—
185C13×#103—21no—
186C13×#103—21no—
187C13×#102—21no—
188C13×#102—21no—
189C13×#102—21no—
190C13×#102—21no—
191C13×#102—21no—
192C13×#102—21no—
193C13×C22⋊C8—21no—
194C13×C22⋊C8—21no—
195C13×C22⋊C8C2311yescharacteristic
196C13×C22⋊C8C2311yescharacteristic
197C13×C22⋊C8C2311yescharacteristic
198C13×C22⋊C8C2311yescharacteristic
199C13×#95—21no—
200C13×#95—21no—
201C13×#95—21no—
202C13×#95—21no—
203C13×#95—21no—
204C13×#95C2311yescharacteristic
205C13×#95C2311yescharacteristic
206#18262C1311yesmaximal, characteristic, direct product factor, Sylow
207C24×C13—21no—
208C24×C13—21no—
209C24×C13C2×D411yescharacteristic
210C24×C13C2×D411yescharacteristic
211C13×#41—42no—
212C13×#41—81no—
213C13×#41—81no—
214C2×Q8×C13—21no—
215C2×Q8×C13C2×D411yescharacteristic
216C2×D4×C13—21no—
217C2×D4×C13—21no—
218C2×D4×C13—21no—
219C2×D4×C13—21no—
220C2×D4×C13—21no—
221C2×D4×C13—21no—
222C2×D4×C13—21no—
223C2×D4×C13—21no—
224C2×D4×C13—21no—
225C2×D4×C13—21no—
226C2×D4×C13—21no—
227C2×D4×C13—21no—
228C2×D4×C13—21no—
229C2×D4×C13—21no—
230C2×D4×C13—21no—
231C2×D4×C13—21no—
232C2×D4×C13—21no—
233C2×D4×C13—42no—
234C2×D4×C13—42no—
235C2×D4×C13—81no—
236C2×D4×C13—81no—
237C2×D4×C13—81no—
238C2×D4×C13—81no—
239C2×D4×C13—82no—
240C2×D4×C13C2×D411yescharacteristic
241C2×D4×C13C2×D411yescharacteristic
242C2×D4×C13C2×D411yescharacteristic
243C22×C4×C13—21no—
244C22×C4×C13—21no—
245C22×C4×C13—21no—
246C22×C4×C13—21no—
247C22×C4×C13—21no—
248C22×C4×C13—21no—
249C22×C4×C13—21no—
250C22×C4×C13—21no—
251C22×C4×C13—21no—
252C22×C4×C13—21no—
253C22×C4×C13—21no—
254C22×C4×C13—42no—
255C22×C4×C13—42no—
256C22×C4×C13—42no—
257C22×C4×C13—81no—
258C22×C4×C13C2×D411yescharacteristic
259C22×C4×C13C2×D411yescharacteristic
260C22×C4×C13C2×D411yescharacteristic
261C22×C4×C13C2×D411yescharacteristic
262C22×C4×C13C2×D411yescharacteristic
263C22×C4×C13C2×D411yescharacteristic
264C22×C4×C13C2×D411yescharacteristic
265C22×C4×C13C2×D411yescharacteristic
266C22×C4×C13C2411yescharacteristic
267C13×M16—42no—
268C2×C8×C13—21no—
269C2×C8×C13—21no—
270C2×C8×C13—21no—
271C2×C8×C13—21no—
272C2×C8×C13—42no—
273C13×C4⋊C4—21no—
274C13×C4⋊C4—21no—
275C13×C4⋊C4—21no—
276C13×C4⋊C4—21no—
277C13×C4⋊C4—21no—
278C13×C4⋊C4—21no—
279C13×C4⋊C4—21no—
280C13×C4⋊C4—21no—
281C13×C4⋊C4—21no—
282C13×C4⋊C4—21no—
283C13×C4⋊C4—21no—
284C13×C4⋊C4—21no—
285C13×C4⋊C4—21no—
286C13×C4⋊C4—21no—
287C13×C4⋊C4—21no—
288C13×C4⋊C4—21no—
289C13×C4⋊C4—21no—
290C13×C4⋊C4—42no—
291C13×C4⋊C4—81no—
292C13×C4⋊C4C2×D411yescharacteristic
293C13×C4⋊C4C2×D411yescharacteristic
294C13×C4⋊C4C2×D411yescharacteristic
295C13×C4⋊C4C2×D411yescharacteristic
296C13×C22⋊C4—21no—
297C13×C22⋊C4—21no—
298C13×C22⋊C4—21no—
299C13×C22⋊C4—21no—
300C13×C22⋊C4—21no—
301C13×C22⋊C4—21no—
302C13×C22⋊C4—21no—
303C13×C22⋊C4—21no—
304C13×C22⋊C4—21no—
305C13×C22⋊C4—21no—
306C13×C22⋊C4—21no—
307C13×C22⋊C4—21no—
308C13×C22⋊C4—21no—
309C13×C22⋊C4—21no—
310C13×C22⋊C4—21no—
311C13×C22⋊C4—21no—
312C13×C22⋊C4—21no—
313C13×C22⋊C4—21no—
314C13×C22⋊C4—21no—
315C13×C22⋊C4—21no—
316C13×C22⋊C4—21no—
317C13×C22⋊C4—21no—
318C13×C22⋊C4—21no—
319C13×C22⋊C4—21no—
320C13×C22⋊C4—21no—
321C13×C22⋊C4—42no—
322C13×C22⋊C4—41no—
323C13×C22⋊C4—41no—
324C13×C22⋊C4—81no—
325C42×C13—21no—
326C42×C13—21no—
327C42×C13—21no—
328C42×C13—41no—
329C42×C13—41no—
330#3534C2×C1311yescharacteristic
331#3094C2×C1311yescharacteristic, complemented
332#3091C2×C1311yescharacteristic, complemented
333#2498C2×C1311yescharacteristic, complemented
334#1618C2×C1311yescharacteristic, complemented
335#1616C2×C1311yescharacteristic, complemented
336#1615C2×C1311yescharacteristic, complemented
337#1613C2×C1311yescharacteristic, complemented
338#1612C2×C1311yescharacteristic, complemented
339#1610C2×C1311yescharacteristic, complemented
340#1609C2×C1311yescharacteristic, complemented
341#1607C2×C1311yescharacteristic, complemented
342#1504C2×C1311yescharacteristic, complemented
343C2×#327C2×C1311yescharacteristic, complemented
344#1468C2×C1311yescharacteristic, complemented
345C23×C13—21no—
346C23×C13—21no—
347C23×C13—22no—
348C23×C13—21no—
349C23×C13—21no—
350C23×C13—21no—
351C23×C13—21no—
352C23×C13—21no—
353C23×C13—21no—
354C23×C13—41no—
355C23×C13—41no—
356C23×C13—41no—
357C23×C13—42no—
358C23×C13—81no—
359C23×C13—81no—
360C23×C13—81no—
361C23×C13—81no—
362C23×C13—81no—
363C23×C13#12011yescharacteristic
364C23×C13#12011yescharacteristic
365C23×C13C22×D411yescharacteristic
366Q8×C13—41no—
367Q8×C13—81no—
368D4×C13—41no—
369D4×C13—41no—
370D4×C13—41no—
371D4×C13—41no—
372D4×C13—41no—
373D4×C13—41no—
374D4×C13—41no—
375D4×C13—41no—
376D4×C13—41no—
377D4×C13—42no—
378D4×C13—42no—
379D4×C13—81no—
380D4×C13—81no—
381D4×C13—81no—
382D4×C13—81no—
383D4×C13—81no—
384D4×C13—81no—
385D4×C13—81no—
386D4×C13—81no—
387D4×C13—81no—
388D4×C13—81no—
389D4×C13—81no—
390D4×C13—81no—
391C2×C4×C13—22no—
392C2×C4×C13—22no—
393C2×C4×C13—22no—
394C2×C4×C13—21no—
395C2×C4×C13—21no—
396C2×C4×C13—21no—
397C2×C4×C13—21no—
398C2×C4×C13—21no—
399C2×C4×C13—21no—
400C2×C4×C13—21no—
401C2×C4×C13—21no—
402C2×C4×C13—21no—
403C2×C4×C13—21no—
404C2×C4×C13—41no—
405C2×C4×C13—41no—
406C2×C4×C13—41no—
407C2×C4×C13—41no—
408C2×C4×C13—41no—
409C2×C4×C13—41no—
410C2×C4×C13—41no—
411C2×C4×C13—41no—
412C2×C4×C13—41no—
413C2×C4×C13—41no—
414C2×C4×C13—41no—
415C2×C4×C13—41no—
416C2×C4×C13—41no—
417C2×C4×C13—41no—
418C2×C4×C13—41no—
419C2×C4×C13—41no—
420C2×C4×C13—41no—
421C2×C4×C13—81no—
422C2×C4×C13—81no—
423C2×C4×C13—81no—
424C2×C4×C13—81no—
425C2×C4×C13—81no—
426C2×C4×C13—81no—
427C2×C4×C13—81no—
428C2×C4×C13—84no—
429C2×C4×C13#12011yescharacteristic
430C2×C4×C13#12011yescharacteristic
431C2×C4×C13C22×D411yescharacteristic
432C2×C4×C13C22×D411yescharacteristic
433C8×C13—41no—
434C8×C13—41no—
435C8×C13—41no—
436C8×C13—41no—
437#562—21no—
438#560—21no—
439#553—21no—
440#551—21no—
441#546—21no—
442#546—21no—
443#546—21no—
444D42—21no—
445#540—21no—
446#539—21no—
447#539C22×C1311yescharacteristic
448#538—21no—
449#538C22×C1311yescharacteristic
450#537C22×C1311yescharacteristic
451#534—21no—
452#534C22×C1311yescharacteristic
453#525C22×C1311yescharacteristic
454C2×#123C22×C1311yescharacteristic
455C2×#121C22×C1311yescharacteristic
456C2×#117C22×C1311yescharacteristic, complemented
457#485—21no—
458#484C22×C1311yescharacteristic, complemented
459#483C22×C1311yescharacteristic, complemented
460#482—21no—
461#482—21no—
462#482—21no—
463#481C22×C1311yescharacteristic
464#481C22×C1311yescharacteristic, complemented
465#481C22×C1311yescharacteristic, complemented
466#480C22×C1311yescharacteristic
467#480C22×C1311yescharacteristic, complemented
468#480C22×C1311yescharacteristic, complemented
469#428—21no—
470#427—21no—
471#418—21no—
472#416—21no—
473#407C22×C1311yescharacteristic, complemented
474C2×C22⋊C8C22×C1311yescharacteristic, complemented
475#400C22×C1311yescharacteristic, complemented
476#399C22×C1311yescharacteristic, complemented
477#398C22×C1311yescharacteristic, complemented
478#397C22×C1311yescharacteristic, complemented
479#388—21no—
480#387—21no—
481#386—21no—
482#380—21no—
483C2×#95C22×C1311yescharacteristic, complemented
484#328C22×C1311yescharacteristic, complemented
485#328C22×C1311yescharacteristic, complemented
486#327C22×C1311yescharacteristic
487#327C22×C1311yescharacteristic
488#327C22×C1311yescharacteristic, complemented
489#327C22×C1311yescharacteristic, complemented
490#327C22×C1311yescharacteristic, complemented
491#327C22×C1311yescharacteristic, complemented
492#324C22×C1311yescharacteristic, complemented
493#324C22×C1311yescharacteristic, complemented
494#323C22×C1311yescharacteristic, complemented
495#323C22×C1311yescharacteristic, complemented
496C22×C13—21no—
497C22×C13—21no—
498C22×C13—21no—
499C22×C13—21no—
500C22×C13—21no—
501C22×C13—21no—
502C22×C13—21no—
503C22×C13—42no—
504C22×C13—42no—
505C22×C13—41no—
506C22×C13—41no—
507C22×C13—41no—
508C22×C13—41no—
509C22×C13—41no—
510C22×C13—41no—
511C22×C13—41no—
512C22×C13—41no—
513C22×C13—41no—
514C22×C13—41no—
515C22×C13—41no—
516C22×C13—41no—
517C22×C13—81no—
518C22×C13—81no—
519C22×C13—162no—
520C22×C13—162no—
521C22×C13#45812yes—
522C22×C13C2×#12011yescharacteristic
523C22×C13#57611yescharacteristic
524C22×C13#57711yescharacteristic
525C4×C13—21no—
526C4×C13—21no—
527C4×C13—21no—
528C4×C13—21no—
529C4×C13—42no—
530C4×C13—41no—
531C4×C13—41no—
532C4×C13—41no—
533C4×C13—41no—
534C4×C13—41no—
535C4×C13—41no—
536C4×C13—41no—
537C4×C13—41no—
538C4×C13—81no—
539C4×C13—81no—
540C4×C13—81no—
541C2×#41—21no—
542C2×#41D4×C1311yescharacteristic
543C22×D4—21no—
544C22×D4—21no—
545C22×D4—21no—
546C22×D4D4×C1311yescharacteristic
547C22×D4D4×C1311yescharacteristic
548C23×C4—21no—
549C23×C4C23×C1311yescharacteristic
550C2×M16—21no—
551C22×C8—21no—
552#127—21no—
553#126—21no—
554#126—21no—
555#126—21no—
556#126—21no—
557#125—21no—
558#125—21no—
559#124—21no—
560#124—21no—
561#124—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572#123—21no—
573#123—21no—
574#123—21no—
575#123—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8D4×C1311yescharacteristic
582C22⋊Q8C23×C1311yescharacteristic
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121—21no—
597#121—21no—
598#121D4×C1311yescharacteristic
599#121D4×C1311yescharacteristic
600#121D4×C1311yescharacteristic
601#121C23×C1311yescharacteristic
602#121C23×C1311yescharacteristic
603#121C23×C1311yescharacteristic
604#120—21no—
605#120—21no—
606#120—21no—
607#120—21no—
608#120—21no—
609#120—21no—
610#120—21no—
611#120—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4—21no—
620#117—21no—
621#117—21no—
622#117—21no—
623#117—21no—
624#117—21no—
625#117D4×C1311yescharacteristic
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4D4×C1311yescharacteristic
629C2×C4⋊C4D4×C1311yescharacteristic
630C2×C4⋊C4C23×C1311yescharacteristic
631C2×C4⋊C4C23×C1311yescharacteristic
632C2×C4⋊C4C23×C1311yescharacteristic
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4D4×C1311yescharacteristic
640C2×C22⋊C4D4×C1311yescharacteristic
641C2×C22⋊C4C23×C1311yescharacteristic
642C2×C42—21no—
643#107—21no—
644#107—21no—
645#107—21no—
646#107—21no—
647#106—21no—
648#106—21no—
649#106—21no—
650#106—21no—
651#103—21no—
652#103—21no—
653#102—21no—
654#102—21no—
655#102—21no—
656#102—21no—
657#102—21no—
658#102—21no—
659C22⋊C8—21no—
660C22⋊C8—21no—
661C22⋊C8C23×C1311yescharacteristic
662C22⋊C8C23×C1311yescharacteristic
663C22⋊C8C23×C1311yescharacteristic
664C22⋊C8C23×C1311yescharacteristic
665#95—21no—
666#95—21no—
667#95—21no—
668#95—21no—
669#95—21no—
670#95C23×C1311yescharacteristic
671#95C23×C1311yescharacteristic
672C2×C13—21no—
673C2×C13—21no—
674C2×C13—22no—
675C2×C13—41no—
676C2×C13—81no—
677C2×C13—81no—
678C2×C13—81no—
679C2×C13—81no—
680C2×C13#301211yescharacteristic
681C2×C13#301811yescharacteristic
682C2×C13C2×#45811yescharacteristic
683C24—21no—
684C24—21no—
685C24C2×D4×C1311yescharacteristic
686C24C2×D4×C1311yescharacteristic
687#41—42no—
688#41—81no—
689#41—81no—
690C2×Q8—21no—
691C2×Q8C2×D4×C1311yescharacteristic
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—81no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4—82no—
716C2×D4C2×D4×C1311yescharacteristic
717C2×D4C2×D4×C1311yescharacteristic
718C2×D4C2×D4×C1311yescharacteristic
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—81no—
734C22×C4C2×D4×C1311yescharacteristic
735C22×C4C2×D4×C1311yescharacteristic
736C22×C4C2×D4×C1311yescharacteristic
737C22×C4C2×D4×C1311yescharacteristic
738C22×C4C2×D4×C1311yescharacteristic
739C22×C4C2×D4×C1311yescharacteristic
740C22×C4C2×D4×C1311yescharacteristic
741C22×C4C2×D4×C1311yescharacteristic
742C22×C4C24×C1311yescharacteristic
743M16—42no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—42no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—42no—
767C4⋊C4—81no—
768C4⋊C4C2×D4×C1311yescharacteristic
769C4⋊C4C2×D4×C1311yescharacteristic
770C4⋊C4C2×D4×C1311yescharacteristic
771C4⋊C4C2×D4×C1311yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—42no—
798C22⋊C4—41no—
799C22⋊C4—41no—
800C22⋊C4—81no—
801C42—21no—
802C42—21no—
803C42—21no—
804C42—41no—
805C42—41no—
806C13#1826211yescharacteristic, direct product factor, Sylow
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—42no—
820C23—81no—
821C23—81no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23C13×#12011yescharacteristic
826C23C13×#12011yescharacteristic
827C23C22×D4×C1311yescharacteristic
828Q8—41no—
829Q8—81no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—42no—
834D4—42no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—81no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—81no—
852D4—81no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—84no—
891C2×C4C13×#12011yescharacteristic
892C2×C4C13×#12011yescharacteristic
893C2×C4C22×D4×C1311yescharacteristic
894C2×C4C22×D4×C1311yescharacteristic
895C8—41no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—81no—
921C22—81no—
922C22—162no—
923C22—162no—
924C22C13×#45812yes—
925C22C2×C13×#12011yescharacteristic
926C22C13×#57611yescharacteristic
927C22C13×#57711yescharacteristic
928C4—21no—
929C4—21no—
930C4—21no—
931C4—21no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—81no—
942C4—81no—
943C4—81no—
944C2—21no—
945C2—21no—
946C2—22no—
947C2—41no—
948C2—81no—
949C2—81no—
950C2—81no—
951C2—81no—
952C2C13×#301211yescharacteristic
953C2C13×#301811yescharacteristic
954C2C2×C13×#45811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3534C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3094C2semidirect
3. C13×#3091C2semidirect
4. C13×#2498C2semidirect
5. C13×#1618C2semidirect
6. C13×#1616C2semidirect
7. C13×#1615C2semidirect
8. C13×#1613C2semidirect
9. C13×#1612C2semidirect
10. C13×#1610C2semidirect
11. C13×#1609C2semidirect
12. C13×#1607C2semidirect
13. C13×#1504C2semidirect
14. C2×C13×#327C2semidirect
15. C13×#1468C2semidirect
35. C2×C13×#117C22semidirect
37. C13×#484C22semidirect
38. C13×#483C22semidirect
43. C13×#481C22semidirect
44. C13×#481C22semidirect
46. C13×#480C22semidirect
47. C13×#480C22semidirect
52. C13×#407C22semidirect
53. C2×C13×C22⋊C8C22semidirect
54. C13×#400C22semidirect
55. C13×#399C22semidirect
56. C13×#398C22semidirect
57. C13×#397C22semidirect
62. C2×C13×#95C22semidirect
63. C13×#328C22semidirect
64. C13×#328C22semidirect
67. C13×#327C22semidirect
68. C13×#327C22semidirect
69. C13×#327C22semidirect
70. C13×#327C22semidirect
71. C13×#324C22semidirect
72. C13×#324C22semidirect
73. C13×#323C22semidirect
74. C13×#323C22semidirect
206. #18262C13direct (N × H)
331. #3094C2×C13semidirect
332. #3091C2×C13semidirect
333. #2498C2×C13semidirect
334. #1618C2×C13semidirect
335. #1616C2×C13semidirect
336. #1615C2×C13semidirect
337. #1613C2×C13semidirect
338. #1612C2×C13semidirect
339. #1610C2×C13semidirect
340. #1609C2×C13semidirect
341. #1607C2×C13semidirect
342. #1504C2×C13semidirect
343. C2×#327C2×C13semidirect
344. #1468C2×C13semidirect
456. C2×#117C22×C13semidirect
458. #484C22×C13semidirect
459. #483C22×C13semidirect
464. #481C22×C13semidirect
465. #481C22×C13semidirect
467. #480C22×C13semidirect
468. #480C22×C13semidirect
473. #407C22×C13semidirect
474. C2×C22⋊C8C22×C13semidirect
475. #400C22×C13semidirect
476. #399C22×C13semidirect
477. #398C22×C13semidirect
478. #397C22×C13semidirect
483. C2×#95C22×C13semidirect
484. #328C22×C13semidirect
485. #328C22×C13semidirect
488. #327C22×C13semidirect
489. #327C22×C13semidirect
490. #327C22×C13semidirect
491. #327C22×C13semidirect
492. #324C22×C13semidirect
493. #324C22×C13semidirect
494. #323C22×C13semidirect
495. #323C22×C13semidirect
806. C13#18262direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35342
C13×#30942
C13×#30912
C13×#24982
C13×#16182
C13×#16162
C13×#16152
C13×#16132
C13×#16122
C13×#16102
C13×#16092
C13×#16072
C13×#15042
C2×C13×#3272
C13×#14682
#1826213