Finite Group Databasebeta

← C13×#24141 #15710480

Subgroups — C13×#24141 #15710480

Order 3328.

1200 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3505C211yesmaximal, characteristic
2C13×#2855C211yesmaximal, characteristic, complemented
3C13×#2854C211yesmaximal, characteristic, complemented
4C4×C13×#123C211yesmaximal, characteristic, complemented
5C13×#2044C212yesmaximal, complemented
6C13×#2022C212yesmaximal, complemented
7C13×#1996C211yesmaximal, characteristic, complemented
8C13×#1964C211yesmaximal, characteristic, complemented
9C13×#1890C212yesmaximal, complemented
10C13×#1867C212yesmaximal, complemented
11C13×#1799C211yesmaximal, characteristic, complemented
12C13×#553—22no—
13C13×#553—21no—
14C13×#552—21no—
15C13×#551—22no—
16C13×#548—21no—
17C13×#546—21no—
18C13×#539—21no—
19C13×#538—21no—
20C13×#534C2212yes—
21C13×#529—21no—
22C13×#525—21no—
23C2×C13×#123C2211yescharacteristic
24C2×C13×#123C2212yes—
25C2×C13×C22⋊Q8C2211yescharacteristic
26C2×C13×#121C2211yescharacteristic
27C13×#518C2212yes—
28C2×C4×D4×C13C2211yescharacteristic
29C22×C42×C13C2211yescharacteristic
30C2×C13×#99C2212yes—
31C2×C13×#99C2212yes—
32C2×C13×#99C2212yes—
33C13×#391—21no—
34C13×#390—21no—
35C13×#389—21no—
36C13×#389—21no—
37C13×#388—21no—
38C13×#388—22no—
39C13×#387—21no—
40C13×#387—22no—
41C13×#386C2211yescharacteristic
42C13×#386C2212yes—
43C13×#385C2212yes—
44C13×#385C2211yescharacteristic
45C13×#381C2212yes—
46C13×#381C2211yescharacteristic
47C13×#380C2211yescharacteristic
48C13×#380C2211yescharacteristic
49C4×C13×C4⋊C4—21no—
50C4×C13×C22⋊C4—21no—
51C4×C13×C22⋊C4C2211yescharacteristic
52C13×#342C2212yes—
53C13×#342C2212yes—
54C13×#342C2212yes—
55C2×C13×#41—21no—
56C22×Q8×C13D411yescharacteristic
57C22×D4×C13D411yescharacteristic
58C22×D4×C13C2311yescharacteristic
59C22×D4×C13C2312yes—
60C23×C4×C13D411yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C13×#126—22no—
65C13×#126—22no—
66C13×#126—22no—
67C13×#125—21no—
68C13×#125—22no—
69C13×#124—21no—
70C13×#124—22no—
71C13×#123—22no—
72C13×#123—22no—
73C13×#123—22no—
74C13×#123—22no—
75C13×#123—22no—
76C13×#123—22no—
77C13×#123—22no—
78C13×#123—24no—
79C13×#123—42no—
80C13×C22⋊Q8—21no—
81C13×C22⋊Q8—22no—
82C13×C22⋊Q8—21no—
83C13×C22⋊Q8—21no—
84C13×C22⋊Q8—21no—
85C13×C22⋊Q8—21no—
86C13×#121—21no—
87C13×#121—22no—
88C13×#121—21no—
89C13×#121—21no—
90C13×#121—21no—
91C13×#121—21no—
92C13×#121—22no—
93C13×#121—22no—
94C13×#120—22no—
95C13×#120—22no—
96C4×Q8×C13—21no—
97C4×D4×C13—22no—
98C4×D4×C13—21no—
99C4×D4×C13—21no—
100C4×D4×C13—21no—
101C4×D4×C13—21no—
102C4×D4×C13—21no—
103C4×D4×C13—22no—
104C4×D4×C13—22no—
105C4×D4×C13—22no—
106C4×D4×C13—22no—
107C13×#117—21no—
108C13×#117—22no—
109C13×#117—22no—
110C2×C13×C4⋊C4—21no—
111C2×C13×C4⋊C4—21no—
112C2×C13×C4⋊C4—21no—
113C2×C13×C4⋊C4—21no—
114C2×C13×C4⋊C4—22no—
115C2×C13×C4⋊C4—22no—
116C2×C13×C4⋊C4D411yescharacteristic
117C2×C13×C4⋊C4D412yes—
118C2×C13×C4⋊C4D411yescharacteristic
119C2×C13×C4⋊C4D411yescharacteristic
120C2×C13×C22⋊C4—21no—
121C2×C13×C22⋊C4—22no—
122C2×C13×C22⋊C4—21no—
123C2×C13×C22⋊C4—22no—
124C2×C13×C22⋊C4—22no—
125C2×C13×C22⋊C4D411yescharacteristic
126C2×C13×C22⋊C4D412yes—
127C2×C13×C22⋊C4C2311yescharacteristic
128C2×C13×C22⋊C4C2312yes—
129C2×C13×C22⋊C4C2312yes—
130C2×C13×C22⋊C4C2311yescharacteristic
131C2×C13×C22⋊C4C2312yes—
132C2×C13×C22⋊C4C2311yescharacteristic
133C2×C42×C13—21no—
134C2×C42×C13—21no—
135C2×C42×C13—21no—
136C2×C42×C13—21no—
137C2×C42×C13—21no—
138C2×C42×C13—21no—
139C2×C42×C13—21no—
140C2×C42×C13D411yescharacteristic
141C13×#99—24no—
142C13×#99—42no—
143C13×#99—42no—
144C13×#95—21no—
145C13×#95—21no—
146C13×#95—21no—
147C13×#95—21no—
148C13×#95—21no—
149C13×#95—21no—
150C13×#95—21no—
151C13×#95—22no—
152C13×#95—22no—
153C13×#95—22no—
154C13×#95—22no—
155#24141C1311yesmaximal, characteristic, direct product factor, Sylow
156C24×C13C2×D412yes—
157C24×C13C2×D411yescharacteristic
158C24×C13C2411yescharacteristic
159C13×#41—82no—
160C2×Q8×C13—21no—
161C2×Q8×C13—21no—
162C2×Q8×C13—42no—
163C2×D4×C13—21no—
164C2×D4×C13—22no—
165C2×D4×C13—21no—
166C2×D4×C13—22no—
167C2×D4×C13—22no—
168C2×D4×C13—21no—
169C2×D4×C13—21no—
170C2×D4×C13—22no—
171C2×D4×C13—21no—
172C2×D4×C13—22no—
173C2×D4×C13—21no—
174C2×D4×C13—22no—
175C2×D4×C13—22no—
176C2×D4×C13—22no—
177C2×D4×C13—21no—
178C2×D4×C13—21no—
179C2×D4×C13—42no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—22no—
191C22×C4×C13—22no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—22no—
196C22×C4×C13—22no—
197C22×C4×C13—42no—
198C22×C4×C13—42no—
199C22×C4×C13—42no—
200C22×C4×C13C2×D411yescharacteristic
201C22×C4×C13C2×D412yes—
202C22×C4×C13C2×D411yescharacteristic
203C22×C4×C13C2×D411yescharacteristic
204C22×C4×C13C2×D411yescharacteristic
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13C2×D412yes—
207C22×C4×C13C2×D411yescharacteristic
208C22×C4×C13C2×D412yes—
209C22×C4×C13C2×D411yescharacteristic
210C22×C4×C13C2×D411yescharacteristic
211C22×C4×C13C2×D411yescharacteristic
212C22×C4×C13#4112yescomplemented
213C13×C4⋊C4—24no—
214C13×C4⋊C4—22no—
215C13×C4⋊C4—22no—
216C13×C4⋊C4—22no—
217C13×C4⋊C4—22no—
218C13×C4⋊C4—21no—
219C13×C4⋊C4—22no—
220C13×C4⋊C4—21no—
221C13×C4⋊C4—21no—
222C13×C4⋊C4—21no—
223C13×C4⋊C4—21no—
224C13×C4⋊C4—22no—
225C13×C4⋊C4—21no—
226C13×C4⋊C4—44no—
227C13×C4⋊C4—42no—
228C13×C4⋊C4—42no—
229C13×C4⋊C4—42no—
230C13×C4⋊C4—44no—
231C13×C22⋊C4—22no—
232C13×C22⋊C4—22no—
233C13×C22⋊C4—24no—
234C13×C22⋊C4—22no—
235C13×C22⋊C4—22no—
236C13×C22⋊C4—22no—
237C13×C22⋊C4—22no—
238C13×C22⋊C4—21no—
239C13×C22⋊C4—22no—
240C13×C22⋊C4—21no—
241C13×C22⋊C4—22no—
242C13×C22⋊C4—21no—
243C13×C22⋊C4—22no—
244C13×C22⋊C4—21no—
245C13×C22⋊C4—21no—
246C13×C22⋊C4—22no—
247C13×C22⋊C4—22no—
248C13×C22⋊C4—22no—
249C13×C22⋊C4—21no—
250C13×C22⋊C4—22no—
251C13×C22⋊C4—22no—
252C13×C22⋊C4—21no—
253C13×C22⋊C4—44no—
254C13×C22⋊C4—44no—
255C13×C22⋊C4—42no—
256C13×C22⋊C4#4112yescomplemented
257C42×C13—22no—
258C42×C13—22no—
259C42×C13—21no—
260C42×C13—21no—
261C42×C13—42no—
262C42×C13—41no—
263C42×C13—41no—
264C42×C13—41no—
265C42×C13—41no—
266#3505C2×C1311yescharacteristic
267#2855C2×C1311yescharacteristic, complemented
268#2854C2×C1311yescharacteristic, complemented
269C4×#123C2×C1311yescharacteristic, complemented
270#2044C2×C1312yescomplemented
271#2022C2×C1312yescomplemented
272#1996C2×C1311yescharacteristic, complemented
273#1964C2×C1311yescharacteristic, complemented
274#1890C2×C1312yescomplemented
275#1867C2×C1312yescomplemented
276#1799C2×C1311yescharacteristic, complemented
277C23×C13—21no—
278C23×C13—22no—
279C23×C13—21no—
280C23×C13—21no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—41no—
284C23×C13—41no—
285C23×C13—41no—
286C23×C13—41no—
287C23×C13—42no—
288C23×C13—42no—
289C23×C13C22×D411yescharacteristic
290C23×C13C22×D411yescharacteristic
291C23×C13C22×D411yescharacteristic
292C23×C13C2×#4111yescharacteristic
293C23×C13C2×#4111yescharacteristic
294C23×C13H(5,𝔽2)11yescharacteristic
295C23×C132−1+411yescharacteristic
296Q8×C13—42no—
297Q8×C13—81no—
298D4×C13—42no—
299D4×C13—42no—
300D4×C13—41no—
301D4×C13—41no—
302D4×C13—41no—
303D4×C13—42no—
304D4×C13—42no—
305D4×C13—41no—
306D4×C13—42no—
307D4×C13—81no—
308D4×C13—82no—
309D4×C13—82no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—21no—
317C2×C4×C13—22no—
318C2×C4×C13—21no—
319C2×C4×C13—21no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—21no—
325C2×C4×C13—21no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—41no—
331C2×C4×C13—41no—
332C2×C4×C13—41no—
333C2×C4×C13—41no—
334C2×C4×C13—41no—
335C2×C4×C13—41no—
336C2×C4×C13—41no—
337C2×C4×C13—41no—
338C2×C4×C13—41no—
339C2×C4×C13—41no—
340C2×C4×C13—41no—
341C2×C4×C13—41no—
342C2×C4×C13—41no—
343C2×C4×C13—42no—
344C2×C4×C13—41no—
345C2×C4×C13—42no—
346C2×C4×C13—41no—
347C2×C4×C13—42no—
348C2×C4×C13—41no—
349C2×C4×C13—41no—
350C2×C4×C13—42no—
351C2×C4×C13—42no—
352C2×C4×C13—42no—
353C2×C4×C13—42no—
354C2×C4×C13—41no—
355C2×C4×C13—42no—
356C2×C4×C13—42no—
357C2×C4×C13—81no—
358C2×C4×C13—82no—
359C2×C4×C13—82no—
360C2×C4×C13#12011yescharacteristic
361C2×C4×C13#12011yescharacteristic
362C2×C4×C13#12011yescharacteristic
363C2×C4×C13#12011yescharacteristic
364#553—22no—
365#553—21no—
366#552—21no—
367#551—22no—
368#548—21no—
369#546—21no—
370#539—21no—
371#538—21no—
372#534C22×C1312yes—
373#529—21no—
374#525—21no—
375C2×#123C22×C1311yescharacteristic
376C2×#123C22×C1312yes—
377C2×C22⋊Q8C22×C1311yescharacteristic
378C2×#121C22×C1311yescharacteristic
379#518C22×C1312yes—
380C2×C4×D4C22×C1311yescharacteristic
381C22×C42C22×C1311yescharacteristic
382C2×#99C22×C1312yes—
383C2×#99C22×C1312yes—
384C2×#99C22×C1312yes—
385#391—21no—
386#390—21no—
387#389—21no—
388#389—21no—
389#388—22no—
390#388—21no—
391#387—22no—
392#387—21no—
393#386C22×C1312yes—
394#386C22×C1311yescharacteristic
395#385C22×C1312yes—
396#385C22×C1311yescharacteristic
397#381C22×C1312yes—
398#381C22×C1311yescharacteristic
399#380C22×C1311yescharacteristic
400#380C22×C1311yescharacteristic
401C4×C4⋊C4—21no—
402C4×C22⋊C4—21no—
403C4×C22⋊C4C22×C1311yescharacteristic
404#342C22×C1312yes—
405#342C22×C1312yes—
406#342C22×C1312yes—
407C22×C13—21no—
408C22×C13—21no—
409C22×C13—21no—
410C22×C13—21no—
411C22×C13—21no—
412C22×C13—21no—
413C22×C13—41no—
414C22×C13—41no—
415C22×C13—41no—
416C22×C13—41no—
417C22×C13—42no—
418C22×C13—41no—
419C22×C13—42no—
420C22×C13—41no—
421C22×C13—42no—
422C22×C13—42no—
423C22×C13—41no—
424C22×C13—82no—
425C22×C13—81no—
426C22×C13—82no—
427C22×C13C2×#12011yescharacteristic
428C22×C13#52511yescharacteristic
429C22×C13#53711yescharacteristic
430C22×C13#54611yescharacteristic
431C22×C13#54711yescharacteristic
432C22×C13#54811yescharacteristic
433C22×C13#55011yescharacteristic
434C4×C13—21no—
435C4×C13—21no—
436C4×C13—21no—
437C4×C13—42no—
438C4×C13—42no—
439C4×C13—41no—
440C4×C13—42no—
441C4×C13—41no—
442C4×C13—42no—
443C4×C13—42no—
444C4×C13—41no—
445C4×C13—42no—
446C4×C13—82no—
447C4×C13—82no—
448C4×C13—81no—
449C4×C13#45812yes—
450C2×#41—21no—
451C22×Q8D4×C1311yescharacteristic
452C22×D4D4×C1311yescharacteristic
453C22×D4C23×C1311yescharacteristic
454C22×D4C23×C1312yes—
455C23×C4D4×C1311yescharacteristic
456C23×C4C23×C1311yescharacteristic
457C23×C4C23×C1311yescharacteristic
458C23×C4C23×C1311yescharacteristic
459#126—22no—
460#126—22no—
461#126—22no—
462#125—21no—
463#125—22no—
464#124—21no—
465#124—22no—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—22no—
470#123—22no—
471#123—22no—
472#123—22no—
473#123—24no—
474#123—42no—
475C22⋊Q8—21no—
476C22⋊Q8—22no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481#121—21no—
482#121—22no—
483#121—21no—
484#121—21no—
485#121—21no—
486#121—21no—
487#121—22no—
488#121—22no—
489#120—22no—
490#120—22no—
491C4×Q8—21no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—21no—
503#117—22no—
504#117—22no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4D4×C1311yescharacteristic
512C2×C4⋊C4D4×C1311yescharacteristic
513C2×C4⋊C4D4×C1312yes—
514C2×C4⋊C4D4×C1311yescharacteristic
515C2×C22⋊C4—22no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4D4×C1311yescharacteristic
521C2×C22⋊C4D4×C1312yes—
522C2×C22⋊C4C23×C1312yes—
523C2×C22⋊C4C23×C1311yescharacteristic
524C2×C22⋊C4C23×C1312yes—
525C2×C22⋊C4C23×C1311yescharacteristic
526C2×C22⋊C4C23×C1312yes—
527C2×C22⋊C4C23×C1311yescharacteristic
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—21no—
531C2×C42—21no—
532C2×C42—21no—
533C2×C42—21no—
534C2×C42—21no—
535C2×C42D4×C1311yescharacteristic
536#99—24no—
537#99—42no—
538#99—42no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550C2×C13—21no—
551C2×C13—21no—
552C2×C13—21no—
553C2×C13—21no—
554C2×C13—21no—
555C2×C13—21no—
556C2×C13—81no—
557C2×C13—82no—
558C2×C13#240711yescharacteristic
559C2×C13C2×#45811yescharacteristic
560C2×C13#302511yescharacteristic
561C24C2×D4×C1312yes—
562C24C2×D4×C1311yescharacteristic
563C24C24×C1311yescharacteristic
564#41—82no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—42no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—22no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—42no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4C2×D4×C1311yescharacteristic
606C22×C4C2×D4×C1312yes—
607C22×C4C2×D4×C1311yescharacteristic
608C22×C4C2×D4×C1311yescharacteristic
609C22×C4C2×D4×C1311yescharacteristic
610C22×C4C2×D4×C1311yescharacteristic
611C22×C4C2×D4×C1312yes—
612C22×C4C2×D4×C1311yescharacteristic
613C22×C4C2×D4×C1312yes—
614C22×C4C2×D4×C1311yescharacteristic
615C22×C4C2×D4×C1311yescharacteristic
616C22×C4C2×D4×C1311yescharacteristic
617C22×C4C13×#4112yescomplemented
618C4⋊C4—24no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—21no—
624C4⋊C4—22no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—22no—
630C4⋊C4—21no—
631C4⋊C4—44no—
632C4⋊C4—42no—
633C4⋊C4—42no—
634C4⋊C4—42no—
635C4⋊C4—44no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—24no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—22no—
645C22⋊C4—21no—
646C22⋊C4—22no—
647C22⋊C4—21no—
648C22⋊C4—22no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—21no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—21no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—42no—
661C22⋊C4C13×#4112yescomplemented
662C42—22no—
663C42—22no—
664C42—21no—
665C42—21no—
666C42—42no—
667C42—41no—
668C42—41no—
669C42—41no—
670C42—41no—
671C13#2414111yescharacteristic, direct product factor, Sylow
672C23—21no—
673C23—22no—
674C23—21no—
675C23—21no—
676C23—22no—
677C23—22no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—42no—
683C23—42no—
684C23C22×D4×C1311yescharacteristic
685C23C22×D4×C1311yescharacteristic
686C23C22×D4×C1311yescharacteristic
687C23C2×C13×#4111yescharacteristic
688C23C2×C13×#4111yescharacteristic
689C23C13×H(5,𝔽2)11yescharacteristic
690C23C13×2−1+411yescharacteristic
691Q8—42no—
692Q8—81no—
693D4—42no—
694D4—42no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—42no—
699D4—42no—
700D4—41no—
701D4—42no—
702D4—81no—
703D4—82no—
704D4—82no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—81no—
753C2×C4—82no—
754C2×C4—82no—
755C2×C4C13×#12011yescharacteristic
756C2×C4C13×#12011yescharacteristic
757C2×C4C13×#12011yescharacteristic
758C2×C4C13×#12011yescharacteristic
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—82no—
777C22—81no—
778C22—82no—
779C22C2×C13×#12011yescharacteristic
780C22C13×#52511yescharacteristic
781C22C13×#53711yescharacteristic
782C22C13×#54611yescharacteristic
783C22C13×#54711yescharacteristic
784C22C13×#54811yescharacteristic
785C22C13×#55011yescharacteristic
786C4—21no—
787C4—21no—
788C4—21no—
789C4—42no—
790C4—41no—
791C4—42no—
792C4—42no—
793C4—41no—
794C4—42no—
795C4—42no—
796C4—41no—
797C4—42no—
798C4—82no—
799C4—82no—
800C4—81no—
801C4C13×#45812yes—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—21no—
807C2—21no—
808C2—81no—
809C2—82no—
810C2C13×#240711yescharacteristic
811C2C2×C13×#45811yescharacteristic
812C2C13×#302511yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC24C24×C13
prime radicalC13×#3505C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2855C2semidirect
3. C13×#2854C2semidirect
4. C4×C13×#123C2semidirect
5. C13×#2044C2semidirect
6. C13×#2022C2semidirect
7. C13×#1996C2semidirect
8. C13×#1964C2semidirect
9. C13×#1890C2semidirect
10. C13×#1867C2semidirect
11. C13×#1799C2semidirect
155. #24141C13direct (N × H)
212. C22×C4×C13#41semidirect
256. C13×C22⋊C4#41semidirect
267. #2855C2×C13semidirect
268. #2854C2×C13semidirect
269. C4×#123C2×C13semidirect
270. #2044C2×C13semidirect
271. #2022C2×C13semidirect
272. #1996C2×C13semidirect
273. #1964C2×C13semidirect
274. #1890C2×C13semidirect
275. #1867C2×C13semidirect
276. #1799C2×C13semidirect
617. C22×C4C13×#41semidirect
661. C22⋊C4C13×#41semidirect
671. C13#24141direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35052
C13×#28552
C13×#28542
C4×C13×#1232
C13×#20442
C13×#20222
C13×#19962
C13×#19642
C13×#18902
C13×#18672
C13×#17992
#2414113