Finite Group Databasebeta

← C13×#13993 #15700332

Subgroups — C13×#13993 #15700332

Order 3328.

1746 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
1C2×C13×#389C211yesmaximal, characteristic, complemented
2C2×C13×#380C211yesmaximal, characteristic
3C2×C13×#380C211yesmaximal, characteristic
4C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
6C13×#1443C212yesmaximal, complemented
7C13×#1439C212yesmaximal
8C13×#1437C212yesmaximal
9C13×#1436C212yesmaximal, complemented
10C13×C4⋊#95C211yesmaximal, characteristic, complemented
11C13×C4⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2212yes—
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2212yes—
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2212yes—
22C22×C42×C13C2211yescharacteristic
23C22×C42×C13C2211yescharacteristic
24C22×C42×C13C2212yes—
25C13×#389—24no—
26C13×#380—24no—
27C13×#380C418yescomplemented
28C4×C13×C4⋊C4—24no—
29C4×C13×C22⋊C4—24no—
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2212yes—
33C2×C13×#95C2212yes—
34C2×C13×#95C2212yes—
35C2×C13×#95C2212yes—
36C2×C13×#95C2212yes—
37C2×C13×#95C2212yes—
38C2×C13×#95C2212yes—
39C2×C13×#95C2212yes—
40C25×C13C2311yescharacteristic
41C23×C4×C13—22no—
42C23×C4×C13—22no—
43C23×C4×C13—22no—
44C23×C4×C13—22no—
45C23×C4×C13—22no—
46C23×C4×C13—22no—
47C23×C4×C13C2×C414yes—
48C23×C4×C13C2312yes—
49C23×C4×C13C2312yes—
50C23×C4×C13C2312yes—
51C23×C4×C13C2311yescharacteristic
52C23×C4×C13C2312yes—
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—24no—
66C2×C13×C4⋊C4—24no—
67C2×C13×C4⋊C4—22no—
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—42no—
70C2×C13×C4⋊C4C2×C414yes—
71C2×C13×C4⋊C4C2×C414yes—
72C2×C13×C4⋊C4D414yes—
73C2×C13×C22⋊C4—22no—
74C2×C13×C22⋊C4—22no—
75C2×C13×C22⋊C4—22no—
76C2×C13×C22⋊C4—22no—
77C2×C13×C22⋊C4—22no—
78C2×C13×C22⋊C4—24no—
79C2×C13×C22⋊C4—24no—
80C2×C13×C22⋊C4—42no—
81C2×C13×C22⋊C4—42no—
82C2×C13×C22⋊C4—42no—
83C2×C13×C22⋊C4C2×C418yes—
84C2×C13×C22⋊C4Q814yes—
85C2×C42×C13—22no—
86C2×C42×C13—22no—
87C2×C42×C13—22no—
88C2×C42×C13—24no—
89C2×C42×C13—22no—
90C2×C42×C13—22no—
91C2×C42×C13—42no—
92C2×C42×C13—42no—
93C2×C42×C13D414yes—
94C13×#95—22no—
95C13×#95—22no—
96C13×#95—24no—
97C13×#95—24no—
98C13×#95—24no—
99C13×#95—24no—
100C13×#95—42no—
101C13×#95—42no—
102C13×#95—42no—
103C13×#95C2×C418yes—
104#13993C1311yesmaximal, characteristic, direct product factor, Sylow
105C24×C13—21no—
106C24×C13—21no—
107C24×C13—21no—
108C24×C13—21no—
109C24×C13—21no—
110C24×C13—21no—
111C24×C13—21no—
112C24×C13—21no—
113C24×C13—21no—
114C24×C13—21no—
115C24×C13—21no—
116C24×C13—21no—
117C24×C13C22×C412yes—
118C24×C13C2×Q812yes—
119C24×C13#4112yes—
120C24×C13C2411yescharacteristic
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—21no—
134C22×C4×C13—22no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—21no—
164C22×C4×C13—22no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—28no—
168C22×C4×C13—28no—
169C22×C4×C13—28no—
170C22×C4×C13—22no—
171C22×C4×C13—22no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—22no—
175C22×C4×C13—22no—
176C22×C4×C13—22no—
177C22×C4×C13—44no—
178C22×C4×C13—44no—
179C22×C4×C13—44no—
180C22×C4×C13—44no—
181C22×C4×C13C22×C412yes—
182C22×C4×C13C22×C414yes—
183C22×C4×C13C22×C414yes—
184C22×C4×C13C22×C412yes—
185C22×C4×C13C2×D412yes—
186C22×C4×C13C2×D414yes—
187C22×C4×C13C2×D412yes—
188C22×C4×C13C2×D412yes—
189C22×C4×C13C2×D412yes—
190C22×C4×C13C2×Q812yes—
191C22×C4×C13C2×Q812yes—
192C22×C4×C13#4112yes—
193C22×C4×C13#4112yes—
194C22×C4×C13#4112yes—
195C22×C4×C13#4112yes—
196C22×C4×C13#4112yes—
197C22×C4×C13#4112yes—
198C13×C4⋊C4—28no—
199C13×C4⋊C4—28no—
200C13×C4⋊C4—28no—
201C13×C4⋊C4—48no—
202C13×C4⋊C4—44no—
203C13×C22⋊C4—28no—
204C13×C22⋊C4—28no—
205C13×C22⋊C4—48no—
206C13×C22⋊C4—48no—
207C42×C13—28no—
208C42×C13—48no—
209C42×C13—44no—
210C2×#389C2×C1311yescharacteristic, complemented
211C2×#380C2×C1311yescharacteristic
212C2×#380C2×C1311yescharacteristic
213C2×C4×C4⋊C4C2×C1311yescharacteristic, complemented
214C2×C4×C22⋊C4C2×C1311yescharacteristic
215#1443C2×C1312yescomplemented
216#1439C2×C1312yes—
217#1437C2×C1312yes—
218#1436C2×C1312yescomplemented
219C4⋊#95C2×C1311yescharacteristic, complemented
220C4⋊#95C2×C1311yescharacteristic, complemented
221C23×C13—22no—
222C23×C13—22no—
223C23×C13—22no—
224C23×C13—22no—
225C23×C13—22no—
226C23×C13—22no—
227C23×C13—22no—
228C23×C13—22no—
229C23×C13—22no—
230C23×C13—22no—
231C23×C13—22no—
232C23×C13—22no—
233C23×C13—22no—
234C23×C13—22no—
235C23×C13—22no—
236C23×C13—22no—
237C23×C13—22no—
238C23×C13—22no—
239C23×C13—41no—
240C23×C13—41no—
241C23×C13—41no—
242C23×C13—41no—
243C23×C13—41no—
244C23×C13—41no—
245C23×C13—41no—
246C23×C13—41no—
247C23×C13—41no—
248C23×C13—41no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13—41no—
252C23×C13—41no—
253C23×C13—41no—
254C23×C13—41no—
255C23×C13C4×Q814yes—
256C23×C13C23×C411yescharacteristic
257C23×C13C22×D411yescharacteristic
258C23×C13C22×D411yescharacteristic
259C23×C13C22×Q811yescharacteristic
260C23×C13C2×#4111yescharacteristic
261C23×C13C2×#4111yescharacteristic
262C23×C13C2×#4111yescharacteristic
263C23×C13C2×#4111yescharacteristic
264C23×C13C2×#4111yescharacteristic
265C23×C13C2×#4111yescharacteristic
266C23×C13C2×#4111yescharacteristic
267C23×C13H(5,𝔽2)11yescharacteristic
268C23×C13H(5,𝔽2)11yescharacteristic
269C23×C13H(5,𝔽2)11yescharacteristic
270C23×C132−1+411yescharacteristic
271C2×C4×C13—22no—
272C2×C4×C13—22no—
273C2×C4×C13—22no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—22no—
278C2×C4×C13—24no—
279C2×C4×C13—24no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—24no—
283C2×C4×C13—24no—
284C2×C4×C13—24no—
285C2×C4×C13—24no—
286C2×C4×C13—24no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—24no—
293C2×C4×C13—22no—
294C2×C4×C13—24no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—41no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—42no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—42no—
306C2×C4×C13—42no—
307C2×C4×C13—41no—
308C2×C4×C13—42no—
309C2×C4×C13—41no—
310C2×C4×C13—42no—
311C2×C4×C13—42no—
312C2×C4×C13—42no—
313C2×C4×C13—41no—
314C2×C4×C13—42no—
315C2×C4×C13—41no—
316C2×C4×C13—41no—
317C2×C4×C13—42no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13—42no—
321C2×C4×C13—42no—
322C2×C4×C13—42no—
323C2×C4×C13—41no—
324C2×C4×C13—41no—
325C2×C4×C13—41no—
326C2×C4×C13—416no—
327C2×C4×C13—42no—
328C2×C4×C13—42no—
329C2×C4×C13—42no—
330C2×C4×C13—42no—
331C2×C4×C13—42no—
332C2×C4×C13—42no—
333C2×C4×C13—42no—
334C2×C4×C13#11714yes—
335C2×C4×C13C4×D414yes—
336C2×C4×C13C4×D414yes—
337C2×C4×C13#12114yes—
338C2×C4×C13C22⋊Q814yes—
339C2×C4×C13#12314yes—
340C2×C4×C13#12414yes—
341C2×C4×C13#12614yes—
342C24×C4C22×C1311yescharacteristic
343C22×C4⋊C4C22×C1311yescharacteristic
344C22×C4⋊C4C22×C1312yes—
345C22×C4⋊C4C22×C1311yescharacteristic
346C22×C4⋊C4C22×C1311yescharacteristic
347C22×C4⋊C4C22×C1311yescharacteristic
348C22×C22⋊C4C22×C1311yescharacteristic
349C22×C22⋊C4C22×C1312yes—
350C22×C22⋊C4C22×C1311yescharacteristic
351C22×C22⋊C4C22×C1312yes—
352C22×C42C22×C1311yescharacteristic
353C22×C42C22×C1311yescharacteristic
354C22×C42C22×C1312yes—
355#389—24no—
356#380—24no—
357#380C4×C1318yescomplemented
358C4×C4⋊C4—24no—
359C4×C22⋊C4—24no—
360C2×#95C22×C1312yes—
361C2×#95C22×C1311yescharacteristic
362C2×#95C22×C1312yes—
363C2×#95C22×C1312yes—
364C2×#95C22×C1312yes—
365C2×#95C22×C1311yescharacteristic
366C2×#95C22×C1312yes—
367C2×#95C22×C1312yes—
368C2×#95C22×C1312yes—
369C2×#95C22×C1312yes—
370C22×C13—24no—
371C22×C13—24no—
372C22×C13—24no—
373C22×C13—42no—
374C22×C13—42no—
375C22×C13—42no—
376C22×C13—42no—
377C22×C13—42no—
378C22×C13—42no—
379C22×C13—42no—
380C22×C13—42no—
381C22×C13—42no—
382C22×C13—42no—
383C22×C13—42no—
384C22×C13—42no—
385C22×C13C2×#11711yescharacteristic
386C22×C13C2×C4×D411yescharacteristic
387C22×C13C2×C4×D411yescharacteristic
388C22×C13C2×C4×Q811yescharacteristic
389C22×C13C4×#4111yescharacteristic
390C22×C13#51811yescharacteristic
391C22×C13#52011yescharacteristic
392C22×C13C2×#12111yescharacteristic
393C22×C13C2×C22⋊Q811yescharacteristic
394C22×C13C2×#12311yescharacteristic
395C22×C13#52511yescharacteristic
396C22×C13C2×#12411yescharacteristic
397C22×C13C2×#12611yescharacteristic
398C22×C13#52911yescharacteristic
399C22×C13#53311yescharacteristic
400C22×C13#53511yescharacteristic
401C22×C13#53711yescharacteristic
402C22×C13#54011yescharacteristic
403C22×C13#54211yescharacteristic
404C22×C13#54611yescharacteristic
405C22×C13#54611yescharacteristic
406C22×C13D4×Q811yescharacteristic
407C22×C13#55011yescharacteristic
408C22×C13#55211yescharacteristic
409C22×C13#55311yescharacteristic
410C22×C13#55311yescharacteristic
411C22×C13#55311yescharacteristic
412C22×C13#55311yescharacteristic
413C22×C13#55311yescharacteristic
414C22×C13#55411yescharacteristic
415C22×C13#55411yescharacteristic
416C22×C13#55411yescharacteristic
417C22×C13#55511yescharacteristic
418C22×C13#55611yescharacteristic
419C22×C13#55611yescharacteristic
420C4×C13—24no—
421C4×C13—44no—
422C4×C13—44no—
423C4×C13—42no—
424C4×C13—44no—
425C4×C13—42no—
426C4×C13—42no—
427C4×C13—42no—
428C4×C13—82no—
429C4×C13#38818yes—
430C25C23×C1311yescharacteristic
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4C2×C4×C1314yes—
438C23×C4C23×C1312yes—
439C23×C4C23×C1312yes—
440C23×C4C23×C1312yes—
441C23×C4C23×C1311yescharacteristic
442C23×C4C23×C1312yes—
443C23×C4C23×C1311yescharacteristic
444C23×C4C23×C1311yescharacteristic
445C23×C4C23×C1311yescharacteristic
446C23×C4C23×C1311yescharacteristic
447C23×C4C23×C1311yescharacteristic
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4C2×C4×C1314yes—
461C2×C4⋊C4C2×C4×C1314yes—
462C2×C4⋊C4D4×C1314yes—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—42no—
471C2×C22⋊C4—42no—
472C2×C22⋊C4—42no—
473C2×C22⋊C4C2×C4×C1318yes—
474C2×C22⋊C4Q8×C1314yes—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—22no—
478C2×C42—24no—
479C2×C42—22no—
480C2×C42—22no—
481C2×C42—42no—
482C2×C42—42no—
483C2×C42D4×C1314yes—
484#95—22no—
485#95—22no—
486#95—24no—
487#95—24no—
488#95—24no—
489#95—24no—
490#95—42no—
491#95—42no—
492#95—42no—
493#95C2×C4×C1318yes—
494C2×C13—44no—
495C2×C13C2×#38811yescharacteristic
496C2×C13C4×C22⋊Q811yescharacteristic
497C2×C13#232411yescharacteristic
498C2×C13#234511yescharacteristic
499C2×C13#234711yescharacteristic
500C2×C13#236011yescharacteristic
501C2×C13#236311yescharacteristic
502C2×C13#248511yescharacteristic
503C2×C13#248711yescharacteristic
504C2×C13#249011yescharacteristic
505C2×C13#249211yescharacteristic
506C2×C13#249411yescharacteristic
507C2×C13#249711yescharacteristic
508C2×C13#253511yescharacteristic
509C2×C13#253811yescharacteristic
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24C22×C4×C1312yes—
523C24C2×Q8×C1312yes—
524C24C13×#4112yes—
525C24C24×C1311yescharacteristic
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—28no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4C22×C4×C1312yes—
587C22×C4C22×C4×C1314yes—
588C22×C4C22×C4×C1314yes—
589C22×C4C22×C4×C1312yes—
590C22×C4C2×D4×C1312yes—
591C22×C4C2×D4×C1314yes—
592C22×C4C2×D4×C1312yes—
593C22×C4C2×D4×C1312yes—
594C22×C4C2×D4×C1312yes—
595C22×C4C2×Q8×C1312yes—
596C22×C4C2×Q8×C1312yes—
597C22×C4C13×#4112yes—
598C22×C4C13×#4112yes—
599C22×C4C13×#4112yes—
600C22×C4C13×#4112yes—
601C22×C4C13×#4112yes—
602C22×C4C13×#4112yes—
603C4⋊C4—28no—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—48no—
607C4⋊C4—44no—
608C22⋊C4—28no—
609C22⋊C4—28no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C42—28no—
613C42—48no—
614C42—44no—
615C13#1399311yescharacteristic, direct product factor, Sylow
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23C4×Q8×C1314yes—
651C23C23×C4×C1311yescharacteristic
652C23C22×D4×C1311yescharacteristic
653C23C22×D4×C1311yescharacteristic
654C23C22×Q8×C1311yescharacteristic
655C23C2×C13×#4111yescharacteristic
656C23C2×C13×#4111yescharacteristic
657C23C2×C13×#4111yescharacteristic
658C23C2×C13×#4111yescharacteristic
659C23C2×C13×#4111yescharacteristic
660C23C2×C13×#4111yescharacteristic
661C23C2×C13×#4111yescharacteristic
662C23C13×H(5,𝔽2)11yescharacteristic
663C23C13×H(5,𝔽2)11yescharacteristic
664C23C13×H(5,𝔽2)11yescharacteristic
665C23C13×2−1+411yescharacteristic
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—416no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4C13×#11714yes—
730C2×C4C4×D4×C1314yes—
731C2×C4C4×D4×C1314yes—
732C2×C4C13×#12114yes—
733C2×C4C13×C22⋊Q814yes—
734C2×C4C13×#12314yes—
735C2×C4C13×#12414yes—
736C2×C4C13×#12614yes—
737C22—24no—
738C22—24no—
739C22—24no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22C2×C13×#11711yescharacteristic
753C22C2×C4×D4×C1311yescharacteristic
754C22C2×C4×D4×C1311yescharacteristic
755C22C2×C4×Q8×C1311yescharacteristic
756C22C4×C13×#4111yescharacteristic
757C22C13×#51811yescharacteristic
758C22C13×#52011yescharacteristic
759C22C2×C13×#12111yescharacteristic
760C22C2×C13×C22⋊Q811yescharacteristic
761C22C2×C13×#12311yescharacteristic
762C22C13×#52511yescharacteristic
763C22C2×C13×#12411yescharacteristic
764C22C2×C13×#12611yescharacteristic
765C22C13×#52911yescharacteristic
766C22C13×#53311yescharacteristic
767C22C13×#53511yescharacteristic
768C22C13×#53711yescharacteristic
769C22C13×#54011yescharacteristic
770C22C13×#54211yescharacteristic
771C22C13×#54611yescharacteristic
772C22C13×#54611yescharacteristic
773C22D4×Q8×C1311yescharacteristic
774C22C13×#55011yescharacteristic
775C22C13×#55211yescharacteristic
776C22C13×#55311yescharacteristic
777C22C13×#55311yescharacteristic
778C22C13×#55311yescharacteristic
779C22C13×#55311yescharacteristic
780C22C13×#55311yescharacteristic
781C22C13×#55411yescharacteristic
782C22C13×#55411yescharacteristic
783C22C13×#55411yescharacteristic
784C22C13×#55511yescharacteristic
785C22C13×#55611yescharacteristic
786C22C13×#55611yescharacteristic
787C4—24no—
788C4—44no—
789C4—42no—
790C4—42no—
791C4—42no—
792C4—44no—
793C4—44no—
794C4—42no—
795C4—82no—
796C4C13×#38818yes—
797C2—44no—
798C2C2×C13×#38811yescharacteristic
799C2C4×C13×C22⋊Q811yescharacteristic
800C2C13×#232411yescharacteristic
801C2C13×#234511yescharacteristic
802C2C13×#234711yescharacteristic
803C2C13×#236011yescharacteristic
804C2C13×#236311yescharacteristic
805C2C13×#248511yescharacteristic
806C2C13×#248711yescharacteristic
807C2C13×#249011yescharacteristic
808C2C13×#249211yescharacteristic
809C2C13×#249411yescharacteristic
810C2C13×#249711yescharacteristic
811C2C13×#253511yescharacteristic
812C2C13×#253811yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutatorC23C23×C4×C13
Frattini, cosocleC24C24×C13
prime radicalC25×C13C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#389C2semidirect
4. C2×C4×C13×C4⋊C4C2semidirect
6. C13×#1443C2semidirect
9. C13×#1436C2semidirect
10. C13×C4⋊#95C2semidirect
11. C13×C4⋊#95C2semidirect
27. C13×#380C4semidirect
104. #13993C13direct (N × H)
210. C2×#389C2×C13semidirect
213. C2×C4×C4⋊C4C2×C13semidirect
215. #1443C2×C13semidirect
218. #1436C2×C13semidirect
219. C4⋊#95C2×C13semidirect
220. C4⋊#95C2×C13semidirect
357. #380C4×C13semidirect
615. C13#13993direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3892
C2×C13×#3802
C2×C4×C13×C4⋊C42
C2×C4×C13×C22⋊C42
C13×#14432
C13×#14392
C13×#14372
C13×#14362
C13×C4⋊#952
#1399313