Finite Group Databasebeta

← C13×#13994 #15700333

Subgroups — C13×#13994 #15700333

Order 3328.

1802 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#389C211yesmaximal, characteristic, complemented
2C2×C13×#388C212yesmaximal
3C2×C13×#380C211yesmaximal, characteristic
4C2×C13×#380C211yesmaximal, characteristic
5C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
6C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
7C13×#1442C212yesmaximal, complemented
8C13×#1440C212yesmaximal
9C13×C4⋊#95C211yesmaximal, characteristic, complemented
10C13×C4⋊#95C211yesmaximal, characteristic, complemented
11C13×#1434C212yesmaximal, 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⋊C4C2212yes—
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C42×C13C2211yescharacteristic
23C22×C42×C13C2212yes—
24C22×C42×C13C2211yescharacteristic
25C13×#389—24no—
26C13×#388—28no—
27C13×#380—24no—
28C13×#380C418yescomplemented
29C4×C13×C4⋊C4—24no—
30C4×C13×C22⋊C4—24no—
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2212yes—
34C2×C13×#95C2212yes—
35C2×C13×#95C2212yes—
36C2×C13×#95C2212yes—
37C2×C13×#95C2212yes—
38C2×C13×#95C2212yes—
39C2×C13×#95C2212yes—
40C2×C13×#95C2212yes—
41C25×C13C2311yescharacteristic
42C23×C4×C13—22no—
43C23×C4×C13—22no—
44C23×C4×C13—22no—
45C23×C4×C13—22no—
46C23×C4×C13—22no—
47C23×C4×C13—22no—
48C23×C4×C13C2×C414yes—
49C23×C4×C13C2312yes—
50C23×C4×C13C2312yes—
51C23×C4×C13C2312yes—
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2312yes—
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
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—22no—
66C2×C13×C4⋊C4—24no—
67C2×C13×C4⋊C4—24no—
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—42no—
71C2×C13×C4⋊C4C2×C414yes—
72C2×C13×C4⋊C4C2×C414yes—
73C2×C13×C4⋊C4D414yes—
74C2×C13×C22⋊C4—24no—
75C2×C13×C22⋊C4—22no—
76C2×C13×C22⋊C4—24no—
77C2×C13×C22⋊C4—22no—
78C2×C13×C22⋊C4—22no—
79C2×C13×C22⋊C4—22no—
80C2×C13×C22⋊C4—22no—
81C2×C13×C22⋊C4—24no—
82C2×C13×C22⋊C4—24no—
83C2×C13×C22⋊C4—42no—
84C2×C13×C22⋊C4C2×C418yes—
85C2×C13×C22⋊C4D414yes—
86C2×C42×C13—22no—
87C2×C42×C13—22no—
88C2×C42×C13—22no—
89C2×C42×C13—24no—
90C2×C42×C13—24no—
91C2×C42×C13—22no—
92C2×C42×C13—24no—
93C2×C42×C13—22no—
94C2×C42×C13D414yes—
95C13×#95—22no—
96C13×#95—22no—
97C13×#95—24no—
98C13×#95—24no—
99C13×#95—24no—
100C13×#95—24no—
101C13×#95—24no—
102C13×#95—24no—
103C13×#95—42no—
104C13×#95C2×C418yes—
105#13994C1311yesmaximal, characteristic, direct product factor, Sylow
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×C13—21no—
118C24×C13C22×C412yes—
119C24×C13C2×D412yes—
120C24×C13#4112yes—
121C24×C13C2411yescharacteristic
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—22no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—21no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—22no—
144C22×C4×C13—21no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—21no—
162C22×C4×C13—22no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—22no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—28no—
169C22×C4×C13—28no—
170C22×C4×C13—28no—
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—22no—
178C22×C4×C13—44no—
179C22×C4×C13—44no—
180C22×C4×C13—44no—
181C22×C4×C13—44no—
182C22×C4×C13C22×C412yes—
183C22×C4×C13C22×C414yes—
184C22×C4×C13C22×C414yes—
185C22×C4×C13C22×C412yes—
186C22×C4×C13C2×D412yes—
187C22×C4×C13C2×D414yes—
188C22×C4×C13C2×D412yes—
189C22×C4×C13C2×D412yes—
190C22×C4×C13C2×D412yes—
191C22×C4×C13C2×D412yes—
192C22×C4×C13C2×D412yes—
193C22×C4×C13#4112yes—
194C22×C4×C13#4112yes—
195C22×C4×C13#4112yes—
196C22×C4×C13#4112yes—
197C22×C4×C13#4112yes—
198C22×C4×C13#4112yes—
199C13×C4⋊C4—28no—
200C13×C4⋊C4—28no—
201C13×C4⋊C4—28no—
202C13×C4⋊C4—48no—
203C13×C4⋊C4—44no—
204C13×C22⋊C4—28no—
205C13×C22⋊C4—216no—
206C13×C22⋊C4—28no—
207C13×C22⋊C4—48no—
208C42×C13—28no—
209C42×C13—48no—
210C42×C13—44no—
211C2×#389C2×C1311yescharacteristic, complemented
212C2×#388C2×C1312yes—
213C2×#380C2×C1311yescharacteristic
214C2×#380C2×C1311yescharacteristic
215C2×C4×C4⋊C4C2×C1311yescharacteristic, complemented
216C2×C4×C22⋊C4C2×C1311yescharacteristic
217#1442C2×C1312yescomplemented
218#1440C2×C1312yes—
219C4⋊#95C2×C1311yescharacteristic, complemented
220C4⋊#95C2×C1311yescharacteristic, complemented
221#1434C2×C1312yescomplemented
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—22no—
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×C13—41no—
256C23×C13C4×D414yes—
257C23×C13C23×C411yescharacteristic
258C23×C13C22×D411yescharacteristic
259C23×C13C22×D411yescharacteristic
260C23×C13C22×D411yescharacteristic
261C23×C13C2×#4111yescharacteristic
262C23×C13C2×#4111yescharacteristic
263C23×C13C2×#4111yescharacteristic
264C23×C13C2×#4111yescharacteristic
265C23×C13C2×#4111yescharacteristic
266C23×C13C2×#4111yescharacteristic
267C23×C13C2×#4111yescharacteristic
268C23×C13H(5,𝔽2)11yescharacteristic
269C23×C132−1+411yescharacteristic
270C23×C132−1+411yescharacteristic
271C23×C132−1+411yescharacteristic
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—22no—
279C2×C4×C13—24no—
280C2×C4×C13—24no—
281C2×C4×C13—24no—
282C2×C4×C13—24no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—24no—
286C2×C4×C13—24no—
287C2×C4×C13—22no—
288C2×C4×C13—24no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—24no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—24no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—41no—
300C2×C4×C13—42no—
301C2×C4×C13—41no—
302C2×C4×C13—42no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—42no—
306C2×C4×C13—41no—
307C2×C4×C13—41no—
308C2×C4×C13—42no—
309C2×C4×C13—42no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—42no—
313C2×C4×C13—42no—
314C2×C4×C13—42no—
315C2×C4×C13—42no—
316C2×C4×C13—41no—
317C2×C4×C13—42no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×C4×C13—42no—
322C2×C4×C13—41no—
323C2×C4×C13—41no—
324C2×C4×C13—41no—
325C2×C4×C13—42no—
326C2×C4×C13—41no—
327C2×C4×C13—416no—
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—42no—
335C2×C4×C13#11714yes—
336C2×C4×C13C4×D414yes—
337C2×C4×C13C4×D414yes—
338C2×C4×C13#12114yes—
339C2×C4×C13#12114yes—
340C2×C4×C13#12314yes—
341C2×C4×C13#12414yes—
342C2×C4×C13#12614yes—
343C24×C4C22×C1311yescharacteristic
344C22×C4⋊C4C22×C1311yescharacteristic
345C22×C4⋊C4C22×C1312yes—
346C22×C4⋊C4C22×C1311yescharacteristic
347C22×C4⋊C4C22×C1311yescharacteristic
348C22×C4⋊C4C22×C1311yescharacteristic
349C22×C22⋊C4C22×C1311yescharacteristic
350C22×C22⋊C4C22×C1312yes—
351C22×C22⋊C4C22×C1312yes—
352C22×C22⋊C4C22×C1311yescharacteristic
353C22×C42C22×C1312yes—
354C22×C42C22×C1311yescharacteristic
355C22×C42C22×C1311yescharacteristic
356#389—24no—
357#388—28no—
358#380—24no—
359#380C4×C1318yescomplemented
360C4×C4⋊C4—24no—
361C4×C22⋊C4—24no—
362C2×#95C22×C1311yescharacteristic
363C2×#95C22×C1312yes—
364C2×#95C22×C1312yes—
365C2×#95C22×C1312yes—
366C2×#95C22×C1312yes—
367C2×#95C22×C1312yes—
368C2×#95C22×C1312yes—
369C2×#95C22×C1311yescharacteristic
370C2×#95C22×C1312yes—
371C2×#95C22×C1312yes—
372C22×C13—24no—
373C22×C13—24no—
374C22×C13—24no—
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×C13—42no—
386C22×C13—42no—
387C22×C13C2×#11711yescharacteristic
388C22×C13C2×C4×D411yescharacteristic
389C22×C13C2×C4×D411yescharacteristic
390C22×C13C2×C4×D411yescharacteristic
391C22×C13C4×#4111yescharacteristic
392C22×C13#51911yescharacteristic
393C22×C13#52011yescharacteristic
394C22×C13C2×#12111yescharacteristic
395C22×C13C2×#12111yescharacteristic
396C22×C13C2×#12311yescharacteristic
397C22×C13#52511yescharacteristic
398C22×C13C2×#12411yescharacteristic
399C22×C13C2×#12611yescharacteristic
400C22×C13#52911yescharacteristic
401C22×C13#53211yescharacteristic
402C22×C13#53611yescharacteristic
403C22×C13#53711yescharacteristic
404C22×C13#54111yescharacteristic
405C22×C13#54211yescharacteristic
406C22×C13D4211yescharacteristic
407C22×C13#54711yescharacteristic
408C22×C13#54711yescharacteristic
409C22×C13#54711yescharacteristic
410C22×C13#54711yescharacteristic
411C22×C13#54811yescharacteristic
412C22×C13#54811yescharacteristic
413C22×C13#55211yescharacteristic
414C22×C13#55211yescharacteristic
415C22×C13#55211yescharacteristic
416C22×C13#55211yescharacteristic
417C22×C13#55211yescharacteristic
418C22×C13#55311yescharacteristic
419C22×C13#55511yescharacteristic
420C22×C13#55511yescharacteristic
421C22×C13#55611yescharacteristic
422C4×C13—24no—
423C4×C13—44no—
424C4×C13—42no—
425C4×C13—42no—
426C4×C13—42no—
427C4×C13—44no—
428C4×C13—42no—
429C4×C13—44no—
430C4×C13—82no—
431C4×C13#38818yescomplemented
432C25C23×C1311yescharacteristic
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—22no—
439C23×C4C2×C4×C1314yes—
440C23×C4C23×C1312yes—
441C23×C4C23×C1312yes—
442C23×C4C23×C1312yes—
443C23×C4C23×C1311yescharacteristic
444C23×C4C23×C1311yescharacteristic
445C23×C4C23×C1312yes—
446C23×C4C23×C1311yescharacteristic
447C23×C4C23×C1311yescharacteristic
448C23×C4C23×C1311yescharacteristic
449C23×C4C23×C1311yescharacteristic
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4C2×C4×C1314yes—
463C2×C4⋊C4C2×C4×C1314yes—
464C2×C4⋊C4D4×C1314yes—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—42no—
475C2×C22⋊C4C2×C4×C1318yes—
476C2×C22⋊C4D4×C1314yes—
477C2×C42—22no—
478C2×C42—22no—
479C2×C42—22no—
480C2×C42—24no—
481C2×C42—24no—
482C2×C42—22no—
483C2×C42—24no—
484C2×C42—22no—
485C2×C42D4×C1314yes—
486#95—22no—
487#95—22no—
488#95—24no—
489#95—24no—
490#95—24no—
491#95—24no—
492#95—24no—
493#95—24no—
494#95—42no—
495#95C2×C4×C1318yes—
496C2×C13—44no—
497C2×C13C2×#38811yescharacteristic
498C2×C13C4×#12111yescharacteristic
499C2×C13#232311yescharacteristic
500C2×C13#234411yescharacteristic
501C2×C13#234611yescharacteristic
502C2×C13#236111yescharacteristic
503C2×C13#236211yescharacteristic
504C2×C13#248511yescharacteristic
505C2×C13#248611yescharacteristic
506C2×C13#248911yescharacteristic
507C2×C13#249111yescharacteristic
508C2×C13#249511yescharacteristic
509C2×C13#249611yescharacteristic
510C2×C13#253611yescharacteristic
511C2×C13#253711yescharacteristic
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24C22×C4×C1312yes—
525C24C2×D4×C1312yes—
526C24C13×#4112yes—
527C24C24×C1311yescharacteristic
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—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—28no—
575C22×C4—28no—
576C22×C4—28no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4C22×C4×C1312yes—
589C22×C4C22×C4×C1314yes—
590C22×C4C22×C4×C1314yes—
591C22×C4C22×C4×C1312yes—
592C22×C4C2×D4×C1312yes—
593C22×C4C2×D4×C1314yes—
594C22×C4C2×D4×C1312yes—
595C22×C4C2×D4×C1312yes—
596C22×C4C2×D4×C1312yes—
597C22×C4C2×D4×C1312yes—
598C22×C4C2×D4×C1312yes—
599C22×C4C13×#4112yes—
600C22×C4C13×#4112yes—
601C22×C4C13×#4112yes—
602C22×C4C13×#4112yes—
603C22×C4C13×#4112yes—
604C22×C4C13×#4112yes—
605C4⋊C4—28no—
606C4⋊C4—28no—
607C4⋊C4—28no—
608C4⋊C4—48no—
609C4⋊C4—44no—
610C22⋊C4—28no—
611C22⋊C4—216no—
612C22⋊C4—28no—
613C22⋊C4—48no—
614C42—28no—
615C42—48no—
616C42—44no—
617C13#1399411yescharacteristic, direct product factor, Sylow
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—22no—
635C23—22no—
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—
650C23—41no—
651C23—41no—
652C23C4×D4×C1314yes—
653C23C23×C4×C1311yescharacteristic
654C23C22×D4×C1311yescharacteristic
655C23C22×D4×C1311yescharacteristic
656C23C22×D4×C1311yescharacteristic
657C23C2×C13×#4111yescharacteristic
658C23C2×C13×#4111yescharacteristic
659C23C2×C13×#4111yescharacteristic
660C23C2×C13×#4111yescharacteristic
661C23C2×C13×#4111yescharacteristic
662C23C2×C13×#4111yescharacteristic
663C23C2×C13×#4111yescharacteristic
664C23C13×H(5,𝔽2)11yescharacteristic
665C23C13×2−1+411yescharacteristic
666C23C13×2−1+411yescharacteristic
667C23C13×2−1+411yescharacteristic
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—416no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4C13×#11714yes—
732C2×C4C4×D4×C1314yes—
733C2×C4C4×D4×C1314yes—
734C2×C4C13×#12114yes—
735C2×C4C13×#12114yes—
736C2×C4C13×#12314yes—
737C2×C4C13×#12414yes—
738C2×C4C13×#12614yes—
739C22—24no—
740C22—24no—
741C22—24no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22C2×C13×#11711yescharacteristic
755C22C2×C4×D4×C1311yescharacteristic
756C22C2×C4×D4×C1311yescharacteristic
757C22C2×C4×D4×C1311yescharacteristic
758C22C4×C13×#4111yescharacteristic
759C22C13×#51911yescharacteristic
760C22C13×#52011yescharacteristic
761C22C2×C13×#12111yescharacteristic
762C22C2×C13×#12111yescharacteristic
763C22C2×C13×#12311yescharacteristic
764C22C13×#52511yescharacteristic
765C22C2×C13×#12411yescharacteristic
766C22C2×C13×#12611yescharacteristic
767C22C13×#52911yescharacteristic
768C22C13×#53211yescharacteristic
769C22C13×#53611yescharacteristic
770C22C13×#53711yescharacteristic
771C22C13×#54111yescharacteristic
772C22C13×#54211yescharacteristic
773C22D42×C1311yescharacteristic
774C22C13×#54711yescharacteristic
775C22C13×#54711yescharacteristic
776C22C13×#54711yescharacteristic
777C22C13×#54711yescharacteristic
778C22C13×#54811yescharacteristic
779C22C13×#54811yescharacteristic
780C22C13×#55211yescharacteristic
781C22C13×#55211yescharacteristic
782C22C13×#55211yescharacteristic
783C22C13×#55211yescharacteristic
784C22C13×#55211yescharacteristic
785C22C13×#55311yescharacteristic
786C22C13×#55511yescharacteristic
787C22C13×#55511yescharacteristic
788C22C13×#55611yescharacteristic
789C4—24no—
790C4—42no—
791C4—42no—
792C4—44no—
793C4—42no—
794C4—44no—
795C4—44no—
796C4—42no—
797C4—82no—
798C4C13×#38818yescomplemented
799C2—44no—
800C2C2×C13×#38811yescharacteristic
801C2C4×C13×#12111yescharacteristic
802C2C13×#232311yescharacteristic
803C2C13×#234411yescharacteristic
804C2C13×#234611yescharacteristic
805C2C13×#236111yescharacteristic
806C2C13×#236211yescharacteristic
807C2C13×#248511yescharacteristic
808C2C13×#248611yescharacteristic
809C2C13×#248911yescharacteristic
810C2C13×#249111yescharacteristic
811C2C13×#249511yescharacteristic
812C2C13×#249611yescharacteristic
813C2C13×#253611yescharacteristic
814C2C13×#253711yescharacteristic
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
5. C2×C4×C13×C4⋊C4C2semidirect
7. C13×#1442C2semidirect
9. C13×C4⋊#95C2semidirect
10. C13×C4⋊#95C2semidirect
11. C13×#1434C2semidirect
28. C13×#380C4semidirect
105. #13994C13direct (N × H)
211. C2×#389C2×C13semidirect
215. C2×C4×C4⋊C4C2×C13semidirect
217. #1442C2×C13semidirect
219. C4⋊#95C2×C13semidirect
220. C4⋊#95C2×C13semidirect
221. #1434C2×C13semidirect
359. #380C4×C13semidirect
431. C4×C13#388semidirect
617. C13#13994direct (N × H)
798. C4C13×#388semidirect

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×#3882
C2×C13×#3802
C2×C4×C13×C4⋊C42
C2×C4×C13×C22⋊C42
C13×#14422
C13×#14402
C13×C4⋊#952
C13×#14342
#1399413