Finite Group Databasebeta

← C13×#14073 #15700412

Subgroups — C13×#14073 #15700412

Order 3328.

1282 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#387C211yesmaximal, characteristic
2C2×C13×#387C211yesmaximal, characteristic
3C2×C13×#376C211yesmaximal, characteristic
4C13×#1445C211yesmaximal, characteristic
5C13×#1443C211yesmaximal, characteristic
6C13×#1443C211yesmaximal, characteristic
7C13×#1442C211yesmaximal, characteristic
8C13×#1436C211yesmaximal, characteristic
9C13×#1436C211yesmaximal, characteristic
10C13×#1436C211yesmaximal, characteristic
11C13×#1436C211yesmaximal, characteristic
12C13×C4⋊#95C211yesmaximal, characteristic
13C13×#1434C211yesmaximal, characteristic
14C13×#1434C211yesmaximal, characteristic
15C4×C13×#95C211yesmaximal, characteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×C42×C13C2211yescharacteristic
22C22×C42×C13C2211yescharacteristic
23C22×C42×C13C2211yescharacteristic
24C22×C42×C13C2211yescharacteristic
25C13×#387—24no—
26C13×#387C418yescomplemented
27C13×#376—24no—
28C2×C13×#95C2211yescharacteristic
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
38C2×C13×#95C2211yescharacteristic
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2211yescharacteristic
41C2×C13×#95C2211yescharacteristic
42C2×C13×#95C2211yescharacteristic
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×C13×#95C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×C13×#95C2211yescharacteristic
52C2×C13×#95C2211yescharacteristic
53C2×C13×#95C2211yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—22no—
74C2×C13×C4⋊C4—22no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—22no—
78C2×C13×C4⋊C4—41no—
79C2×C13×C4⋊C4C2×C414yes—
80C2×C13×C4⋊C4C2×C414yes—
81C2×C42×C13—22no—
82C2×C42×C13—22no—
83C2×C42×C13—22no—
84C2×C42×C13—22no—
85C2×C42×C13—22no—
86C2×C42×C13—22no—
87C2×C42×C13—22no—
88C2×C42×C13—22no—
89C2×C42×C13—22no—
90C2×C42×C13—22no—
91C2×C42×C13—22no—
92C2×C42×C13—41no—
93C2×C42×C13—41no—
94C2×C42×C13C2×C414yes—
95C2×C42×C13D414yes—
96C13×#95—22no—
97C13×#95—22no—
98C13×#95—22no—
99C13×#95—22no—
100C13×#95—22no—
101C13×#95—22no—
102C13×#95—22no—
103C13×#95—22no—
104C13×#95—22no—
105C13×#95—22no—
106C13×#95—22no—
107C13×#95—22no—
108C13×#95—22no—
109C13×#95—22no—
110C13×#95—22no—
111C13×#95—22no—
112C13×#95—22no—
113C13×#95—22no—
114C13×#95—22no—
115C13×#95—41no—
116C13×#95—41no—
117C13×#95—41no—
118C13×#95C2×C414yes—
119C13×#95C2×C414yes—
120C13×#95C2×C414yes—
121C13×#95C2×C414yes—
122#14073C1311yesmaximal, characteristic, direct product factor, Sylow
123C24×C13C2411yescharacteristic
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—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
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—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
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—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
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—21no—
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—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13—21no—
210C22×C4×C13C22×C412yes—
211C22×C4×C13C22×C412yes—
212C22×C4×C13C22×C412yes—
213C22×C4×C13C22×C412yes—
214C22×C4×C13C22×C412yes—
215C22×C4×C13C22×C412yes—
216C22×C4×C13C22×C412yes—
217C22×C4×C13C2×D412yes—
218C22×C4×C13C2×D412yes—
219C22×C4×C13C2×D412yes—
220C22×C4×C13#4112yes—
221C22×C4×C13#4112yes—
222C22×C4×C13#4112yes—
223C22×C4×C13#4112yes—
224C22×C4×C13#4112yes—
225C22×C4×C13#4112yes—
226C22×C4×C13#4112yes—
227C22×C4×C13#4112yes—
228C22×C4×C13#4112yes—
229C13×C4⋊C4—28no—
230C13×C4⋊C4—28no—
231C13×C4⋊C4—44no—
232C13×C4⋊C4—44no—
233C42×C13—28no—
234C42×C13—28no—
235C42×C13—28no—
236C42×C13—44no—
237C42×C13—44no—
238C2×#387C2×C1311yescharacteristic
239C2×#387C2×C1311yescharacteristic
240C2×#376C2×C1311yescharacteristic
241#1445C2×C1311yescharacteristic
242#1443C2×C1311yescharacteristic
243#1443C2×C1311yescharacteristic
244#1442C2×C1311yescharacteristic
245#1436C2×C1311yescharacteristic
246#1436C2×C1311yescharacteristic
247#1436C2×C1311yescharacteristic
248#1436C2×C1311yescharacteristic
249C4⋊#95C2×C1311yescharacteristic
250#1434C2×C1311yescharacteristic
251#1434C2×C1311yescharacteristic
252C4×#95C2×C1311yescharacteristic
253C23×C13C23×C411yescharacteristic
254C23×C13C22×D411yescharacteristic
255C23×C13C2×#4111yescharacteristic
256C23×C13C2×#4111yescharacteristic
257C23×C13C2×#4111yescharacteristic
258C23×C13C2×#4111yescharacteristic
259C23×C13C2×#4111yescharacteristic
260C23×C13C2×#4111yescharacteristic
261C23×C13C2×#4111yescharacteristic
262C23×C13C2×#4111yescharacteristic
263C23×C13C2×#4111yescharacteristic
264C23×C13H(5,𝔽2)11yescharacteristic
265C23×C132−1+411yescharacteristic
266C23×C132−1+411yescharacteristic
267C23×C132−1+411yescharacteristic
268C2×C4×C13—22no—
269C2×C4×C13—22no—
270C2×C4×C13—22no—
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—22no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
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—41no—
317C2×C4×C13—41no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×C4×C13—41no—
322C2×C4×C13—41no—
323C2×C4×C13—41no—
324C2×C4×C13—41no—
325C2×C4×C13—41no—
326C2×C4×C13—41no—
327C2×C4×C13—41no—
328C2×C4×C13—41no—
329C2×C4×C13—41no—
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—41no—
344C2×C4×C13—41no—
345C2×C4×C13—41no—
346C2×C4×C13—41no—
347C2×C4×C13—41no—
348C2×C4×C13—41no—
349C2×C4×C13—41no—
350C2×C4×C13—41no—
351C2×C4×C13—41no—
352C2×C4×C13—41no—
353C2×C4×C13—41no—
354C2×C4×C13—41no—
355C2×C4×C13—41no—
356C2×C4×C13—41no—
357C2×C4×C13—41no—
358C2×C4×C13—41no—
359C2×C4×C13—41no—
360C2×C4×C13—41no—
361C2×C4×C13—41no—
362C2×C4×C13—41no—
363C2×C4×C13—41no—
364C2×C4×C13—41no—
365C2×C4×C13—41no—
366C2×C4×C13—41no—
367C2×C4×C13—41no—
368C2×C4×C13—41no—
369C2×C4×C13—41no—
370C2×C4×C13#11714yes—
371C2×C4×C13C4×D414yes—
372C2×C4×C13#12314yes—
373C22×C4⋊C4C22×C1311yescharacteristic
374C22×C4⋊C4C22×C1311yescharacteristic
375C22×C4⋊C4C22×C1311yescharacteristic
376C22×C4⋊C4C22×C1311yescharacteristic
377C22×C42C22×C1311yescharacteristic
378C22×C42C22×C1311yescharacteristic
379C22×C42C22×C1311yescharacteristic
380C22×C42C22×C1311yescharacteristic
381C22×C42C22×C1311yescharacteristic
382#387—24no—
383#387C4×C1318yescomplemented
384#376—24no—
385C2×#95C22×C1311yescharacteristic
386C2×#95C22×C1311yescharacteristic
387C2×#95C22×C1311yescharacteristic
388C2×#95C22×C1311yescharacteristic
389C2×#95C22×C1311yescharacteristic
390C2×#95C22×C1311yescharacteristic
391C2×#95C22×C1311yescharacteristic
392C2×#95C22×C1311yescharacteristic
393C2×#95C22×C1311yescharacteristic
394C2×#95C22×C1311yescharacteristic
395C2×#95C22×C1311yescharacteristic
396C2×#95C22×C1311yescharacteristic
397C2×#95C22×C1311yescharacteristic
398C2×#95C22×C1311yescharacteristic
399C2×#95C22×C1311yescharacteristic
400C2×#95C22×C1311yescharacteristic
401C2×#95C22×C1311yescharacteristic
402C2×#95C22×C1311yescharacteristic
403C2×#95C22×C1311yescharacteristic
404C2×#95C22×C1311yescharacteristic
405C2×#95C22×C1311yescharacteristic
406C2×#95C22×C1311yescharacteristic
407C2×#95C22×C1311yescharacteristic
408C2×#95C22×C1311yescharacteristic
409C2×#95C22×C1311yescharacteristic
410C2×#95C22×C1311yescharacteristic
411C22×C13C2×#11711yescharacteristic
412C22×C13C2×C4×D411yescharacteristic
413C22×C13C4×#4111yescharacteristic
414C22×C13C4×#4111yescharacteristic
415C22×C13C4×#4111yescharacteristic
416C22×C13#51911yescharacteristic
417C22×C13#52011yescharacteristic
418C22×C13C2×#12311yescharacteristic
419C22×C13#52511yescharacteristic
420C22×C13#52911yescharacteristic
421C22×C13#52911yescharacteristic
422C22×C13#52911yescharacteristic
423C22×C13#52911yescharacteristic
424C22×C13#53211yescharacteristic
425C22×C13#53211yescharacteristic
426C22×C13#53611yescharacteristic
427C22×C13#53711yescharacteristic
428C22×C13#54111yescharacteristic
429C22×C13#54211yescharacteristic
430C22×C13#55111yescharacteristic
431C22×C13#55111yescharacteristic
432C22×C13#55111yescharacteristic
433C22×C13#55211yescharacteristic
434C22×C13#55211yescharacteristic
435C22×C13#55211yescharacteristic
436C22×C13#55211yescharacteristic
437C22×C13#55211yescharacteristic
438C22×C13#55211yescharacteristic
439C22×C13#55211yescharacteristic
440C22×C13#55211yescharacteristic
441C22×C13#55211yescharacteristic
442C22×C13#55311yescharacteristic
443C22×C13#55611yescharacteristic
444C22×C13#55611yescharacteristic
445C22×C13#55611yescharacteristic
446C4×C13—24no—
447C4×C13—24no—
448C4×C13—24no—
449C4×C13—42no—
450C4×C13—42no—
451C4×C13—42no—
452C4×C13—42no—
453C4×C13—42no—
454C4×C13—42no—
455C4×C13—42no—
456C4×C13—42no—
457C4×C13—42no—
458C4×C13—42no—
459C4×C13—81no—
460C4×C13—81no—
461C23×C4C23×C1311yescharacteristic
462C23×C4C23×C1311yescharacteristic
463C23×C4C23×C1311yescharacteristic
464C23×C4C23×C1311yescharacteristic
465C23×C4C23×C1311yescharacteristic
466C23×C4C23×C1311yescharacteristic
467C23×C4C23×C1311yescharacteristic
468C23×C4C23×C1311yescharacteristic
469C23×C4C23×C1311yescharacteristic
470C23×C4C23×C1311yescharacteristic
471C23×C4C23×C1311yescharacteristic
472C23×C4C23×C1311yescharacteristic
473C23×C4C23×C1311yescharacteristic
474C23×C4C23×C1311yescharacteristic
475C23×C4C23×C1311yescharacteristic
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—41no—
486C2×C4⋊C4C2×C4×C1314yes—
487C2×C4⋊C4C2×C4×C1314yes—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—22no—
491C2×C42—22no—
492C2×C42—22no—
493C2×C42—22no—
494C2×C42—22no—
495C2×C42—22no—
496C2×C42—22no—
497C2×C42—22no—
498C2×C42—22no—
499C2×C42—41no—
500C2×C42—41no—
501C2×C42C2×C4×C1314yes—
502C2×C42D4×C1314yes—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—22no—
507#95—22no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—41no—
523#95—41no—
524#95—41no—
525#95C2×C4×C1314yes—
526#95C2×C4×C1314yes—
527#95C2×C4×C1314yes—
528#95C2×C4×C1314yes—
529C2×C13#229311yescharacteristic
530C2×C13C4×#12311yescharacteristic
531C2×C13#232311yescharacteristic
532C2×C13#234311yescharacteristic
533C2×C13#235611yescharacteristic
534C2×C13#237111yescharacteristic
535C2×C13#237311yescharacteristic
536C2×C13#249811yescharacteristic
537C2×C13#249911yescharacteristic
538C2×C13#252711yescharacteristic
539C2×C13#252811yescharacteristic
540C2×C13#253011yescharacteristic
541C2×C13#253311yescharacteristic
542C2×C13#260111yescharacteristic
543C2×C13#261111yescharacteristic
544C24C24×C1311yescharacteristic
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
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—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4C22×C4×C1312yes—
632C22×C4C22×C4×C1312yes—
633C22×C4C22×C4×C1312yes—
634C22×C4C22×C4×C1312yes—
635C22×C4C22×C4×C1312yes—
636C22×C4C22×C4×C1312yes—
637C22×C4C22×C4×C1312yes—
638C22×C4C2×D4×C1312yes—
639C22×C4C2×D4×C1312yes—
640C22×C4C2×D4×C1312yes—
641C22×C4C13×#4112yes—
642C22×C4C13×#4112yes—
643C22×C4C13×#4112yes—
644C22×C4C13×#4112yes—
645C22×C4C13×#4112yes—
646C22×C4C13×#4112yes—
647C22×C4C13×#4112yes—
648C22×C4C13×#4112yes—
649C22×C4C13×#4112yes—
650C4⋊C4—28no—
651C4⋊C4—28no—
652C4⋊C4—44no—
653C4⋊C4—44no—
654C42—28no—
655C42—28no—
656C42—28no—
657C42—44no—
658C42—44no—
659C13#1407311yescharacteristic, direct product factor, Sylow
660C23C23×C4×C1311yescharacteristic
661C23C22×D4×C1311yescharacteristic
662C23C2×C13×#4111yescharacteristic
663C23C2×C13×#4111yescharacteristic
664C23C2×C13×#4111yescharacteristic
665C23C2×C13×#4111yescharacteristic
666C23C2×C13×#4111yescharacteristic
667C23C2×C13×#4111yescharacteristic
668C23C2×C13×#4111yescharacteristic
669C23C2×C13×#4111yescharacteristic
670C23C2×C13×#4111yescharacteristic
671C23C13×H(5,𝔽2)11yescharacteristic
672C23C13×2−1+411yescharacteristic
673C23C13×2−1+411yescharacteristic
674C23C13×2−1+411yescharacteristic
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—41no—
724C2×C4—41no—
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—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4C13×#11714yes—
778C2×C4C4×D4×C1314yes—
779C2×C4C13×#12314yes—
780C22C2×C13×#11711yescharacteristic
781C22C2×C4×D4×C1311yescharacteristic
782C22C4×C13×#4111yescharacteristic
783C22C4×C13×#4111yescharacteristic
784C22C4×C13×#4111yescharacteristic
785C22C13×#51911yescharacteristic
786C22C13×#52011yescharacteristic
787C22C2×C13×#12311yescharacteristic
788C22C13×#52511yescharacteristic
789C22C13×#52911yescharacteristic
790C22C13×#52911yescharacteristic
791C22C13×#52911yescharacteristic
792C22C13×#52911yescharacteristic
793C22C13×#53211yescharacteristic
794C22C13×#53211yescharacteristic
795C22C13×#53611yescharacteristic
796C22C13×#53711yescharacteristic
797C22C13×#54111yescharacteristic
798C22C13×#54211yescharacteristic
799C22C13×#55111yescharacteristic
800C22C13×#55111yescharacteristic
801C22C13×#55111yescharacteristic
802C22C13×#55211yescharacteristic
803C22C13×#55211yescharacteristic
804C22C13×#55211yescharacteristic
805C22C13×#55211yescharacteristic
806C22C13×#55211yescharacteristic
807C22C13×#55211yescharacteristic
808C22C13×#55211yescharacteristic
809C22C13×#55211yescharacteristic
810C22C13×#55211yescharacteristic
811C22C13×#55311yescharacteristic
812C22C13×#55611yescharacteristic
813C22C13×#55611yescharacteristic
814C22C13×#55611yescharacteristic
815C4—24no—
816C4—24no—
817C4—24no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—81no—
829C4—81no—
830C2C13×#229311yescharacteristic
831C2C4×C13×#12311yescharacteristic
832C2C13×#232311yescharacteristic
833C2C13×#234311yescharacteristic
834C2C13×#235611yescharacteristic
835C2C13×#237111yescharacteristic
836C2C13×#237311yescharacteristic
837C2C13×#249811yescharacteristic
838C2C13×#249911yescharacteristic
839C2C13×#252711yescharacteristic
840C2C13×#252811yescharacteristic
841C2C13×#253011yescharacteristic
842C2C13×#253311yescharacteristic
843C2C13×#260111yescharacteristic
844C2C13×#261111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C13C24
commutatorC23C23×C4×C13
Frattini, cosocleC24C24×C13
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
26. C13×#387C4semidirect
122. #14073C13direct (N × H)
383. #387C4×C13semidirect
659. C13#14073direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3872
C2×C13×#3762
C13×#14452
C13×#14432
C13×#14422
C13×#14362
C13×C4⋊#952
C13×#14342
C4×C13×#952
#1407313