Finite Group Databasebeta

← C13×#13970 #15700309

Subgroups — C13×#13970 #15700309

Order 3328.

3058 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#121C211yesmaximal, characteristic
2C22×C4×D4×C13C211yesmaximal, characteristic, complemented
3C2×C13×#390C211yesmaximal, characteristic, complemented
4C2×C13×#386C212yesmaximal, complemented
5C2×C13×#380C211yesmaximal, characteristic, complemented
6C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
7C13×#1440C212yesmaximal, complemented
8C13×#1438C212yesmaximal, complemented
9C13×C4⋊#95C211yesmaximal, characteristic, complemented
10C13×C4⋊#95C211yesmaximal, characteristic, complemented
11C13×C22⋊#95C212yesmaximal, complemented
12C23×D4×C13C2212yes—
13C23×D4×C13C2211yescharacteristic
14C24×C4×C13C2211yescharacteristic
15C24×C4×C13C2212yes—
16C2×C13×#121—24no—
17C2×C13×#121—24no—
18C2×C13×#121C418yescomplemented
19C2×C4×D4×C13—24no—
20C2×C4×D4×C13—24no—
21C2×C4×D4×C13—24no—
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2212yes—
27C22×C13×C22⋊C4C2212yes—
28C22×C13×C22⋊C4C2212yes—
29C22×C13×C22⋊C4C2212yes—
30C22×C13×C22⋊C4C2212yes—
31C22×C13×C22⋊C4C2211yescharacteristic
32C22×C42×C13C2211yescharacteristic
33C22×C42×C13C2211yescharacteristic
34C13×#390—24no—
35C13×#386—28no—
36C13×#380—24no—
37C4×C13×C22⋊C4—24no—
38C2×C13×#95C2211yescharacteristic
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2212yes—
41C2×C13×#95C2212yes—
42C2×C13×#95C2212yes—
43C2×C13×#95C2212yes—
44C2×C13×#95C2212yes—
45C25×C13C2312yes—
46C25×C13C2311yescharacteristic
47C22×D4×C13—24no—
48C22×D4×C13—24no—
49C22×D4×C13—24no—
50C22×D4×C13—24no—
51C22×D4×C13—22no—
52C22×D4×C13—22no—
53C22×D4×C13—22no—
54C22×D4×C13—22no—
55C22×D4×C13—42no—
56C22×D4×C13—42no—
57C22×D4×C13C2×C414yes—
58C22×D4×C13C2×C418yescomplemented
59C22×D4×C13D414yes—
60C22×D4×C13D414yes—
61C23×C4×C13—24no—
62C23×C4×C13—22no—
63C23×C4×C13—22no—
64C23×C4×C13—24no—
65C23×C4×C13—24no—
66C23×C4×C13—22no—
67C23×C4×C13—22no—
68C23×C4×C13—22no—
69C23×C4×C13—22no—
70C23×C4×C13—24no—
71C23×C4×C13—24no—
72C23×C4×C13—42no—
73C23×C4×C13—42no—
74C23×C4×C13C2×C414yescomplemented
75C23×C4×C13C2312yes—
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2312yes—
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2312yes—
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C13×#121—232no—
85C4×D4×C13—232no—
86C2×C13×C4⋊C4—22no—
87C2×C13×C4⋊C4—22no—
88C2×C13×C4⋊C4—22no—
89C2×C13×C4⋊C4—22no—
90C2×C13×C4⋊C4—22no—
91C2×C13×C4⋊C4—22no—
92C2×C13×C4⋊C4—22no—
93C2×C13×C4⋊C4C2×C414yescomplemented
94C2×C13×C4⋊C4D414yescomplemented
95C2×C13×C22⋊C4—24no—
96C2×C13×C22⋊C4—24no—
97C2×C13×C22⋊C4—24no—
98C2×C13×C22⋊C4—22no—
99C2×C13×C22⋊C4—22no—
100C2×C13×C22⋊C4—22no—
101C2×C13×C22⋊C4—24no—
102C2×C13×C22⋊C4—24no—
103C2×C13×C22⋊C4—22no—
104C2×C13×C22⋊C4—22no—
105C2×C13×C22⋊C4—24no—
106C2×C13×C22⋊C4—24no—
107C2×C13×C22⋊C4—24no—
108C2×C13×C22⋊C4—24no—
109C2×C13×C22⋊C4—24no—
110C2×C13×C22⋊C4—24no—
111C2×C13×C22⋊C4—42no—
112C2×C13×C22⋊C4—42no—
113C2×C13×C22⋊C4—42no—
114C2×C13×C22⋊C4C2×C418yescomplemented
115C2×C13×C22⋊C4D414yescomplemented
116C2×C42×C13—22no—
117C2×C42×C13—22no—
118C2×C42×C13—22no—
119C2×C42×C13—22no—
120C2×C42×C13—22no—
121C2×C42×C13D414yescomplemented
122C13×#95—22no—
123C13×#95—22no—
124C13×#95—24no—
125C13×#95—24no—
126C13×#95—24no—
127C13×#95—42no—
128C13×#95—42no—
129#13970C1311yesmaximal, characteristic, direct product factor, Sylow
130C24×C13—21no—
131C24×C13—21no—
132C24×C13—22no—
133C24×C13—22no—
134C24×C13—22no—
135C24×C13—21no—
136C24×C13—21no—
137C24×C13—21no—
138C24×C13—21no—
139C24×C13—22no—
140C24×C13—21no—
141C24×C13—21no—
142C24×C13—22no—
143C24×C13—22no—
144C24×C13—22no—
145C24×C13—22no—
146C24×C13—21no—
147C24×C13—22no—
148C24×C13—22no—
149C24×C13—22no—
150C24×C13—21no—
151C24×C13—21no—
152C24×C13—22no—
153C24×C13—21no—
154C24×C13C22×C414yes—
155C24×C13C22×C412yes—
156C24×C13C2×D414yes—
157C24×C13C2×D414yes—
158C24×C13C2×D412yes—
159C24×C13#4112yes—
160C24×C13C2411yescharacteristic
161C2×D4×C13—216no—
162C2×D4×C13—216no—
163C2×D4×C13—28no—
164C2×D4×C13—28no—
165C2×D4×C13—28no—
166C2×D4×C13—28no—
167C2×D4×C13—28no—
168C2×D4×C13—28no—
169C2×D4×C13—48no—
170C2×D4×C13—48no—
171C2×D4×C13—48no—
172C2×D4×C13—48no—
173C2×D4×C13—48no—
174C2×D4×C13C22⋊C4116yescomplemented
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—216no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—22no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—22no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—22no—
193C22×C4×C13—22no—
194C22×C4×C13—22no—
195C22×C4×C13—22no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—22no—
205C22×C4×C13—22no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—22no—
209C22×C4×C13—22no—
210C22×C4×C13—22no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—22no—
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—28no—
217C22×C4×C13—28no—
218C22×C4×C13—28no—
219C22×C4×C13—22no—
220C22×C4×C13—22no—
221C22×C4×C13—22no—
222C22×C4×C13—22no—
223C22×C4×C13—22no—
224C22×C4×C13—22no—
225C22×C4×C13—22no—
226C22×C4×C13—48no—
227C22×C4×C13—48no—
228C22×C4×C13—48no—
229C22×C4×C13—48no—
230C22×C4×C13—48no—
231C22×C4×C13—44no—
232C22×C4×C13—44no—
233C22×C4×C13—44no—
234C22×C4×C13—48no—
235C22×C4×C13—44no—
236C22×C4×C13C22×C412yes—
237C22×C4×C13C22×C414yes—
238C22×C4×C13C22×C412yes—
239C22×C4×C13C2×D412yes—
240C22×C4×C13C2×D412yes—
241C22×C4×C13C2×D414yes—
242C22×C4×C13C2×D412yes—
243C22×C4×C13C2×D412yes—
244C22×C4×C13C2×D412yes—
245C22×C4×C13C2×D412yes—
246C22×C4×C13C2×D412yes—
247C22×C4×C13C2×D412yes—
248C22×C4×C13#4112yes—
249C22×C4×C13#4112yes—
250C22×C4×C13#4112yes—
251C22×C4×C13#4112yes—
252C13×C4⋊C4—28no—
253C13×C4⋊C4—28no—
254C13×C4⋊C4—44no—
255C13×C22⋊C4—28no—
256C13×C22⋊C4—216no—
257C13×C22⋊C4—216no—
258C13×C22⋊C4—28no—
259C13×C22⋊C4—48no—
260C13×C22⋊C4—48no—
261C13×C22⋊C4—48no—
262C42×C13—28no—
263C42×C13—44no—
264C22×#121C2×C1311yescharacteristic
265C22×C4×D4C2×C1311yescharacteristic, complemented
266C2×#390C2×C1311yescharacteristic, complemented
267C2×#386C2×C1312yescomplemented
268C2×#380C2×C1311yescharacteristic, complemented
269C2×C4×C22⋊C4C2×C1311yescharacteristic, complemented
270#1440C2×C1312yescomplemented
271#1438C2×C1312yescomplemented
272C4⋊#95C2×C1311yescharacteristic, complemented
273C4⋊#95C2×C1311yescharacteristic, complemented
274C22⋊#95C2×C1312yescomplemented
275C23×C13—22no—
276C23×C13—22no—
277C23×C13—22no—
278C23×C13—24no—
279C23×C13—24no—
280C23×C13—24no—
281C23×C13—24no—
282C23×C13—22no—
283C23×C13—22no—
284C23×C13—24no—
285C23×C13—24no—
286C23×C13—22no—
287C23×C13—24no—
288C23×C13—22no—
289C23×C13—24no—
290C23×C13—24no—
291C23×C13—24no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—24no—
297C23×C13—24no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—24no—
301C23×C13—24no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—24no—
305C23×C13—24no—
306C23×C13—24no—
307C23×C13—24no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—41no—
312C23×C13—42no—
313C23×C13—41no—
314C23×C13—41no—
315C23×C13—41no—
316C23×C13—42no—
317C23×C13—42no—
318C23×C13—42no—
319C23×C13—42no—
320C23×C13—41no—
321C23×C13—41no—
322C23×C13—42no—
323C23×C13—41no—
324C23×C13—42no—
325C23×C13—41no—
326C23×C13—42no—
327C23×C13—42no—
328C23×C13—42no—
329C23×C13—41no—
330C23×C13—41no—
331C23×C13—41no—
332C23×C13—41no—
333C23×C13—41no—
334C23×C13—42no—
335C23×C13—42no—
336C23×C13—41no—
337C23×C13—42no—
338C23×C13—42no—
339C23×C13—41no—
340C23×C13—42no—
341C23×C13—41no—
342C23×C13—42no—
343C23×C13C2×C22⋊C418yes—
344C23×C13C4×D414yescomplemented
345C23×C13C23×C411yescharacteristic
346C23×C13C22×D411yescharacteristic
347C23×C13C22×D411yescharacteristic
348C23×C13C22×D411yescharacteristic
349C23×C13C22×D411yescharacteristic
350C23×C13C22×D411yescharacteristic
351C23×C13C2×#4111yescharacteristic
352C23×C13C2×#4111yescharacteristic
353C23×C13C2×#4111yescharacteristic
354C23×C13C2×#4111yescharacteristic
355C23×C13C2×#4111yescharacteristic
356C23×C13H(5,𝔽2)11yescharacteristic
357C23×C13H(5,𝔽2)11yescharacteristic
358C23×C13H(5,𝔽2)11yescharacteristic
359C23×C132−1+411yescharacteristic
360D4×C13—232no—
361D4×C13—432no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—24no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—24no—
373C2×C4×C13—24no—
374C2×C4×C13—22no—
375C2×C4×C13—24no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—24no—
382C2×C4×C13—22no—
383C2×C4×C13—24no—
384C2×C4×C13—22no—
385C2×C4×C13—22no—
386C2×C4×C13—432no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—42no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13—42no—
396C2×C4×C13—41no—
397C2×C4×C13—42no—
398C2×C4×C13—42no—
399C2×C4×C13—42no—
400C2×C4×C13—41no—
401C2×C4×C13—41no—
402C2×C4×C13—42no—
403C2×C4×C13—42no—
404C2×C4×C13—42no—
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—416no—
412C2×C4×C13—42no—
413C2×C4×C13—42no—
414C2×C4×C13—42no—
415C2×C4×C13—42no—
416C2×C4×C13—42no—
417C2×C4×C13—42no—
418C2×C4×C13—42no—
419C2×C4×C13C2×C22⋊C414yes—
420C2×C4×C13C4×D414yes—
421C2×C4×C13C4×D414yes—
422C2×C4×C13#12014yes—
423C2×C4×C13#12114yes—
424C2×C4×C13#12114yes—
425C2×C4×C13#12114yescomplemented
426C2×C4×C13#12314yes—
427C23×D4C22×C1312yes—
428C23×D4C22×C1311yescharacteristic
429C24×C4C22×C1311yescharacteristic
430C24×C4C22×C1312yes—
431C2×#121—24no—
432C2×#121—24no—
433C2×#121C4×C1318yescomplemented
434C2×C4×D4—24no—
435C2×C4×D4—24no—
436C2×C4×D4—24no—
437C22×C4⋊C4C22×C1311yescharacteristic
438C22×C4⋊C4C22×C1311yescharacteristic
439C22×C4⋊C4C22×C1311yescharacteristic
440C22×C22⋊C4C22×C1312yes—
441C22×C22⋊C4C22×C1311yescharacteristic
442C22×C22⋊C4C22×C1312yes—
443C22×C22⋊C4C22×C1312yes—
444C22×C22⋊C4C22×C1312yes—
445C22×C22⋊C4C22×C1312yes—
446C22×C22⋊C4C22×C1311yescharacteristic
447C22×C42C22×C1311yescharacteristic
448C22×C42C22×C1311yescharacteristic
449#390—24no—
450#386—28no—
451#380—24no—
452C4×C22⋊C4—24no—
453C2×#95C22×C1311yescharacteristic
454C2×#95C22×C1312yes—
455C2×#95C22×C1312yes—
456C2×#95C22×C1312yes—
457C2×#95C22×C1311yescharacteristic
458C2×#95C22×C1312yes—
459C2×#95C22×C1312yes—
460C22×C13—24no—
461C22×C13—28no—
462C22×C13—28no—
463C22×C13—24no—
464C22×C13—28no—
465C22×C13—24no—
466C22×C13—42no—
467C22×C13—44no—
468C22×C13—42no—
469C22×C13—44no—
470C22×C13—42no—
471C22×C13—44no—
472C22×C13—44no—
473C22×C13—42no—
474C22×C13—44no—
475C22×C13—42no—
476C22×C13—44no—
477C22×C13—42no—
478C22×C13—44no—
479C22×C13—42no—
480C22×C13—44no—
481C22×C13—42no—
482C22×C13—44no—
483C22×C13—42no—
484C22×C13—44no—
485C22×C13—42no—
486C22×C13—42no—
487C22×C13—44no—
488C22×C13—42no—
489C22×C13—44no—
490C22×C13C22×C22⋊C411yescharacteristic
491C22×C13C2×C4×D411yescharacteristic
492C22×C13C2×C4×D411yescharacteristic
493C22×C13C2×C4×D411yescharacteristic
494C22×C13C4×#4111yescharacteristic
495C22×C13#51811yescharacteristic
496C22×C13#52011yescharacteristic
497C22×C13C2×#12011yescharacteristic
498C22×C13C2×#12111yescharacteristic
499C22×C13C2×#12111yescharacteristic
500C22×C13C2×#12111yescharacteristic
501C22×C13C2×#12311yescharacteristic
502C22×C13#52511yescharacteristic
503C22×C13#52911yescharacteristic
504C22×C13#53211yescharacteristic
505C22×C13#53511yescharacteristic
506C22×C13#53711yescharacteristic
507C22×C13#54011yescharacteristic
508C22×C13#54211yescharacteristic
509C22×C13D4211yescharacteristic
510C22×C13D4211yescharacteristic
511C22×C13D4211yescharacteristic
512C22×C13#54611yescharacteristic
513C22×C13#54611yescharacteristic
514C22×C13#54611yescharacteristic
515C22×C13#54611yescharacteristic
516C22×C13#54611yescharacteristic
517C22×C13#54711yescharacteristic
518C22×C13#54711yescharacteristic
519C22×C13#54711yescharacteristic
520C22×C13#54811yescharacteristic
521C22×C13#55011yescharacteristic
522C22×C13#55311yescharacteristic
523C22×C13#55311yescharacteristic
524C22×C13#55511yescharacteristic
525C4×C13—24no—
526C4×C13—44no—
527C4×C13—42no—
528C4×C13—44no—
529C4×C13—42no—
530C4×C13—42no—
531C4×C13—42no—
532C4×C13—82no—
533C4×C13#38618yescomplemented
534C25C23×C1312yes—
535C25C23×C1311yescharacteristic
536C22×D4—24no—
537C22×D4—24no—
538C22×D4—24no—
539C22×D4—24no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—42no—
545C22×D4—42no—
546C22×D4C2×C4×C1314yes—
547C22×D4C2×C4×C1318yescomplemented
548C22×D4D4×C1314yes—
549C22×D4D4×C1314yes—
550C23×C4—24no—
551C23×C4—24no—
552C23×C4—24no—
553C23×C4—22no—
554C23×C4—22no—
555C23×C4—22no—
556C23×C4—22no—
557C23×C4—22no—
558C23×C4—22no—
559C23×C4—24no—
560C23×C4—24no—
561C23×C4—42no—
562C23×C4—42no—
563C23×C4C2×C4×C1314yescomplemented
564C23×C4C23×C1312yes—
565C23×C4C23×C1311yescharacteristic
566C23×C4C23×C1312yes—
567C23×C4C23×C1311yescharacteristic
568C23×C4C23×C1311yescharacteristic
569C23×C4C23×C1312yes—
570C23×C4C23×C1311yescharacteristic
571C23×C4C23×C1311yescharacteristic
572C23×C4C23×C1311yescharacteristic
573#121—232no—
574C4×D4—232no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4C2×C4×C1314yescomplemented
583C2×C4⋊C4D4×C1314yescomplemented
584C2×C22⋊C4—24no—
585C2×C22⋊C4—24no—
586C2×C22⋊C4—24no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—24no—
589C2×C22⋊C4—24no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—24no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—42no—
601C2×C22⋊C4—42no—
602C2×C22⋊C4—42no—
603C2×C22⋊C4C2×C4×C1318yescomplemented
604C2×C22⋊C4D4×C1314yescomplemented
605C2×C42—22no—
606C2×C42—22no—
607C2×C42—22no—
608C2×C42—22no—
609C2×C42—22no—
610C2×C42D4×C1314yescomplemented
611#95—22no—
612#95—22no—
613#95—24no—
614#95—24no—
615#95—24no—
616#95—42no—
617#95—42no—
618C2×C13—44no—
619C2×C13—48no—
620C2×C13C2×#38611yescharacteristic
621C2×C13C4×#12111yescharacteristic
622C2×C13#232411yescharacteristic
623C2×C13D4×C22⋊C411yescharacteristic
624C2×C13#233911yescharacteristic
625C2×C13#236111yescharacteristic
626C2×C13#236311yescharacteristic
627C2×C13#240711yescharacteristic
628C2×C13#240811yescharacteristic
629C2×C13#242011yescharacteristic
630C2×C13#242211yescharacteristic
631C2×C13#242711yescharacteristic
632C2×C13#242811yescharacteristic
633C2×C13#253511yescharacteristic
634C2×C13#253711yescharacteristic
635C24—21no—
636C24—21no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—22no—
645C24—21no—
646C24—21no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—21no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—21no—
656C24—21no—
657C24—22no—
658C24—21no—
659C24C22×C4×C1314yes—
660C24C22×C4×C1312yes—
661C24C2×D4×C1314yes—
662C24C2×D4×C1314yes—
663C24C2×D4×C1312yes—
664C24C13×#4112yes—
665C24C24×C1311yescharacteristic
666C2×D4—216no—
667C2×D4—216no—
668C2×D4—28no—
669C2×D4—28no—
670C2×D4—28no—
671C2×D4—28no—
672C2×D4—28no—
673C2×D4—28no—
674C2×D4—48no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—48no—
679C2×D4C13×C22⋊C4116yescomplemented
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—216no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—22no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—22no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—28no—
722C22×C4—28no—
723C22×C4—28no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—48no—
732C22×C4—48no—
733C22×C4—48no—
734C22×C4—48no—
735C22×C4—48no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—48no—
740C22×C4—44no—
741C22×C4C22×C4×C1312yes—
742C22×C4C22×C4×C1314yes—
743C22×C4C22×C4×C1312yes—
744C22×C4C2×D4×C1312yes—
745C22×C4C2×D4×C1312yes—
746C22×C4C2×D4×C1314yes—
747C22×C4C2×D4×C1312yes—
748C22×C4C2×D4×C1312yes—
749C22×C4C2×D4×C1312yes—
750C22×C4C2×D4×C1312yes—
751C22×C4C2×D4×C1312yes—
752C22×C4C2×D4×C1312yes—
753C22×C4C13×#4112yes—
754C22×C4C13×#4112yes—
755C22×C4C13×#4112yes—
756C22×C4C13×#4112yes—
757C4⋊C4—28no—
758C4⋊C4—28no—
759C4⋊C4—44no—
760C22⋊C4—216no—
761C22⋊C4—28no—
762C22⋊C4—216no—
763C22⋊C4—28no—
764C22⋊C4—48no—
765C22⋊C4—48no—
766C22⋊C4—48no—
767C42—28no—
768C42—44no—
769C13#1397011yescharacteristic, direct product factor, Sylow
770C23—22no—
771C23—22no—
772C23—22no—
773C23—24no—
774C23—24no—
775C23—24no—
776C23—22no—
777C23—24no—
778C23—22no—
779C23—24no—
780C23—24no—
781C23—22no—
782C23—24no—
783C23—22no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—24no—
792C23—24no—
793C23—22no—
794C23—22no—
795C23—24no—
796C23—24no—
797C23—22no—
798C23—22no—
799C23—24no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—41no—
807C23—41no—
808C23—42no—
809C23—41no—
810C23—41no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—41no—
816C23—41no—
817C23—42no—
818C23—41no—
819C23—42no—
820C23—41no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—42no—
831C23—41no—
832C23—42no—
833C23—42no—
834C23—41no—
835C23—42no—
836C23—41no—
837C23—42no—
838C23C2×C13×C22⋊C418yes—
839C23C4×D4×C1314yescomplemented
840C23C23×C4×C1311yescharacteristic
841C23C22×D4×C1311yescharacteristic
842C23C22×D4×C1311yescharacteristic
843C23C22×D4×C1311yescharacteristic
844C23C22×D4×C1311yescharacteristic
845C23C22×D4×C1311yescharacteristic
846C23C2×C13×#4111yescharacteristic
847C23C2×C13×#4111yescharacteristic
848C23C2×C13×#4111yescharacteristic
849C23C2×C13×#4111yescharacteristic
850C23C2×C13×#4111yescharacteristic
851C23C13×H(5,𝔽2)11yescharacteristic
852C23C13×H(5,𝔽2)11yescharacteristic
853C23C13×H(5,𝔽2)11yescharacteristic
854C23C13×2−1+411yescharacteristic
855D4—232no—
856D4—432no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—24no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—22no—
870C2×C4—24no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—24no—
877C2×C4—22no—
878C2×C4—24no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—432no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—42no—
888C2×C4—41no—
889C2×C4—42no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—416no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4C2×C13×C22⋊C414yes—
915C2×C4C4×D4×C1314yes—
916C2×C4C4×D4×C1314yes—
917C2×C4C13×#12014yes—
918C2×C4C13×#12114yes—
919C2×C4C13×#12114yes—
920C2×C4C13×#12114yescomplemented
921C2×C4C13×#12314yes—
922C22—28no—
923C22—24no—
924C22—24no—
925C22—28no—
926C22—28no—
927C22—24no—
928C22—44no—
929C22—42no—
930C22—42no—
931C22—44no—
932C22—42no—
933C22—44no—
934C22—42no—
935C22—44no—
936C22—42no—
937C22—44no—
938C22—42no—
939C22—44no—
940C22—44no—
941C22—42no—
942C22—44no—
943C22—42no—
944C22—44no—
945C22—42no—
946C22—44no—
947C22—42no—
948C22—44no—
949C22—42no—
950C22—44no—
951C22—42no—
952C22C22×C13×C22⋊C411yescharacteristic
953C22C2×C4×D4×C1311yescharacteristic
954C22C2×C4×D4×C1311yescharacteristic
955C22C2×C4×D4×C1311yescharacteristic
956C22C4×C13×#4111yescharacteristic
957C22C13×#51811yescharacteristic
958C22C13×#52011yescharacteristic
959C22C2×C13×#12011yescharacteristic
960C22C2×C13×#12111yescharacteristic
961C22C2×C13×#12111yescharacteristic
962C22C2×C13×#12111yescharacteristic
963C22C2×C13×#12311yescharacteristic
964C22C13×#52511yescharacteristic
965C22C13×#52911yescharacteristic
966C22C13×#53211yescharacteristic
967C22C13×#53511yescharacteristic
968C22C13×#53711yescharacteristic
969C22C13×#54011yescharacteristic
970C22C13×#54211yescharacteristic
971C22D42×C1311yescharacteristic
972C22D42×C1311yescharacteristic
973C22D42×C1311yescharacteristic
974C22C13×#54611yescharacteristic
975C22C13×#54611yescharacteristic
976C22C13×#54611yescharacteristic
977C22C13×#54611yescharacteristic
978C22C13×#54611yescharacteristic
979C22C13×#54711yescharacteristic
980C22C13×#54711yescharacteristic
981C22C13×#54711yescharacteristic
982C22C13×#54811yescharacteristic
983C22C13×#55011yescharacteristic
984C22C13×#55311yescharacteristic
985C22C13×#55311yescharacteristic
986C22C13×#55511yescharacteristic
987C4—24no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—44no—
992C4—42no—
993C4—44no—
994C4—82no—
995C4C13×#38618yescomplemented
996C2—48no—
997C2—44no—
998C2C2×C13×#38611yescharacteristic
999C2C4×C13×#12111yescharacteristic
1000C2C13×#232411yescharacteristic
1001C2D4×C13×C22⋊C411yescharacteristic
1002C2C13×#233911yescharacteristic
1003C2C13×#236111yescharacteristic
1004C2C13×#236311yescharacteristic
1005C2C13×#240711yescharacteristic
1006C2C13×#240811yescharacteristic
1007C2C13×#242011yescharacteristic
1008C2C13×#242211yescharacteristic
1009C2C13×#242711yescharacteristic
1010C2C13×#242811yescharacteristic
1011C2C13×#253511yescharacteristic
1012C2C13×#253711yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutatorC23C23×C4×C13
Frattini, cosocleC24C24×C13
prime radicalC22×C13×#121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4×D4×C13C2semidirect
3. C2×C13×#390C2semidirect
4. C2×C13×#386C2semidirect
5. C2×C13×#380C2semidirect
6. C2×C4×C13×C22⋊C4C2semidirect
7. C13×#1440C2semidirect
8. C13×#1438C2semidirect
9. C13×C4⋊#95C2semidirect
10. C13×C4⋊#95C2semidirect
11. C13×C22⋊#95C2semidirect
18. C2×C13×#121C4semidirect
58. C22×D4×C13C2×C4semidirect
74. C23×C4×C13C2×C4semidirect
93. C2×C13×C4⋊C4C2×C4semidirect
94. C2×C13×C4⋊C4D4semidirect
114. C2×C13×C22⋊C4C2×C4semidirect
115. C2×C13×C22⋊C4D4semidirect
121. C2×C42×C13D4semidirect
129. #13970C13direct (N × H)
174. C2×D4×C13C22⋊C4semidirect
265. C22×C4×D4C2×C13semidirect
266. C2×#390C2×C13semidirect
267. C2×#386C2×C13semidirect
268. C2×#380C2×C13semidirect
269. C2×C4×C22⋊C4C2×C13semidirect
270. #1440C2×C13semidirect
271. #1438C2×C13semidirect
272. C4⋊#95C2×C13semidirect
273. C4⋊#95C2×C13semidirect
274. C22⋊#95C2×C13semidirect
344. C23×C13C4×D4semidirect
425. C2×C4×C13#121semidirect
433. C2×#121C4×C13semidirect
533. C4×C13#386semidirect
547. C22×D4C2×C4×C13semidirect
563. C23×C4C2×C4×C13semidirect
582. C2×C4⋊C4C2×C4×C13semidirect
583. C2×C4⋊C4D4×C13semidirect
603. C2×C22⋊C4C2×C4×C13semidirect
604. C2×C22⋊C4D4×C13semidirect
610. C2×C42D4×C13semidirect
679. C2×D4C13×C22⋊C4semidirect
769. C13#13970direct (N × H)
839. C23C4×D4×C13semidirect
920. C2×C4C13×#121semidirect
995. C4C13×#386semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#1212
C22×C4×D4×C132
C2×C13×#3902
C2×C13×#3862
C2×C13×#3802
C2×C4×C13×C22⋊C42
C13×#14402
C13×#14382
C13×C4⋊#952
C13×C22⋊#952
#1397013