Finite Group Databasebeta

← C13×#13998 #15700337

Subgroups — C13×#13998 #15700337

Order 3328.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#121C211yesmaximal, characteristic
2C2×C13×#390C211yesmaximal, characteristic, complemented
3C2×C13×#390C212yesmaximal, complemented
4C2×C13×#390C211yesmaximal, characteristic, complemented
5C2×C13×#389C211yesmaximal, characteristic, complemented
6C2×C13×#380C211yesmaximal, characteristic, complemented
7C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
8C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
9C13×#1439C212yesmaximal, complemented
10C13×#1438C212yesmaximal, complemented
11C13×#1437C212yesmaximal, complemented
12C23×D4×C13C2211yescharacteristic
13C23×D4×C13C2212yes—
14C24×C4×C13C2211yescharacteristic
15C2×C13×#121—24no—
16C2×C13×#121—24no—
17C2×C13×#121C418yescomplemented
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2212yes—
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2212yes—
24C22×C13×C22⋊C4C2212yes—
25C22×C13×C22⋊C4C2212yes—
26C22×C13×C22⋊C4C2212yes—
27C22×C13×C22⋊C4C2212yes—
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2212yes—
30C22×C42×C13C2211yescharacteristic
31C22×C42×C13C2212yes—
32C22×C42×C13C2211yescharacteristic
33C13×#390—24no—
34C13×#390—28no—
35C13×#390—24no—
36C13×#389—24no—
37C13×#380—24no—
38C4×C13×C4⋊C4—24no—
39C4×C13×C22⋊C4—24no—
40C2×C13×#95C2211yescharacteristic
41C2×C13×#95C2211yescharacteristic
42C2×C13×#95C2212yes—
43C2×C13×#95C2212yes—
44C2×C13×#95C2212yes—
45C25×C13C2312yes—
46C25×C13C2311yescharacteristic
47C22×D4×C13—24no—
48C22×D4×C13—24no—
49C22×D4×C13—22no—
50C22×D4×C13—22no—
51C22×D4×C13—24no—
52C22×D4×C13—24no—
53C22×D4×C13—22no—
54C22×D4×C13—22no—
55C22×D4×C13—22no—
56C22×D4×C13—22no—
57C22×D4×C13—42no—
58C22×D4×C13—42no—
59C22×D4×C13C2×C414yes—
60C22×D4×C13C2×C418yes—
61C23×C4×C13—22no—
62C23×C4×C13—22no—
63C23×C4×C13—22no—
64C23×C4×C13—22no—
65C23×C4×C13—22no—
66C23×C4×C13—22no—
67C23×C4×C13C2×C414yes—
68C23×C4×C13C2312yes—
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2312yes—
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2312yes—
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C13×#121—232no—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—24no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—24no—
84C2×C13×C4⋊C4—22no—
85C2×C13×C4⋊C4—42no—
86C2×C13×C4⋊C4C2×C414yes—
87C2×C13×C4⋊C4D414yes—
88C2×C13×C4⋊C4D414yes—
89C2×C13×C4⋊C4D414yescomplemented
90C2×C13×C22⋊C4—22no—
91C2×C13×C22⋊C4—22no—
92C2×C13×C22⋊C4—22no—
93C2×C13×C22⋊C4—24no—
94C2×C13×C22⋊C4—24no—
95C2×C13×C22⋊C4—22no—
96C2×C13×C22⋊C4—22no—
97C2×C13×C22⋊C4—24no—
98C2×C13×C22⋊C4—24no—
99C2×C13×C22⋊C4—24no—
100C2×C13×C22⋊C4—24no—
101C2×C13×C22⋊C4—24no—
102C2×C13×C22⋊C4—24no—
103C2×C13×C22⋊C4—24no—
104C2×C13×C22⋊C4—24no—
105C2×C13×C22⋊C4—24no—
106C2×C13×C22⋊C4—24no—
107C2×C13×C22⋊C4—42no—
108C2×C13×C22⋊C4—42no—
109C2×C13×C22⋊C4—42no—
110C2×C13×C22⋊C4—42no—
111C2×C13×C22⋊C4—42no—
112C2×C13×C22⋊C4C2×C418yes—
113C2×C13×C22⋊C4D414yescomplemented
114C2×C42×C13—22no—
115C2×C42×C13—22no—
116C2×C42×C13—22no—
117C2×C42×C13—24no—
118C2×C42×C13—22no—
119C2×C42×C13—24no—
120C2×C42×C13—22no—
121C2×C42×C13—42no—
122C2×C42×C13D414yescomplemented
123C13×#95—22no—
124C13×#95—22no—
125C13×#95—24no—
126C13×#95—24no—
127C13×#95—24no—
128#13998C1311yesmaximal, characteristic, direct product factor, Sylow
129C24×C13—21no—
130C24×C13—21no—
131C24×C13—21no—
132C24×C13—21no—
133C24×C13—21no—
134C24×C13—21no—
135C24×C13—21no—
136C24×C13—21no—
137C24×C13—21no—
138C24×C13—21no—
139C24×C13—21no—
140C24×C13—21no—
141C24×C13—22no—
142C24×C13—22no—
143C24×C13—22no—
144C24×C13—22no—
145C24×C13—22no—
146C24×C13—22no—
147C24×C13—22no—
148C24×C13—22no—
149C24×C13—22no—
150C24×C13—22no—
151C24×C13—22no—
152C24×C13—22no—
153C24×C13—22no—
154C24×C13—22no—
155C24×C13C22×C414yes—
156C24×C13C22×C412yes—
157C24×C13C2×D412yes—
158C24×C13#4112yes—
159C24×C13C2411yescharacteristic
160C2×D4×C13—216no—
161C2×D4×C13—216no—
162C2×D4×C13—28no—
163C2×D4×C13—28no—
164C2×D4×C13—28no—
165C2×D4×C13—48no—
166C2×D4×C13—48no—
167C2×D4×C13—48no—
168C2×D4×C13—48no—
169C2×D4×C13—48no—
170C2×D4×C13—44no—
171C2×D4×C13—44no—
172C2×D4×C13—44no—
173C2×D4×C13—44no—
174C22×C4×C13—21no—
175C22×C4×C13—22no—
176C22×C4×C13—21no—
177C22×C4×C13—22no—
178C22×C4×C13—21no—
179C22×C4×C13—22no—
180C22×C4×C13—22no—
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—22no—
189C22×C4×C13—21no—
190C22×C4×C13—22no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—22no—
201C22×C4×C13—22no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—22no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—22no—
209C22×C4×C13—21no—
210C22×C4×C13—21no—
211C22×C4×C13—21no—
212C22×C4×C13—28no—
213C22×C4×C13—28no—
214C22×C4×C13—28no—
215C22×C4×C13—22no—
216C22×C4×C13—22no—
217C22×C4×C13—22no—
218C22×C4×C13—22no—
219C22×C4×C13—22no—
220C22×C4×C13—22no—
221C22×C4×C13—22no—
222C22×C4×C13—44no—
223C22×C4×C13—44no—
224C22×C4×C13—44no—
225C22×C4×C13—44no—
226C22×C4×C13C22×C412yes—
227C22×C4×C13C22×C414yes—
228C22×C4×C13C22×C412yes—
229C22×C4×C13C2×D412yes—
230C22×C4×C13C2×D414yes—
231C22×C4×C13C2×D412yes—
232C22×C4×C13C2×D414yes—
233C22×C4×C13C2×D414yes—
234C22×C4×C13C2×D412yes—
235C22×C4×C13C2×D412yes—
236C22×C4×C13C2×D412yes—
237C22×C4×C13C2×D412yes—
238C22×C4×C13C2×D412yes—
239C22×C4×C13C2×D412yes—
240C22×C4×C13#4112yes—
241C22×C4×C13#4112yes—
242C22×C4×C13#4112yes—
243C22×C4×C13#4112yes—
244C13×C4⋊C4—28no—
245C13×C4⋊C4—48no—
246C13×C4⋊C4—44no—
247C13×C4⋊C4C22⋊C4116yescomplemented
248C13×C22⋊C4—28no—
249C13×C22⋊C4—216no—
250C13×C22⋊C4—28no—
251C13×C22⋊C4—48no—
252C13×C22⋊C4—48no—
253C13×C22⋊C4—48no—
254C13×C22⋊C4—48no—
255C13×C22⋊C4—48no—
256C42×C13—28no—
257C42×C13—48no—
258C42×C13—44no—
259C22×#121C2×C1311yescharacteristic
260C2×#390C2×C1311yescharacteristic, complemented
261C2×#390C2×C1312yescomplemented
262C2×#390C2×C1311yescharacteristic, complemented
263C2×#389C2×C1311yescharacteristic, complemented
264C2×#380C2×C1311yescharacteristic, complemented
265C2×C4×C4⋊C4C2×C1311yescharacteristic, complemented
266C2×C4×C22⋊C4C2×C1311yescharacteristic, complemented
267#1439C2×C1312yescomplemented
268#1438C2×C1312yescomplemented
269#1437C2×C1312yescomplemented
270C23×C13—22no—
271C23×C13—22no—
272C23×C13—22no—
273C23×C13—22no—
274C23×C13—22no—
275C23×C13—22no—
276C23×C13—22no—
277C23×C13—22no—
278C23×C13—22no—
279C23×C13—22no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—24no—
289C23×C13—24no—
290C23×C13—24no—
291C23×C13—24no—
292C23×C13—24no—
293C23×C13—24no—
294C23×C13—24no—
295C23×C13—41no—
296C23×C13—41no—
297C23×C13—41no—
298C23×C13—41no—
299C23×C13—41no—
300C23×C13—41no—
301C23×C13—41no—
302C23×C13—41no—
303C23×C13—41no—
304C23×C13—41no—
305C23×C13—41no—
306C23×C13—41no—
307C23×C13—41no—
308C23×C13—41no—
309C23×C13—41no—
310C23×C13—41no—
311C23×C13—42no—
312C23×C13—42no—
313C23×C13—42no—
314C23×C13—42no—
315C23×C13—42no—
316C23×C13—42no—
317C23×C13—42no—
318C23×C13—42no—
319C23×C13—42no—
320C23×C13—42no—
321C23×C13—42no—
322C23×C13—42no—
323C23×C13—42no—
324C23×C13—42no—
325C23×C13—42no—
326C23×C13—42no—
327C23×C13—42no—
328C23×C13—42no—
329C23×C13—42no—
330C23×C13—42no—
331C23×C13—42no—
332C23×C13—42no—
333C23×C13—42no—
334C23×C13—42no—
335C23×C13—42no—
336C23×C13—42no—
337C23×C13—42no—
338C23×C13—42no—
339C23×C13C4×D414yes—
340C23×C13C23×C411yescharacteristic
341C23×C13C22×D411yescharacteristic
342C23×C13C22×D411yescharacteristic
343C23×C13C22×D411yescharacteristic
344C23×C13C22×D411yescharacteristic
345C23×C13C22×D411yescharacteristic
346C23×C13C2×#4111yescharacteristic
347C23×C13C2×#4111yescharacteristic
348C23×C13C2×#4111yescharacteristic
349C23×C13C2×#4111yescharacteristic
350C23×C13C2×#4111yescharacteristic
351C23×C13H(5,𝔽2)11yescharacteristic
352C23×C13H(5,𝔽2)11yescharacteristic
353C23×C13H(5,𝔽2)11yescharacteristic
354C23×C132−1+411yescharacteristic
355D4×C13—432no—
356D4×C13—416no—
357C2×C4×C13—24no—
358C2×C4×C13—24no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—24no—
363C2×C4×C13—24no—
364C2×C4×C13—24no—
365C2×C4×C13—24no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—24no—
375C2×C4×C13—22no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—24no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—22no—
382C2×C4×C13—24no—
383C2×C4×C13—22no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
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—42no—
394C2×C4×C13—42no—
395C2×C4×C13—41no—
396C2×C4×C13—41no—
397C2×C4×C13—41no—
398C2×C4×C13—41no—
399C2×C4×C13—42no—
400C2×C4×C13—41no—
401C2×C4×C13—41no—
402C2×C4×C13—41no—
403C2×C4×C13—41no—
404C2×C4×C13—416no—
405C2×C4×C13—42no—
406C2×C4×C13—42no—
407C2×C4×C13—42no—
408C2×C4×C13—42no—
409C2×C4×C13—42no—
410C2×C4×C13—42no—
411C2×C4×C13—42no—
412C2×C4×C13C2×C22⋊C418yes—
413C2×C4×C13C2×C22⋊C414yes—
414C2×C4×C13C4×D414yes—
415C2×C4×C13C4×D414yes—
416C2×C4×C13#12114yes—
417C2×C4×C13#12114yes—
418C2×C4×C13#12114yescomplemented
419C2×C4×C13#12414yes—
420C2×C4×C13#12714yes—
421C23×D4C22×C1311yescharacteristic
422C23×D4C22×C1312yes—
423C24×C4C22×C1311yescharacteristic
424C2×#121—24no—
425C2×#121—24no—
426C2×#121C4×C1318yescomplemented
427C22×C4⋊C4C22×C1311yescharacteristic
428C22×C4⋊C4C22×C1312yes—
429C22×C4⋊C4C22×C1311yescharacteristic
430C22×C4⋊C4C22×C1311yescharacteristic
431C22×C22⋊C4C22×C1312yes—
432C22×C22⋊C4C22×C1311yescharacteristic
433C22×C22⋊C4C22×C1312yes—
434C22×C22⋊C4C22×C1312yes—
435C22×C22⋊C4C22×C1312yes—
436C22×C22⋊C4C22×C1312yes—
437C22×C22⋊C4C22×C1311yescharacteristic
438C22×C22⋊C4C22×C1312yes—
439C22×C42C22×C1311yescharacteristic
440C22×C42C22×C1312yes—
441C22×C42C22×C1311yescharacteristic
442#390—24no—
443#390—28no—
444#390—24no—
445#389—24no—
446#380—24no—
447C4×C4⋊C4—24no—
448C4×C22⋊C4—24no—
449C2×#95C22×C1311yescharacteristic
450C2×#95C22×C1312yes—
451C2×#95C22×C1312yes—
452C2×#95C22×C1312yes—
453C2×#95C22×C1311yescharacteristic
454C22×C13—24no—
455C22×C13—24no—
456C22×C13—24no—
457C22×C13—42no—
458C22×C13—42no—
459C22×C13—42no—
460C22×C13—42no—
461C22×C13—42no—
462C22×C13—42no—
463C22×C13—42no—
464C22×C13—42no—
465C22×C13—42no—
466C22×C13—42no—
467C22×C13—42no—
468C22×C13—42no—
469C22×C13—44no—
470C22×C13—44no—
471C22×C13—44no—
472C22×C13—44no—
473C22×C13—44no—
474C22×C13—44no—
475C22×C13—44no—
476C22×C13—82no—
477C22×C13—82no—
478C22×C13—82no—
479C22×C13—82no—
480C22×C13—82no—
481C22×C13—82no—
482C22×C13—82no—
483C22×C13—82no—
484C22×C13C22×C22⋊C411yescharacteristic
485C22×C13C2×C4×D411yescharacteristic
486C22×C13C2×C4×D411yescharacteristic
487C22×C13C2×C4×D411yescharacteristic
488C22×C13C4×#4111yescharacteristic
489C22×C13#51811yescharacteristic
490C22×C13#52011yescharacteristic
491C22×C13C2×#12111yescharacteristic
492C22×C13C2×#12111yescharacteristic
493C22×C13C2×#12111yescharacteristic
494C22×C13#52511yescharacteristic
495C22×C13C2×#12411yescharacteristic
496C22×C13#52911yescharacteristic
497C22×C13C2×#12711yescharacteristic
498C22×C13#53211yescharacteristic
499C22×C13#53511yescharacteristic
500C22×C13#53711yescharacteristic
501C22×C13#54011yescharacteristic
502C22×C13#54211yescharacteristic
503C22×C13D4211yescharacteristic
504C22×C13D4211yescharacteristic
505C22×C13D4211yescharacteristic
506C22×C13#54611yescharacteristic
507C22×C13#54611yescharacteristic
508C22×C13#54611yescharacteristic
509C22×C13#54711yescharacteristic
510C22×C13#54811yescharacteristic
511C22×C13#54811yescharacteristic
512C22×C13#54811yescharacteristic
513C22×C13#55011yescharacteristic
514C22×C13#55011yescharacteristic
515C22×C13#55011yescharacteristic
516C22×C13#55311yescharacteristic
517C22×C13#55311yescharacteristic
518C22×C13#55511yescharacteristic
519C4×C13—28no—
520C4×C13—24no—
521C4×C13—42no—
522C4×C13—44no—
523C4×C13—42no—
524C4×C13—42no—
525C4×C13—42no—
526C4×C13—82no—
527C4×C13#39018yescomplemented
528C25C23×C1312yes—
529C25C23×C1311yescharacteristic
530C22×D4—24no—
531C22×D4—24no—
532C22×D4—24no—
533C22×D4—24no—
534C22×D4—22no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—42no—
541C22×D4—42no—
542C22×D4C2×C4×C1314yes—
543C22×D4C2×C4×C1318yes—
544C23×C4—22no—
545C23×C4—22no—
546C23×C4—22no—
547C23×C4—22no—
548C23×C4—22no—
549C23×C4—22no—
550C23×C4C2×C4×C1314yes—
551C23×C4C23×C1312yes—
552C23×C4C23×C1311yescharacteristic
553C23×C4C23×C1311yescharacteristic
554C23×C4C23×C1312yes—
555C23×C4C23×C1311yescharacteristic
556C23×C4C23×C1311yescharacteristic
557C23×C4C23×C1312yes—
558C23×C4C23×C1311yescharacteristic
559C23×C4C23×C1311yescharacteristic
560#121—232no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—24no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—24no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—42no—
569C2×C4⋊C4C2×C4×C1314yes—
570C2×C4⋊C4D4×C1314yes—
571C2×C4⋊C4D4×C1314yes—
572C2×C4⋊C4D4×C1314yescomplemented
573C2×C22⋊C4—22no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—24no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—24no—
581C2×C22⋊C4—24no—
582C2×C22⋊C4—24no—
583C2×C22⋊C4—24no—
584C2×C22⋊C4—24no—
585C2×C22⋊C4—24no—
586C2×C22⋊C4—24no—
587C2×C22⋊C4—24no—
588C2×C22⋊C4—24no—
589C2×C22⋊C4—24no—
590C2×C22⋊C4—42no—
591C2×C22⋊C4—42no—
592C2×C22⋊C4—42no—
593C2×C22⋊C4—42no—
594C2×C22⋊C4—42no—
595C2×C22⋊C4C2×C4×C1318yes—
596C2×C22⋊C4D4×C1314yescomplemented
597C2×C42—22no—
598C2×C42—22no—
599C2×C42—22no—
600C2×C42—24no—
601C2×C42—22no—
602C2×C42—24no—
603C2×C42—22no—
604C2×C42—42no—
605C2×C42D4×C1314yescomplemented
606#95—22no—
607#95—22no—
608#95—24no—
609#95—24no—
610#95—24no—
611C2×C13—44no—
612C2×C13—84no—
613C2×C13C2×#39011yescharacteristic
614C2×C13C4×#12111yescharacteristic
615C2×C13#232411yescharacteristic
616C2×C13D4×C22⋊C411yescharacteristic
617C2×C13#234111yescharacteristic
618C2×C13#236111yescharacteristic
619C2×C13#236311yescharacteristic
620C2×C13#241411yescharacteristic
621C2×C13#241611yescharacteristic
622C2×C13#242611yescharacteristic
623C2×C13#242811yescharacteristic
624C2×C13#249011yescharacteristic
625C2×C13#249111yescharacteristic
626C2×C13#254011yescharacteristic
627C2×C13#254111yescharacteristic
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24C22×C4×C1314yes—
655C24C22×C4×C1312yes—
656C24C2×D4×C1312yes—
657C24C13×#4112yes—
658C24C24×C1311yescharacteristic
659C2×D4—216no—
660C2×D4—216no—
661C2×D4—28no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—48no—
665C2×D4—48no—
666C2×D4—48no—
667C2×D4—48no—
668C2×D4—48no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C22×C4—21no—
674C22×C4—22no—
675C22×C4—21no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—21no—
689C22×C4—22no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—28no—
712C22×C4—28no—
713C22×C4—28no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4C22×C4×C1312yes—
726C22×C4C22×C4×C1314yes—
727C22×C4C22×C4×C1312yes—
728C22×C4C2×D4×C1312yes—
729C22×C4C2×D4×C1314yes—
730C22×C4C2×D4×C1312yes—
731C22×C4C2×D4×C1314yes—
732C22×C4C2×D4×C1314yes—
733C22×C4C2×D4×C1312yes—
734C22×C4C2×D4×C1312yes—
735C22×C4C2×D4×C1312yes—
736C22×C4C2×D4×C1312yes—
737C22×C4C2×D4×C1312yes—
738C22×C4C2×D4×C1312yes—
739C22×C4C13×#4112yes—
740C22×C4C13×#4112yes—
741C22×C4C13×#4112yes—
742C22×C4C13×#4112yes—
743C4⋊C4—28no—
744C4⋊C4—48no—
745C4⋊C4—44no—
746C4⋊C4C13×C22⋊C4116yescomplemented
747C22⋊C4—28no—
748C22⋊C4—216no—
749C22⋊C4—28no—
750C22⋊C4—48no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C42—28no—
756C42—48no—
757C42—44no—
758C13#1399811yescharacteristic, direct product factor, Sylow
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23C4×D4×C1314yes—
829C23C23×C4×C1311yescharacteristic
830C23C22×D4×C1311yescharacteristic
831C23C22×D4×C1311yescharacteristic
832C23C22×D4×C1311yescharacteristic
833C23C22×D4×C1311yescharacteristic
834C23C22×D4×C1311yescharacteristic
835C23C2×C13×#4111yescharacteristic
836C23C2×C13×#4111yescharacteristic
837C23C2×C13×#4111yescharacteristic
838C23C2×C13×#4111yescharacteristic
839C23C2×C13×#4111yescharacteristic
840C23C13×H(5,𝔽2)11yescharacteristic
841C23C13×H(5,𝔽2)11yescharacteristic
842C23C13×H(5,𝔽2)11yescharacteristic
843C23C13×2−1+411yescharacteristic
844D4—432no—
845D4—416no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—24no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—24no—
872C2×C4—22no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—42no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—42no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—416no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4C2×C13×C22⋊C418yes—
902C2×C4C2×C13×C22⋊C414yes—
903C2×C4C4×D4×C1314yes—
904C2×C4C4×D4×C1314yes—
905C2×C4C13×#12114yes—
906C2×C4C13×#12114yes—
907C2×C4C13×#12114yescomplemented
908C2×C4C13×#12414yes—
909C2×C4C13×#12714yes—
910C22—24no—
911C22—24no—
912C22—24no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22C22×C13×C22⋊C411yescharacteristic
941C22C2×C4×D4×C1311yescharacteristic
942C22C2×C4×D4×C1311yescharacteristic
943C22C2×C4×D4×C1311yescharacteristic
944C22C4×C13×#4111yescharacteristic
945C22C13×#51811yescharacteristic
946C22C13×#52011yescharacteristic
947C22C2×C13×#12111yescharacteristic
948C22C2×C13×#12111yescharacteristic
949C22C2×C13×#12111yescharacteristic
950C22C13×#52511yescharacteristic
951C22C2×C13×#12411yescharacteristic
952C22C13×#52911yescharacteristic
953C22C2×C13×#12711yescharacteristic
954C22C13×#53211yescharacteristic
955C22C13×#53511yescharacteristic
956C22C13×#53711yescharacteristic
957C22C13×#54011yescharacteristic
958C22C13×#54211yescharacteristic
959C22D42×C1311yescharacteristic
960C22D42×C1311yescharacteristic
961C22D42×C1311yescharacteristic
962C22C13×#54611yescharacteristic
963C22C13×#54611yescharacteristic
964C22C13×#54611yescharacteristic
965C22C13×#54711yescharacteristic
966C22C13×#54811yescharacteristic
967C22C13×#54811yescharacteristic
968C22C13×#54811yescharacteristic
969C22C13×#55011yescharacteristic
970C22C13×#55011yescharacteristic
971C22C13×#55011yescharacteristic
972C22C13×#55311yescharacteristic
973C22C13×#55311yescharacteristic
974C22C13×#55511yescharacteristic
975C4—28no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—44no—
982C4—82no—
983C4C13×#39018yescomplemented
984C2—44no—
985C2—84no—
986C2C2×C13×#39011yescharacteristic
987C2C4×C13×#12111yescharacteristic
988C2C13×#232411yescharacteristic
989C2D4×C13×C22⋊C411yescharacteristic
990C2C13×#234111yescharacteristic
991C2C13×#236111yescharacteristic
992C2C13×#236311yescharacteristic
993C2C13×#241411yescharacteristic
994C2C13×#241611yescharacteristic
995C2C13×#242611yescharacteristic
996C2C13×#242811yescharacteristic
997C2C13×#249011yescharacteristic
998C2C13×#249111yescharacteristic
999C2C13×#254011yescharacteristic
1000C2C13×#254111yescharacteristic
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. C2×C13×#390C2semidirect
3. C2×C13×#390C2semidirect
4. C2×C13×#390C2semidirect
5. C2×C13×#389C2semidirect
6. C2×C13×#380C2semidirect
7. C2×C4×C13×C4⋊C4C2semidirect
8. C2×C4×C13×C22⋊C4C2semidirect
9. C13×#1439C2semidirect
10. C13×#1438C2semidirect
11. C13×#1437C2semidirect
17. C2×C13×#121C4semidirect
89. C2×C13×C4⋊C4D4semidirect
113. C2×C13×C22⋊C4D4semidirect
122. C2×C42×C13D4semidirect
128. #13998C13direct (N × H)
247. C13×C4⋊C4C22⋊C4semidirect
260. C2×#390C2×C13semidirect
261. C2×#390C2×C13semidirect
262. C2×#390C2×C13semidirect
263. C2×#389C2×C13semidirect
264. C2×#380C2×C13semidirect
265. C2×C4×C4⋊C4C2×C13semidirect
266. C2×C4×C22⋊C4C2×C13semidirect
267. #1439C2×C13semidirect
268. #1438C2×C13semidirect
269. #1437C2×C13semidirect
418. C2×C4×C13#121semidirect
426. C2×#121C4×C13semidirect
527. C4×C13#390semidirect
572. C2×C4⋊C4D4×C13semidirect
596. C2×C22⋊C4D4×C13semidirect
605. C2×C42D4×C13semidirect
746. C4⋊C4C13×C22⋊C4semidirect
758. C13#13998direct (N × H)
907. C2×C4C13×#121semidirect
983. C4C13×#390semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#1212
C2×C13×#3902
C2×C13×#3892
C2×C13×#3802
C2×C4×C13×C4⋊C42
C2×C4×C13×C22⋊C42
C13×#14392
C13×#14382
C13×#14372
#1399813