Finite Group Databasebeta

← C13×#36902 #15723241

Subgroups — C13×#36902 #15723241

Order 3328.

2268 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2847C212yesmaximal, complemented
2C13×#2781C212yesmaximal, complemented
3C13×#2748C211yesmaximal, characteristic, complemented
4C13×#2714C212yesmaximal, complemented
5C13×#2708C212yesmaximal, complemented
6C13×#2691C212yesmaximal, complemented
7C13×#2679C211yesmaximal, characteristic, complemented
8C13×#2678C212yesmaximal, complemented
9C13×#2669C211yesmaximal, characteristic, complemented
10C13×#2669C211yesmaximal, characteristic, complemented
11C13×#2668C212yesmaximal, complemented
12C13×#2648C212yesmaximal, complemented
13C13×#2531C212yesmaximal, complemented
14C13×#2467C212yesmaximal, complemented
15C13×#2464C212yesmaximal, complemented
16C13×#2424C212yesmaximal, complemented
17C13×#2328C211yesmaximal, characteristic, complemented
18C13×#2321C211yesmaximal, characteristic, complemented
19C4×C13×#120C211yesmaximal, characteristic, complemented
20C24×C4×C13C2211yescharacteristic, complemented
21C2×C13×#127C2211yescharacteristic
22C2×C13×#126C2212yescomplemented
23C2×C13×#123C2212yescomplemented
24C2×C13×#121C2212yes—
25C2×C13×#121C2212yes—
26C2×C13×#121C2212yes—
27C2×C13×#121C2212yes—
28C2×C13×#121C2212yes—
29C2×C13×#120C2211yescharacteristic
30C2×C13×#120C2211yescharacteristic
31C2×C13×#120C2212yes—
32C2×C13×#120C2212yes—
33C2×C13×#120C2212yescomplemented
34C2×C13×#120C2212yescomplemented
35C2×C4×D4×C13C2211yescharacteristic
36C2×C4×D4×C13C2212yes—
37C2×C4×D4×C13C2211yescharacteristic, complemented
38C22×C13×C22⋊C4C2211yescharacteristic, complemented
39C13×#400C2212yescomplemented
40C13×#399C2212yescomplemented
41C13×#398C2212yescomplemented
42C13×#398C2212yescomplemented
43C13×#397C2212yescomplemented
44C13×#397C2212yescomplemented
45C13×#397C2212yescomplemented
46C13×#397C2212yescomplemented
47C13×#396C2212yescomplemented
48C13×#396C2212yescomplemented
49C13×#394C2212yes—
50C13×#394C2212yes—
51C13×#394C2212yes—
52C13×#394C2212yes—
53C13×#394C2212yes—
54C13×#394C2212yescomplemented
55C13×#394C2212yescomplemented
56C13×#394C2212yescomplemented
57C13×#394C2212yescomplemented
58C13×#392C2212yes—
59C13×#392C2212yes—
60C13×#392C2212yes—
61C13×#392C2212yescomplemented
62C13×#392C2212yescomplemented
63C13×#390C2212yes—
64C13×#390C2212yes—
65C13×#390C2211yescharacteristic
66C13×#390C2211yescharacteristic, complemented
67C13×#390C2212yescomplemented
68C13×#390C2212yescomplemented
69C13×#388C2212yescomplemented
70C13×#388C2212yescomplemented
71C13×#388C2212yescomplemented
72C13×#388C2212yescomplemented
73C13×#388C2212yescomplemented
74C13×#388C2212yescomplemented
75C13×#388C2212yescomplemented
76C13×#387C2212yescomplemented
77C13×#387C2212yescomplemented
78C13×#387C2212yescomplemented
79C13×#386C2212yes—
80C13×#386C2212yes—
81C13×#386C2212yes—
82C13×#386C2211yescharacteristic
83C13×#386C2212yes—
84C13×#386C2211yescharacteristic
85C13×#386C2212yescomplemented
86C13×#386C2212yescomplemented
87C13×#386C2212yescomplemented
88C13×#386C2212yescomplemented
89C13×#386C2212yescomplemented
90C13×#386C2212yescomplemented
91C13×#386C2212yescomplemented
92C13×#385C2212yescomplemented
93C13×#385C2211yescharacteristic, complemented
94C13×#385C2211yescharacteristic, complemented
95C13×#385C2212yescomplemented
96C13×#385C2212yescomplemented
97C13×#382C2211yescharacteristic, complemented
98C13×#380C2212yescomplemented
99C13×#380C2212yescomplemented
100C13×#380C2212yescomplemented
101C13×#379C2211yescharacteristic, complemented
102C13×#379C2211yescharacteristic, complemented
103C4×C13×C22⋊C4C2212yescomplemented
104C4×C13×C22⋊C4C2211yescharacteristic, complemented
105C4×C13×C22⋊C4C2211yescharacteristic, complemented
106C13×#376C2211yescharacteristic, complemented
107C25×C13C2311yescharacteristic
108C25×C13C2311yescharacteristic
109C22×D4×C13C2312yes—
110C22×D4×C13C2312yes—
111C22×D4×C13C2312yes—
112C22×D4×C13C2312yes—
113C22×D4×C13C2312yes—
114C22×D4×C13C2312yes—
115C22×D4×C13C2312yes—
116C22×D4×C13C2312yes—
117C22×D4×C13C2312yes—
118C22×D4×C13C2311yescharacteristic
119C22×D4×C13C2312yes—
120C22×D4×C13C2311yescharacteristic
121C23×C4×C13—44no—
122C23×C4×C13—42no—
123C23×C4×C13C2312yes—
124C23×C4×C13C2311yescharacteristic
125C23×C4×C13C2311yescharacteristic
126C23×C4×C13C2311yescharacteristic
127C23×C4×C13C2312yes—
128C23×C4×C13C2311yescharacteristic
129C23×C4×C13C2312yes—
130C13×#127—24no—
131C13×#126—44no—
132C13×#123—44no—
133C13×#121—44no—
134C13×#121—44no—
135C13×#121—44no—
136C13×#121—44no—
137C13×#121—44no—
138C13×#120—24no—
139C13×#120—24no—
140C13×#120—44no—
141C13×#120—44no—
142C13×#120—44no—
143C13×#120—44no—
144C4×D4×C13—42no—
145C4×D4×C13—42no—
146C4×D4×C13—44no—
147C2×C13×C4⋊C4C2312yes—
148C2×C13×C4⋊C4C2312yes—
149C2×C13×C4⋊C4C2312yes—
150C2×C13×C4⋊C4C2312yes—
151C2×C13×C4⋊C4C2311yescharacteristic
152C2×C13×C4⋊C4C2311yescharacteristic
153C2×C13×C4⋊C4C2312yes—
154C2×C13×C4⋊C4C2312yes—
155C2×C13×C4⋊C4C2312yes—
156C2×C13×C4⋊C4C2312yes—
157C2×C13×C4⋊C4C2312yes—
158C2×C13×C4⋊C4C2312yes—
159C2×C13×C22⋊C4—42no—
160C2×C13×C22⋊C4C2312yes—
161C2×C13×C22⋊C4C2312yes—
162C2×C13×C22⋊C4C2311yescharacteristic
163C2×C13×C22⋊C4C2311yescharacteristic
164C2×C13×C22⋊C4C2312yes—
165C2×C13×C22⋊C4C2312yes—
166C2×C13×C22⋊C4C2312yes—
167C2×C13×C22⋊C4C2312yes—
168C2×C13×C22⋊C4C2312yes—
169C2×C13×C22⋊C4C2312yes—
170C2×C13×C22⋊C4C2312yes—
171C2×C13×C22⋊C4C2312yes—
172C2×C13×C22⋊C4C2311yescharacteristic
173C2×C13×C22⋊C4C2311yescharacteristic
174C2×C13×C22⋊C4C2311yescharacteristic
175C2×C13×C22⋊C4C2311yescharacteristic
176C2×C13×C22⋊C4C2312yes—
177C2×C13×C22⋊C4C2312yes—
178C2×C13×C22⋊C4C2312yes—
179C2×C13×C22⋊C4C2312yes—
180C2×C13×C22⋊C4C2312yes—
181C2×C13×C22⋊C4C2312yes—
182C2×C13×C22⋊C4C2312yes—
183C2×C13×C22⋊C4C2312yes—
184C2×C13×C22⋊C4C2312yes—
185C2×C13×C22⋊C4C2312yes—
186C2×C13×C22⋊C4C2312yes—
187C2×C13×C22⋊C4C2312yes—
188C2×C13×C22⋊C4C2312yes—
189C2×C13×C22⋊C4C2312yes—
190C2×C13×C22⋊C4C2312yes—
191C2×C13×C22⋊C4C2312yes—
192C2×C13×C22⋊C4C2312yes—
193C2×C42×C13C2311yescharacteristic
194C2×C42×C13C2311yescharacteristic
195C2×C42×C13C2312yes—
196C2×C42×C13C2312yes—
197C2×C42×C13C2311yescharacteristic
198C13×#95C2312yes—
199C13×#95C2312yes—
200C13×#95C2312yes—
201C13×#95C2312yes—
202C13×#95C2312yes—
203C13×#95C2312yes—
204C13×#95C2312yes—
205C13×#95C2312yes—
206C13×#95C2312yes—
207C13×#95C2312yes—
208C13×#95C2312yes—
209C13×#95C2312yes—
210C13×#95C2312yes—
211C13×#95C2312yes—
212C13×#95C2312yes—
213C13×#95C2312yes—
214#36902C1311yesmaximal, characteristic, direct product factor, Sylow
215C24×C13—22no—
216C24×C13—24no—
217C24×C13—22no—
218C24×C13—41no—
219C24×C13—42no—
220C24×C13—41no—
221C24×C13—41no—
222C24×C13—41no—
223C24×C13—42no—
224C24×C13—42no—
225C24×C13C2412yes—
226C24×C13C2412yes—
227C24×C13C2411yescharacteristic
228C24×C13C2411yescharacteristic
229C24×C13C2412yes—
230C2×D4×C13—24no—
231C2×D4×C13—24no—
232C2×D4×C13—24no—
233C2×D4×C13—24no—
234C2×D4×C13—24no—
235C2×D4×C13—24no—
236C2×D4×C13—24no—
237C2×D4×C13—24no—
238C2×D4×C13—24no—
239C2×D4×C13—22no—
240C2×D4×C13—24no—
241C2×D4×C13—41no—
242C2×D4×C13—41no—
243C2×D4×C13—42no—
244C2×D4×C13—41no—
245C2×D4×C13—41no—
246C2×D4×C13—42no—
247C2×D4×C13—42no—
248C2×D4×C13—42no—
249C2×D4×C13—42no—
250C2×D4×C13—42no—
251C2×D4×C13—42no—
252C2×D4×C13—42no—
253C2×D4×C13—42no—
254C2×D4×C13—42no—
255C2×D4×C13—42no—
256C2×D4×C13—42no—
257C2×D4×C13—42no—
258C2×D4×C13—42no—
259C2×D4×C13—42no—
260C2×D4×C13—42no—
261C2×D4×C13—42no—
262C2×D4×C13—42no—
263C2×D4×C13—42no—
264C2×D4×C13—42no—
265C2×D4×C13#4114yes—
266C22×C4×C13—24no—
267C22×C4×C13—22no—
268C22×C4×C13—24no—
269C22×C4×C13—24no—
270C22×C4×C13—24no—
271C22×C4×C13—22no—
272C22×C4×C13—42no—
273C22×C4×C13—42no—
274C22×C4×C13—41no—
275C22×C4×C13—42no—
276C22×C4×C13—42no—
277C22×C4×C13—41no—
278C22×C4×C13—42no—
279C22×C4×C13—42no—
280C22×C4×C13—42no—
281C22×C4×C13—42no—
282C22×C4×C13—42no—
283C22×C4×C13—416no—
284C22×C4×C13C2412yes—
285C22×C4×C13C2411yescharacteristic
286C22×C4×C13C2412yes—
287C22×C4×C13C2412yes—
288C22×C4×C13C2412yes—
289C22×C4×C13C2412yes—
290C22×C4×C13C2412yes—
291C22×C4×C13C2411yescharacteristic
292C22×C4×C13C2412yes—
293C22×C4×C13C2412yes—
294C22×C4×C13C2411yescharacteristic
295C22×C4×C13C2411yescharacteristic
296C22×C4×C13C2411yescharacteristic
297C22×C4×C13C2412yes—
298C13×C4⋊C4—24no—
299C13×C4⋊C4—24no—
300C13×C4⋊C4—42no—
301C13×C4⋊C4—41no—
302C13×C4⋊C4—41no—
303C13×C4⋊C4—42no—
304C13×C4⋊C4—42no—
305C13×C4⋊C4—42no—
306C13×C4⋊C4—42no—
307C13×C4⋊C4—42no—
308C13×C4⋊C4—42no—
309C13×C4⋊C4—42no—
310C13×C22⋊C4—22no—
311C13×C22⋊C4—22no—
312C13×C22⋊C4—24no—
313C13×C22⋊C4—24no—
314C13×C22⋊C4—24no—
315C13×C22⋊C4—24no—
316C13×C22⋊C4—24no—
317C13×C22⋊C4—24no—
318C13×C22⋊C4—24no—
319C13×C22⋊C4—24no—
320C13×C22⋊C4—24no—
321C13×C22⋊C4—24no—
322C13×C22⋊C4—42no—
323C13×C22⋊C4—41no—
324C13×C22⋊C4—41no—
325C13×C22⋊C4—41no—
326C13×C22⋊C4—41no—
327C13×C22⋊C4—42no—
328C13×C22⋊C4—42no—
329C13×C22⋊C4—42no—
330C13×C22⋊C4—42no—
331C13×C22⋊C4—42no—
332C13×C22⋊C4—42no—
333C13×C22⋊C4—42no—
334C13×C22⋊C4—42no—
335C13×C22⋊C4—42no—
336C13×C22⋊C4—42no—
337C13×C22⋊C4—42no—
338C13×C22⋊C4—42no—
339C13×C22⋊C4—42no—
340C13×C22⋊C4—42no—
341C13×C22⋊C4—42no—
342C13×C22⋊C4—42no—
343C42×C13—22no—
344C42×C13—22no—
345C42×C13—41no—
346C42×C13—42no—
347C42×C13—42no—
348#2847C2×C1312yescomplemented
349#2781C2×C1312yescomplemented
350#2748C2×C1311yescharacteristic, complemented
351#2714C2×C1312yescomplemented
352#2708C2×C1312yescomplemented
353#2691C2×C1312yescomplemented
354#2679C2×C1311yescharacteristic, complemented
355#2678C2×C1312yescomplemented
356#2669C2×C1311yescharacteristic, complemented
357#2669C2×C1311yescharacteristic, complemented
358#2668C2×C1312yescomplemented
359#2648C2×C1312yescomplemented
360#2531C2×C1312yescomplemented
361#2467C2×C1312yescomplemented
362#2464C2×C1312yescomplemented
363#2424C2×C1312yescomplemented
364#2328C2×C1311yescharacteristic, complemented
365#2321C2×C1311yescharacteristic, complemented
366C4×#120C2×C1311yescharacteristic, complemented
367C23×C13—22no—
368C23×C13—22no—
369C23×C13—22no—
370C23×C13—22no—
371C23×C13—21no—
372C23×C13—21no—
373C23×C13—22no—
374C23×C13—22no—
375C23×C13—22no—
376C23×C13—22no—
377C23×C13—22no—
378C23×C13—21no—
379C23×C13—21no—
380C23×C13—22no—
381C23×C13—22no—
382C23×C13—22no—
383C23×C13—22no—
384C23×C13—22no—
385C23×C13—22no—
386C23×C13—22no—
387C23×C13—22no—
388C23×C13—22no—
389C23×C13—22no—
390C23×C13—22no—
391C23×C13—22no—
392C23×C13—22no—
393C23×C13—22no—
394C23×C13—22no—
395C23×C13—48no—
396C23×C13—44no—
397C23×C13—44no—
398C23×C13—48no—
399C23×C13—44no—
400C23×C13—44no—
401C23×C13—84no—
402C23×C13—82no—
403C23×C13—82no—
404C23×C13—84no—
405C23×C13C2×#4112yes—
406C23×C13C2×#4112yes—
407C23×C13H(5,𝔽2)14yes—
408C23×C13C2511yescharacteristic
409D4×C13—44no—
410D4×C13—44no—
411D4×C13—48no—
412D4×C13—84no—
413D4×C13—84no—
414D4×C13—84no—
415D4×C13—84no—
416D4×C13—84no—
417D4×C13—84no—
418D4×C13—84no—
419D4×C13—84no—
420D4×C13—84no—
421C2×C4×C13—21no—
422C2×C4×C13—22no—
423C2×C4×C13—22no—
424C2×C4×C13—22no—
425C2×C4×C13—21no—
426C2×C4×C13—22no—
427C2×C4×C13—22no—
428C2×C4×C13—22no—
429C2×C4×C13—21no—
430C2×C4×C13—22no—
431C2×C4×C13—22no—
432C2×C4×C13—22no—
433C2×C4×C13—22no—
434C2×C4×C13—22no—
435C2×C4×C13—22no—
436C2×C4×C13—22no—
437C2×C4×C13—22no—
438C2×C4×C13—22no—
439C2×C4×C13—22no—
440C2×C4×C13—22no—
441C2×C4×C13—22no—
442C2×C4×C13—22no—
443C2×C4×C13—22no—
444C2×C4×C13—22no—
445C2×C4×C13—21no—
446C2×C4×C13—22no—
447C2×C4×C13—22no—
448C2×C4×C13—22no—
449C2×C4×C13—22no—
450C2×C4×C13—22no—
451C2×C4×C13—21no—
452C2×C4×C13—22no—
453C2×C4×C13—22no—
454C2×C4×C13—22no—
455C2×C4×C13—22no—
456C2×C4×C13—48no—
457C2×C4×C13—44no—
458C2×C4×C13—44no—
459C2×C4×C13—48no—
460C2×C4×C13—82no—
461C2×C4×C13—84no—
462C2×C4×C13—82no—
463C2×C4×C13C2×#4112yes—
464C2×C4×C13H(5,𝔽2)12yes—
465C2×C4×C13H(5,𝔽2)14yes—
466C24×C4C22×C1311yescharacteristic, complemented
467C2×#127C22×C1311yescharacteristic
468C2×#126C22×C1312yescomplemented
469C2×#123C22×C1312yescomplemented
470C2×#121C22×C1312yes—
471C2×#121C22×C1312yes—
472C2×#121C22×C1312yes—
473C2×#121C22×C1312yes—
474C2×#121C22×C1312yes—
475C2×#120C22×C1311yescharacteristic
476C2×#120C22×C1311yescharacteristic
477C2×#120C22×C1312yes—
478C2×#120C22×C1312yes—
479C2×#120C22×C1312yescomplemented
480C2×#120C22×C1312yescomplemented
481C2×C4×D4C22×C1311yescharacteristic
482C2×C4×D4C22×C1312yes—
483C2×C4×D4C22×C1311yescharacteristic, complemented
484C22×C22⋊C4C22×C1311yescharacteristic, complemented
485#400C22×C1312yescomplemented
486#399C22×C1312yescomplemented
487#398C22×C1312yescomplemented
488#398C22×C1312yescomplemented
489#397C22×C1312yescomplemented
490#397C22×C1312yescomplemented
491#397C22×C1312yescomplemented
492#397C22×C1312yescomplemented
493#396C22×C1312yescomplemented
494#396C22×C1312yescomplemented
495#394C22×C1312yes—
496#394C22×C1312yes—
497#394C22×C1312yes—
498#394C22×C1312yes—
499#394C22×C1312yes—
500#394C22×C1312yescomplemented
501#394C22×C1312yescomplemented
502#394C22×C1312yescomplemented
503#394C22×C1312yescomplemented
504#392C22×C1312yes—
505#392C22×C1312yes—
506#392C22×C1312yes—
507#392C22×C1312yescomplemented
508#392C22×C1312yescomplemented
509#390C22×C1312yes—
510#390C22×C1311yescharacteristic
511#390C22×C1312yes—
512#390C22×C1311yescharacteristic, complemented
513#390C22×C1312yescomplemented
514#390C22×C1312yescomplemented
515#388C22×C1312yescomplemented
516#388C22×C1312yescomplemented
517#388C22×C1312yescomplemented
518#388C22×C1312yescomplemented
519#388C22×C1312yescomplemented
520#388C22×C1312yescomplemented
521#388C22×C1312yescomplemented
522#387C22×C1312yescomplemented
523#387C22×C1312yescomplemented
524#387C22×C1312yescomplemented
525#386C22×C1312yes—
526#386C22×C1311yescharacteristic
527#386C22×C1312yes—
528#386C22×C1312yes—
529#386C22×C1312yes—
530#386C22×C1311yescharacteristic
531#386C22×C1312yescomplemented
532#386C22×C1312yescomplemented
533#386C22×C1312yescomplemented
534#386C22×C1312yescomplemented
535#386C22×C1312yescomplemented
536#386C22×C1312yescomplemented
537#386C22×C1312yescomplemented
538#385C22×C1311yescharacteristic, complemented
539#385C22×C1312yescomplemented
540#385C22×C1311yescharacteristic, complemented
541#385C22×C1312yescomplemented
542#385C22×C1312yescomplemented
543#382C22×C1311yescharacteristic, complemented
544#380C22×C1312yescomplemented
545#380C22×C1312yescomplemented
546#380C22×C1312yescomplemented
547#379C22×C1311yescharacteristic, complemented
548#379C22×C1311yescharacteristic, complemented
549C4×C22⋊C4C22×C1311yescharacteristic, complemented
550C4×C22⋊C4C22×C1311yescharacteristic, complemented
551C4×C22⋊C4C22×C1312yescomplemented
552#376C22×C1311yescharacteristic, complemented
553C22×C13—22no—
554C22×C13—22no—
555C22×C13—24no—
556C22×C13—24no—
557C22×C13—24no—
558C22×C13—24no—
559C22×C13—24no—
560C22×C13—416no—
561C22×C13—42no—
562C22×C13—42no—
563C22×C13—41no—
564C22×C13—42no—
565C22×C13—41no—
566C22×C13—41no—
567C22×C13—41no—
568C22×C13—42no—
569C22×C13—42no—
570C22×C13—42no—
571C22×C13—42no—
572C22×C13—42no—
573C22×C13—42no—
574C22×C13—42no—
575C22×C13—42no—
576C22×C13—42no—
577C22×C13—42no—
578C22×C13—42no—
579C22×C13—42no—
580C22×C13—42no—
581C22×C13—42no—
582C22×C13—42no—
583C22×C13—42no—
584C22×C13—42no—
585C22×C13—88no—
586C22×C13C22×#4111yescharacteristic
587C22×C13C2×H(5,𝔽2)11yescharacteristic
588C22×C13C2×H(5,𝔽2)12yes—
589C22×C13C2×H(5,𝔽2)12yes—
590C22×C13#58511yescharacteristic
591C4×C13—22no—
592C4×C13—22no—
593C4×C13—24no—
594C4×C13—42no—
595C4×C13—42no—
596C4×C13—42no—
597C4×C13—41no—
598C4×C13—41no—
599C4×C13—41no—
600C4×C13—42no—
601C4×C13—42no—
602C4×C13—42no—
603C4×C13—42no—
604C4×C13—42no—
605C25C23×C1311yescharacteristic
606C25C23×C1311yescharacteristic
607C22×D4C23×C1312yes—
608C22×D4C23×C1311yescharacteristic
609C22×D4C23×C1312yes—
610C22×D4C23×C1312yes—
611C22×D4C23×C1312yes—
612C22×D4C23×C1312yes—
613C22×D4C23×C1312yes—
614C22×D4C23×C1312yes—
615C22×D4C23×C1312yes—
616C22×D4C23×C1312yes—
617C22×D4C23×C1312yes—
618C22×D4C23×C1311yescharacteristic
619C23×C4—44no—
620C23×C4—42no—
621C23×C4C23×C1312yes—
622C23×C4C23×C1311yescharacteristic
623C23×C4C23×C1311yescharacteristic
624C23×C4C23×C1311yescharacteristic
625C23×C4C23×C1312yes—
626C23×C4C23×C1311yescharacteristic
627C23×C4C23×C1312yes—
628#127—24no—
629#126—44no—
630#123—44no—
631#121—44no—
632#121—44no—
633#121—44no—
634#121—44no—
635#121—44no—
636#120—24no—
637#120—24no—
638#120—44no—
639#120—44no—
640#120—44no—
641#120—44no—
642C4×D4—42no—
643C4×D4—42no—
644C4×D4—44no—
645C2×C4⋊C4C23×C1312yes—
646C2×C4⋊C4C23×C1312yes—
647C2×C4⋊C4C23×C1311yescharacteristic
648C2×C4⋊C4C23×C1311yescharacteristic
649C2×C4⋊C4C23×C1312yes—
650C2×C4⋊C4C23×C1312yes—
651C2×C4⋊C4C23×C1312yes—
652C2×C4⋊C4C23×C1312yes—
653C2×C4⋊C4C23×C1312yes—
654C2×C4⋊C4C23×C1312yes—
655C2×C4⋊C4C23×C1312yes—
656C2×C4⋊C4C23×C1312yes—
657C2×C22⋊C4—42no—
658C2×C22⋊C4C23×C1312yes—
659C2×C22⋊C4C23×C1312yes—
660C2×C22⋊C4C23×C1312yes—
661C2×C22⋊C4C23×C1312yes—
662C2×C22⋊C4C23×C1312yes—
663C2×C22⋊C4C23×C1311yescharacteristic
664C2×C22⋊C4C23×C1311yescharacteristic
665C2×C22⋊C4C23×C1312yes—
666C2×C22⋊C4C23×C1312yes—
667C2×C22⋊C4C23×C1312yes—
668C2×C22⋊C4C23×C1312yes—
669C2×C22⋊C4C23×C1312yes—
670C2×C22⋊C4C23×C1312yes—
671C2×C22⋊C4C23×C1311yescharacteristic
672C2×C22⋊C4C23×C1311yescharacteristic
673C2×C22⋊C4C23×C1312yes—
674C2×C22⋊C4C23×C1312yes—
675C2×C22⋊C4C23×C1312yes—
676C2×C22⋊C4C23×C1312yes—
677C2×C22⋊C4C23×C1312yes—
678C2×C22⋊C4C23×C1312yes—
679C2×C22⋊C4C23×C1312yes—
680C2×C22⋊C4C23×C1312yes—
681C2×C22⋊C4C23×C1312yes—
682C2×C22⋊C4C23×C1312yes—
683C2×C22⋊C4C23×C1312yes—
684C2×C22⋊C4C23×C1312yes—
685C2×C22⋊C4C23×C1312yes—
686C2×C22⋊C4C23×C1312yes—
687C2×C22⋊C4C23×C1312yes—
688C2×C22⋊C4C23×C1312yes—
689C2×C22⋊C4C23×C1311yescharacteristic
690C2×C22⋊C4C23×C1311yescharacteristic
691C2×C42C23×C1311yescharacteristic
692C2×C42C23×C1311yescharacteristic
693C2×C42C23×C1312yes—
694C2×C42C23×C1312yes—
695C2×C42C23×C1311yescharacteristic
696#95C23×C1312yes—
697#95C23×C1312yes—
698#95C23×C1312yes—
699#95C23×C1312yes—
700#95C23×C1312yes—
701#95C23×C1312yes—
702#95C23×C1312yes—
703#95C23×C1312yes—
704#95C23×C1312yes—
705#95C23×C1312yes—
706#95C23×C1312yes—
707#95C23×C1312yes—
708#95C23×C1312yes—
709#95C23×C1312yes—
710#95C23×C1312yes—
711#95C23×C1312yes—
712C2×C13—42no—
713C2×C13—44no—
714C2×C13—42no—
715C2×C13—82no—
716C2×C13—82no—
717C2×C13#345911yescharacteristic
718C2×C13#351912yes—
719C2×C13#353211yescharacteristic
720C2×C13#353711yescharacteristic
721C2×C13#354212yes—
722C24—22no—
723C24—24no—
724C24—22no—
725C24—42no—
726C24—41no—
727C24—41no—
728C24—41no—
729C24—41no—
730C24—42no—
731C24—42no—
732C24C24×C1312yes—
733C24C24×C1312yes—
734C24C24×C1311yescharacteristic
735C24C24×C1311yescharacteristic
736C24C24×C1312yes—
737C2×D4—24no—
738C2×D4—24no—
739C2×D4—24no—
740C2×D4—24no—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—24no—
744C2×D4—24no—
745C2×D4—24no—
746C2×D4—22no—
747C2×D4—24no—
748C2×D4—41no—
749C2×D4—41no—
750C2×D4—42no—
751C2×D4—41no—
752C2×D4—41no—
753C2×D4—42no—
754C2×D4—42no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—42no—
764C2×D4—42no—
765C2×D4—42no—
766C2×D4—42no—
767C2×D4—42no—
768C2×D4—42no—
769C2×D4—42no—
770C2×D4—42no—
771C2×D4—42no—
772C2×D4C13×#4114yes—
773C22×C4—24no—
774C22×C4—22no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—22no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—41no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—41no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—42no—
789C22×C4—42no—
790C22×C4—416no—
791C22×C4C24×C1312yes—
792C22×C4C24×C1311yescharacteristic
793C22×C4C24×C1312yes—
794C22×C4C24×C1312yes—
795C22×C4C24×C1312yes—
796C22×C4C24×C1312yes—
797C22×C4C24×C1312yes—
798C22×C4C24×C1311yescharacteristic
799C22×C4C24×C1312yes—
800C22×C4C24×C1312yes—
801C22×C4C24×C1311yescharacteristic
802C22×C4C24×C1311yescharacteristic
803C22×C4C24×C1311yescharacteristic
804C22×C4C24×C1312yes—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—41no—
808C4⋊C4—41no—
809C4⋊C4—42no—
810C4⋊C4—42no—
811C4⋊C4—42no—
812C4⋊C4—42no—
813C4⋊C4—42no—
814C4⋊C4—42no—
815C4⋊C4—42no—
816C4⋊C4—42no—
817C22⋊C4—22no—
818C22⋊C4—22no—
819C22⋊C4—24no—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—24no—
825C22⋊C4—24no—
826C22⋊C4—24no—
827C22⋊C4—24no—
828C22⋊C4—24no—
829C22⋊C4—42no—
830C22⋊C4—41no—
831C22⋊C4—41no—
832C22⋊C4—42no—
833C22⋊C4—42no—
834C22⋊C4—42no—
835C22⋊C4—42no—
836C22⋊C4—42no—
837C22⋊C4—42no—
838C22⋊C4—42no—
839C22⋊C4—42no—
840C22⋊C4—42no—
841C22⋊C4—42no—
842C22⋊C4—42no—
843C22⋊C4—42no—
844C22⋊C4—42no—
845C22⋊C4—42no—
846C22⋊C4—42no—
847C22⋊C4—42no—
848C22⋊C4—41no—
849C22⋊C4—41no—
850C42—22no—
851C42—22no—
852C42—42no—
853C42—42no—
854C42—41no—
855C13#3690211yescharacteristic, direct product factor, Sylow
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—21no—
862C23—21no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—21no—
868C23—21no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—48no—
885C23—44no—
886C23—48no—
887C23—44no—
888C23—44no—
889C23—44no—
890C23—84no—
891C23—82no—
892C23—82no—
893C23—84no—
894C23C2×C13×#4112yes—
895C23C2×C13×#4112yes—
896C23C13×H(5,𝔽2)14yes—
897C23C25×C1311yescharacteristic
898D4—44no—
899D4—44no—
900D4—48no—
901D4—84no—
902D4—84no—
903D4—84no—
904D4—84no—
905D4—84no—
906D4—84no—
907D4—84no—
908D4—84no—
909D4—84no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—21no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—21no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—48no—
946C2×C4—44no—
947C2×C4—44no—
948C2×C4—48no—
949C2×C4—82no—
950C2×C4—84no—
951C2×C4—82no—
952C2×C4C2×C13×#4112yes—
953C2×C4C13×H(5,𝔽2)12yes—
954C2×C4C13×H(5,𝔽2)14yes—
955C22—24no—
956C22—24no—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—22no—
961C22—22no—
962C22—416no—
963C22—42no—
964C22—42no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—42no—
986C22—42no—
987C22—88no—
988C22C22×C13×#4111yescharacteristic
989C22C2×C13×H(5,𝔽2)12yes—
990C22C2×C13×H(5,𝔽2)12yes—
991C22C2×C13×H(5,𝔽2)11yescharacteristic
992C22C13×#58511yescharacteristic
993C4—22no—
994C4—24no—
995C4—22no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—41no—
1000C4—41no—
1001C4—41no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C2—44no—
1008C2—42no—
1009C2—42no—
1010C2—82no—
1011C2—82no—
1012C2C13×#345911yescharacteristic
1013C2C13×#351912yes—
1014C2C13×#353211yescharacteristic
1015C2C13×#353711yescharacteristic
1016C2C13×#354212yes—
subgroupG/H
center, socleC23×C13C25
commutator, Frattini, cosocleC23C25×C13
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2847C2semidirect
2. C13×#2781C2semidirect
3. C13×#2748C2semidirect
4. C13×#2714C2semidirect
5. C13×#2708C2semidirect
6. C13×#2691C2semidirect
7. C13×#2679C2semidirect
8. C13×#2678C2semidirect
9. C13×#2669C2semidirect
10. C13×#2669C2semidirect
11. C13×#2668C2semidirect
12. C13×#2648C2semidirect
13. C13×#2531C2semidirect
14. C13×#2467C2semidirect
15. C13×#2464C2semidirect
16. C13×#2424C2semidirect
17. C13×#2328C2semidirect
18. C13×#2321C2semidirect
19. C4×C13×#120C2semidirect
20. C24×C4×C13C22semidirect
22. C2×C13×#126C22semidirect
23. C2×C13×#123C22semidirect
33. C2×C13×#120C22semidirect
34. C2×C13×#120C22semidirect
37. C2×C4×D4×C13C22semidirect
38. C22×C13×C22⋊C4C22semidirect
39. C13×#400C22semidirect
40. C13×#399C22semidirect
41. C13×#398C22semidirect
42. C13×#398C22semidirect
43. C13×#397C22semidirect
44. C13×#397C22semidirect
45. C13×#397C22semidirect
46. C13×#397C22semidirect
47. C13×#396C22semidirect
48. C13×#396C22semidirect
54. C13×#394C22semidirect
55. C13×#394C22semidirect
56. C13×#394C22semidirect
57. C13×#394C22semidirect
61. C13×#392C22semidirect
62. C13×#392C22semidirect
66. C13×#390C22semidirect
67. C13×#390C22semidirect
68. C13×#390C22semidirect
69. C13×#388C22semidirect
70. C13×#388C22semidirect
71. C13×#388C22semidirect
72. C13×#388C22semidirect
73. C13×#388C22semidirect
74. C13×#388C22semidirect
75. C13×#388C22semidirect
76. C13×#387C22semidirect
77. C13×#387C22semidirect
78. C13×#387C22semidirect
85. C13×#386C22semidirect
86. C13×#386C22semidirect
87. C13×#386C22semidirect
88. C13×#386C22semidirect
89. C13×#386C22semidirect
90. C13×#386C22semidirect
91. C13×#386C22semidirect
92. C13×#385C22semidirect
93. C13×#385C22semidirect
94. C13×#385C22semidirect
95. C13×#385C22semidirect
96. C13×#385C22semidirect
97. C13×#382C22semidirect
98. C13×#380C22semidirect
99. C13×#380C22semidirect
100. C13×#380C22semidirect
101. C13×#379C22semidirect
102. C13×#379C22semidirect
103. C4×C13×C22⋊C4C22semidirect
104. C4×C13×C22⋊C4C22semidirect
105. C4×C13×C22⋊C4C22semidirect
106. C13×#376C22semidirect
214. #36902C13direct (N × H)
348. #2847C2×C13semidirect
349. #2781C2×C13semidirect
350. #2748C2×C13semidirect
351. #2714C2×C13semidirect
352. #2708C2×C13semidirect
353. #2691C2×C13semidirect
354. #2679C2×C13semidirect
355. #2678C2×C13semidirect
356. #2669C2×C13semidirect
357. #2669C2×C13semidirect
358. #2668C2×C13semidirect
359. #2648C2×C13semidirect
360. #2531C2×C13semidirect
361. #2467C2×C13semidirect
362. #2464C2×C13semidirect
363. #2424C2×C13semidirect
364. #2328C2×C13semidirect
365. #2321C2×C13semidirect
366. C4×#120C2×C13semidirect
466. C24×C4C22×C13semidirect
468. C2×#126C22×C13semidirect
469. C2×#123C22×C13semidirect
479. C2×#120C22×C13semidirect
480. C2×#120C22×C13semidirect
483. C2×C4×D4C22×C13semidirect
484. C22×C22⋊C4C22×C13semidirect
485. #400C22×C13semidirect
486. #399C22×C13semidirect
487. #398C22×C13semidirect
488. #398C22×C13semidirect
489. #397C22×C13semidirect
490. #397C22×C13semidirect
491. #397C22×C13semidirect
492. #397C22×C13semidirect
493. #396C22×C13semidirect
494. #396C22×C13semidirect
500. #394C22×C13semidirect
501. #394C22×C13semidirect
502. #394C22×C13semidirect
503. #394C22×C13semidirect
507. #392C22×C13semidirect
508. #392C22×C13semidirect
512. #390C22×C13semidirect
513. #390C22×C13semidirect
514. #390C22×C13semidirect
515. #388C22×C13semidirect
516. #388C22×C13semidirect
517. #388C22×C13semidirect
518. #388C22×C13semidirect
519. #388C22×C13semidirect
520. #388C22×C13semidirect
521. #388C22×C13semidirect
522. #387C22×C13semidirect
523. #387C22×C13semidirect
524. #387C22×C13semidirect
531. #386C22×C13semidirect
532. #386C22×C13semidirect
533. #386C22×C13semidirect
534. #386C22×C13semidirect
535. #386C22×C13semidirect
536. #386C22×C13semidirect
537. #386C22×C13semidirect
538. #385C22×C13semidirect
539. #385C22×C13semidirect
540. #385C22×C13semidirect
541. #385C22×C13semidirect
542. #385C22×C13semidirect
543. #382C22×C13semidirect
544. #380C22×C13semidirect
545. #380C22×C13semidirect
546. #380C22×C13semidirect
547. #379C22×C13semidirect
548. #379C22×C13semidirect
549. C4×C22⋊C4C22×C13semidirect
550. C4×C22⋊C4C22×C13semidirect
551. C4×C22⋊C4C22×C13semidirect
552. #376C22×C13semidirect
855. C13#36902direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28472
C13×#27812
C13×#27482
C13×#27142
C13×#27082
C13×#26912
C13×#26792
C13×#26782
C13×#26692
C13×#26682
C13×#26482
C13×#25312
C13×#24672
C13×#24642
C13×#24242
C13×#23282
C13×#23212
C4×C13×#1202
#3690213