Finite Group Databasebeta

← C13×#34424 #15720763

Subgroups — C13×#34424 #15720763

Order 3328.

2442 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#538C211yesmaximal, characteristic
2C13×#2379C212yesmaximal, complemented
3C13×#2376C212yesmaximal, complemented
4C13×#2367C212yesmaximal, complemented
5C13×#2359C212yesmaximal, complemented
6C13×#2358C212yesmaximal, complemented
7C13×#2358C212yesmaximal, complemented
8C13×#2352C212yesmaximal, complemented
9C13×#2349C212yesmaximal, complemented
10C13×#2334C212yesmaximal, complemented
11C13×#2334C212yesmaximal, complemented
12C13×#2329C211yesmaximal, characteristic, complemented
13C13×#2325C211yesmaximal, characteristic, complemented
14C13×#2325C212yesmaximal, complemented
15C13×#2324C212yesmaximal, complemented
16C13×#2315C211yesmaximal, characteristic, complemented
17C4×C13×C22⋊Q8C211yesmaximal, characteristic, complemented
18C4×C13×#121C211yesmaximal, characteristic, complemented
19C2×C13×#388C211yesmaximal, characteristic, complemented
20C13×#538C4116yescomplemented
21C2×C13×#126C2212yes—
22C2×C13×#124C2212yes—
23C2×C13×#123C2212yes—
24C2×C13×C22⋊Q8C2211yescharacteristic
25C2×C13×#121C2211yescharacteristic
26C2×C13×#121C2212yes—
27C2×C13×#120C2212yes—
28C2×C4×Q8×C13C2211yescharacteristic, complemented
29C2×C4×D4×C13C2212yes—
30C2×C4×D4×C13C2212yes—
31C2×C4×D4×C13C2212yes—
32C2×C4×D4×C13C2212yes—
33C2×C4×D4×C13C2212yes—
34C2×C4×D4×C13C2211yescharacteristic, complemented
35C2×C13×#117C2212yescomplemented
36C22×C13×C4⋊C4C2211yescharacteristic
37C22×C13×C22⋊C4C2211yescharacteristic
38C22×C13×C22⋊C4C2211yescharacteristic
39C22×C13×C22⋊C4C2212yes—
40C22×C13×C22⋊C4C2211yescharacteristic
41C22×C42×C13C2211yescharacteristic
42C13×#391C2211yescharacteristic, complemented
43C13×#391C2212yescomplemented
44C13×#390C2212yes—
45C13×#390C2212yes—
46C13×#390C2211yescharacteristic, complemented
47C13×#389C2211yescharacteristic, complemented
48C13×#389C2211yescharacteristic, complemented
49C13×#389C2212yescomplemented
50C13×#389C2212yescomplemented
51C13×#389C2212yescomplemented
52C13×#388C2212yes—
53C13×#388C2212yes—
54C13×#388C2212yes—
55C13×#388C2212yes—
56C13×#388C2212yes—
57C13×#388C2212yes—
58C13×#388C2212yes—
59C13×#388C2212yes—
60C13×#388C2212yescomplemented
61C13×#388C2212yescomplemented
62C13×#388C2212yescomplemented
63C13×#388C2212yescomplemented
64C13×#387C2212yescomplemented
65C13×#387C2212yescomplemented
66C13×#387C2212yescomplemented
67C13×#387C2212yescomplemented
68C13×#387C2212yescomplemented
69C13×#387C2212yescomplemented
70C13×#386C2212yes—
71C13×#386C2212yes—
72C13×#386C2212yes—
73C13×#386C2212yes—
74C13×#386C2212yes—
75C13×#386C2212yes—
76C13×#386C2212yescomplemented
77C13×#385C2212yes—
78C13×#385C2212yes—
79C13×#385C2212yes—
80C13×#385C2212yes—
81C13×#385C2212yes—
82C13×#385C2212yes—
83C13×#385C2212yes—
84C13×#385C2212yes—
85C13×#385C2212yescomplemented
86C13×#385C2212yescomplemented
87C13×#385C2212yescomplemented
88C13×#382C2212yescomplemented
89C13×#382C2212yescomplemented
90C13×#380C2211yescharacteristic
91C13×#380C2211yescharacteristic
92C13×#380C2212yes—
93C13×#380C2212yescomplemented
94C13×#380C2212yescomplemented
95C4×C13×C4⋊C4C2211yescharacteristic, complemented
96C4×C13×C4⋊C4C2212yescomplemented
97C4×C13×C4⋊C4C2211yescharacteristic, complemented
98C4×C13×C4⋊C4C2212yescomplemented
99C4×C13×C4⋊C4C2212yescomplemented
100C4×C13×C22⋊C4C2212yes—
101C4×C13×C22⋊C4C2212yes—
102C4×C13×C22⋊C4C2212yes—
103C4×C13×C22⋊C4C2212yes—
104C4×C13×C22⋊C4C2212yescomplemented
105C2×C13×#95C2211yescharacteristic
106C2×C13×#95C2211yescharacteristic
107C2×C13×#95C2212yescomplemented
108C25×C13C2311yescharacteristic
109C22×Q8×C13C2311yescharacteristic
110C22×D4×C13C2312yes—
111C22×D4×C13C2312yes—
112C22×D4×C13C2312yes—
113C22×D4×C13C2311yescharacteristic
114C23×C4×C13C2311yescharacteristic
115C23×C4×C13C2311yescharacteristic
116C23×C4×C13C2311yescharacteristic
117C23×C4×C13C2312yes—
118C23×C4×C13C2311yescharacteristic
119C23×C4×C13C2312yes—
120C23×C4×C13C2312yes—
121C23×C4×C13C2312yes—
122C23×C4×C13C2311yescharacteristic
123C23×C4×C13C2311yescharacteristic
124C23×C4×C13C2312yes—
125C13×#126C2×C4116yescomplemented
126C13×#124C2×C4116yescomplemented
127C13×#123C2×C4116yescomplemented
128C13×C22⋊Q8C2×C418yescomplemented
129C13×#121C2×C4116yescomplemented
130C13×#121C2×C418yescomplemented
131C13×#120C2×C4116yescomplemented
132C4×Q8×C13—42no—
133C4×D4×C13—44no—
134C4×D4×C13—42no—
135C4×D4×C13—44no—
136C4×D4×C13—44no—
137C4×D4×C13—44no—
138C4×D4×C13C2×C4116yescomplemented
139C13×#117—44no—
140C2×C13×C4⋊C4—42no—
141C2×C13×C4⋊C4C2312yes—
142C2×C13×C4⋊C4C2312yes—
143C2×C13×C4⋊C4C2312yes—
144C2×C13×C4⋊C4C2311yescharacteristic
145C2×C13×C4⋊C4C2311yescharacteristic
146C2×C13×C4⋊C4C2312yes—
147C2×C13×C4⋊C4C2312yes—
148C2×C13×C4⋊C4C2312yes—
149C2×C13×C4⋊C4C2311yescharacteristic
150C2×C13×C4⋊C4C2311yescharacteristic
151C2×C13×C4⋊C4C2312yes—
152C2×C13×C4⋊C4C2312yes—
153C2×C13×C4⋊C4C2312yes—
154C2×C13×C4⋊C4C2312yes—
155C2×C13×C4⋊C4C2312yes—
156C2×C13×C4⋊C4C2311yescharacteristic
157C2×C13×C4⋊C4C2311yescharacteristic
158C2×C13×C4⋊C4C2312yes—
159C2×C13×C22⋊C4—42no—
160C2×C13×C22⋊C4—42no—
161C2×C13×C22⋊C4—44no—
162C2×C13×C22⋊C4C2×C418yescomplemented
163C2×C13×C22⋊C4C2312yes—
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⋊C4C2312yes—
173C2×C13×C22⋊C4C2312yes—
174C2×C13×C22⋊C4C2312yes—
175C2×C13×C22⋊C4C2312yes—
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×C42×C13—42no—
185C2×C42×C13C2312yes—
186C2×C42×C13C2311yescharacteristic
187C2×C42×C13C2311yescharacteristic
188C2×C42×C13C2312yes—
189C2×C42×C13C2312yes—
190C2×C42×C13C2312yes—
191C2×C42×C13C2312yes—
192C2×C42×C13C2312yes—
193C2×C42×C13C2311yescharacteristic
194C2×C42×C13C2311yescharacteristic
195C2×C42×C13C2312yes—
196C13×#95C2312yes—
197C13×#95C2312yes—
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—
214C13×#95C2312yes—
215C13×#95C2312yes—
216#34424C1311yesmaximal, characteristic, direct product factor, Sylow
217C24×C13—22no—
218C24×C13—22no—
219C24×C13—41no—
220C24×C13—41no—
221C24×C13—41no—
222C24×C13—41no—
223C24×C13C22×C414yes—
224C24×C13C2412yes—
225C24×C13C2412yes—
226C24×C13C2411yescharacteristic
227C2×Q8×C13—41no—
228C2×Q8×C13—41no—
229C2×Q8×C13C22×C414yes—
230C2×D4×C13—24no—
231C2×D4×C13—24no—
232C2×D4×C13—42no—
233C2×D4×C13—41no—
234C2×D4×C13—42no—
235C2×D4×C13—42no—
236C2×D4×C13—41no—
237C2×D4×C13—42no—
238C2×D4×C13C22×C418yes—
239C2×D4×C13C22×C418yes—
240C2×D4×C13C22×C418yes—
241C2×D4×C13C22×C414yes—
242C22×C4×C13—22no—
243C22×C4×C13—22no—
244C22×C4×C13—22no—
245C22×C4×C13—22no—
246C22×C4×C13—22no—
247C22×C4×C13—22no—
248C22×C4×C13—24no—
249C22×C4×C13—41no—
250C22×C4×C13—41no—
251C22×C4×C13—41no—
252C22×C4×C13—42no—
253C22×C4×C13—41no—
254C22×C4×C13—42no—
255C22×C4×C13—41no—
256C22×C4×C13—41no—
257C22×C4×C13—41no—
258C22×C4×C13—42no—
259C22×C4×C13—42no—
260C22×C4×C13—41no—
261C22×C4×C13—41no—
262C22×C4×C13—42no—
263C22×C4×C13—42no—
264C22×C4×C13—42no—
265C22×C4×C13—42no—
266C22×C4×C13—42no—
267C22×C4×C13—42no—
268C22×C4×C13—42no—
269C22×C4×C13—42no—
270C22×C4×C13—41no—
271C22×C4×C13—42no—
272C22×C4×C13C22×C414yes—
273C22×C4×C13C22×C414yes—
274C22×C4×C13C22×C418yes—
275C22×C4×C13C2411yescharacteristic
276C22×C4×C13C2412yes—
277C22×C4×C13C2412yes—
278C22×C4×C13C2412yes—
279C22×C4×C13C2412yes—
280C22×C4×C13C2411yescharacteristic
281C22×C4×C13C2412yes—
282C22×C4×C13C2412yes—
283C22×C4×C13C2412yes—
284C22×C4×C13C2412yes—
285C22×C4×C13C2411yescharacteristic
286C22×C4×C13C2412yes—
287C22×C4×C13C2411yescharacteristic
288C22×C4×C13C2412yes—
289C22×C4×C13C2411yescharacteristic
290C22×C4×C13C2411yescharacteristic
291C13×C4⋊C4—24no—
292C13×C4⋊C4—24no—
293C13×C4⋊C4—42no—
294C13×C4⋊C4—42no—
295C13×C4⋊C4—41no—
296C13×C4⋊C4—42no—
297C13×C4⋊C4—41no—
298C13×C4⋊C4—42no—
299C13×C4⋊C4—42no—
300C13×C4⋊C4—42no—
301C13×C4⋊C4—41no—
302C13×C4⋊C4—42no—
303C13×C4⋊C4—42no—
304C13×C4⋊C4—41no—
305C13×C4⋊C4C22×C418yes—
306C13×C4⋊C4C22×C418yes—
307C13×C4⋊C4C22×C414yes—
308C13×C4⋊C4C22×C414yes—
309C13×C22⋊C4—24no—
310C13×C22⋊C4—24no—
311C13×C22⋊C4—24no—
312C13×C22⋊C4—24no—
313C13×C22⋊C4—24no—
314C13×C22⋊C4—42no—
315C13×C22⋊C4—42no—
316C13×C22⋊C4—42no—
317C13×C22⋊C4—42no—
318C13×C22⋊C4—42no—
319C13×C22⋊C4—42no—
320C13×C22⋊C4—42no—
321C13×C22⋊C4—42no—
322C13×C22⋊C4—42no—
323C13×C22⋊C4C22×C418yes—
324C13×C22⋊C4C22×C418yes—
325C13×C22⋊C4C22×C418yes—
326C13×C22⋊C4C22×C418yes—
327C13×C22⋊C4C22×C418yes—
328C13×C22⋊C4C22×C418yes—
329C13×C22⋊C4C22×C418yes—
330C42×C13—22no—
331C42×C13—22no—
332C42×C13—24no—
333C42×C13—41no—
334C42×C13—41no—
335C42×C13—42no—
336C42×C13—42no—
337C42×C13—42no—
338C42×C13—42no—
339C42×C13—42no—
340C42×C13C22×C418yes—
341C2×#538C2×C1311yescharacteristic
342#2379C2×C1312yescomplemented
343#2376C2×C1312yescomplemented
344#2367C2×C1312yescomplemented
345#2359C2×C1312yescomplemented
346#2358C2×C1312yescomplemented
347#2358C2×C1312yescomplemented
348#2352C2×C1312yescomplemented
349#2349C2×C1312yescomplemented
350#2334C2×C1312yescomplemented
351#2334C2×C1312yescomplemented
352#2329C2×C1311yescharacteristic, complemented
353#2325C2×C1311yescharacteristic, complemented
354#2325C2×C1312yescomplemented
355#2324C2×C1312yescomplemented
356#2315C2×C1311yescharacteristic, complemented
357C4×C22⋊Q8C2×C1311yescharacteristic, complemented
358C4×#121C2×C1311yescharacteristic, complemented
359C2×#388C2×C1311yescharacteristic, complemented
360C23×C13—21no—
361C23×C13—21no—
362C23×C13—21no—
363C23×C13—21no—
364C23×C13—22no—
365C23×C13—22no—
366C23×C13—22no—
367C23×C13—22no—
368C23×C13—22no—
369C23×C13—22no—
370C23×C13—22no—
371C23×C13—22no—
372C23×C13—22no—
373C23×C13—22no—
374C23×C13—22no—
375C23×C13—22no—
376C23×C13—28no—
377C23×C13—44no—
378C23×C13—44no—
379C23×C13—82no—
380C23×C13—82no—
381C23×C13—82no—
382C23×C13—82no—
383C23×C13C23×C414yes—
384C23×C13C23×C414yes—
385C23×C13C23×C412yes—
386C23×C13H(5,𝔽2)12yes—
387C23×C132−1+412yes—
388C23×C13C2511yescharacteristic
389Q8×C13—44no—
390D4×C13—216no—
391D4×C13—48no—
392D4×C13—44no—
393D4×C13—48no—
394C2×C4×C13—21no—
395C2×C4×C13—21no—
396C2×C4×C13—22no—
397C2×C4×C13—21no—
398C2×C4×C13—22no—
399C2×C4×C13—22no—
400C2×C4×C13—21no—
401C2×C4×C13—22no—
402C2×C4×C13—21no—
403C2×C4×C13—22no—
404C2×C4×C13—22no—
405C2×C4×C13—22no—
406C2×C4×C13—21no—
407C2×C4×C13—21no—
408C2×C4×C13—22no—
409C2×C4×C13—21no—
410C2×C4×C13—21no—
411C2×C4×C13—22no—
412C2×C4×C13—21no—
413C2×C4×C13—22no—
414C2×C4×C13—22no—
415C2×C4×C13—22no—
416C2×C4×C13—22no—
417C2×C4×C13—22no—
418C2×C4×C13—22no—
419C2×C4×C13—22no—
420C2×C4×C13—22no—
421C2×C4×C13—22no—
422C2×C4×C13—22no—
423C2×C4×C13—22no—
424C2×C4×C13—21no—
425C2×C4×C13—21no—
426C2×C4×C13—21no—
427C2×C4×C13—22no—
428C2×C4×C13—21no—
429C2×C4×C13—22no—
430C2×C4×C13—22no—
431C2×C4×C13—22no—
432C2×C4×C13—22no—
433C2×C4×C13—22no—
434C2×C4×C13—44no—
435C2×C4×C13—48no—
436C2×C4×C13—44no—
437C2×C4×C13—44no—
438C2×C4×C13—44no—
439C2×C4×C13—84no—
440C2×C4×C13—82no—
441C2×C4×C13—82no—
442C2×C4×C13—84no—
443C2×C4×C13—84no—
444C2×C4×C13—84no—
445C2×C4×C13C23×C414yes—
446C2×C4×C13C23×C414yes—
447C2×C4×C13C23×C414yes—
448C2×C4×C13C23×C412yes—
449C2×C4×C13C23×C412yes—
450C2×C4×C13C23×C414yes—
451C2×C4×C13H(5,𝔽2)12yes—
452C2×C4×C13H(5,𝔽2)12yes—
453#538C4×C13116yescomplemented
454C2×#126C22×C1312yes—
455C2×#124C22×C1312yes—
456C2×#123C22×C1312yes—
457C2×C22⋊Q8C22×C1311yescharacteristic
458C2×#121C22×C1312yes—
459C2×#121C22×C1311yescharacteristic
460C2×#120C22×C1312yes—
461C2×C4×Q8C22×C1311yescharacteristic, complemented
462C2×C4×D4C22×C1312yes—
463C2×C4×D4C22×C1312yes—
464C2×C4×D4C22×C1312yes—
465C2×C4×D4C22×C1312yes—
466C2×C4×D4C22×C1312yes—
467C2×C4×D4C22×C1311yescharacteristic, complemented
468C2×#117C22×C1312yescomplemented
469C22×C4⋊C4C22×C1311yescharacteristic
470C22×C22⋊C4C22×C1312yes—
471C22×C22⋊C4C22×C1311yescharacteristic
472C22×C22⋊C4C22×C1311yescharacteristic
473C22×C22⋊C4C22×C1311yescharacteristic
474C22×C42C22×C1311yescharacteristic
475#391C22×C1312yescomplemented
476#391C22×C1311yescharacteristic, complemented
477#390C22×C1312yes—
478#390C22×C1312yes—
479#390C22×C1311yescharacteristic, complemented
480#389C22×C1312yescomplemented
481#389C22×C1311yescharacteristic, complemented
482#389C22×C1312yescomplemented
483#389C22×C1312yescomplemented
484#389C22×C1311yescharacteristic, complemented
485#388C22×C1312yes—
486#388C22×C1312yes—
487#388C22×C1312yes—
488#388C22×C1312yes—
489#388C22×C1312yes—
490#388C22×C1312yes—
491#388C22×C1312yes—
492#388C22×C1312yes—
493#388C22×C1312yescomplemented
494#388C22×C1312yescomplemented
495#388C22×C1312yescomplemented
496#388C22×C1312yescomplemented
497#387C22×C1312yescomplemented
498#387C22×C1312yescomplemented
499#387C22×C1312yescomplemented
500#387C22×C1312yescomplemented
501#387C22×C1312yescomplemented
502#387C22×C1312yescomplemented
503#386C22×C1312yes—
504#386C22×C1312yes—
505#386C22×C1312yes—
506#386C22×C1312yes—
507#386C22×C1312yes—
508#386C22×C1312yes—
509#386C22×C1312yescomplemented
510#385C22×C1312yes—
511#385C22×C1312yes—
512#385C22×C1312yes—
513#385C22×C1312yes—
514#385C22×C1312yes—
515#385C22×C1312yes—
516#385C22×C1312yes—
517#385C22×C1312yes—
518#385C22×C1312yescomplemented
519#385C22×C1312yescomplemented
520#385C22×C1312yescomplemented
521#382C22×C1312yescomplemented
522#382C22×C1312yescomplemented
523#380C22×C1311yescharacteristic
524#380C22×C1311yescharacteristic
525#380C22×C1312yes—
526#380C22×C1312yescomplemented
527#380C22×C1312yescomplemented
528C4×C4⋊C4C22×C1312yescomplemented
529C4×C4⋊C4C22×C1311yescharacteristic, complemented
530C4×C4⋊C4C22×C1312yescomplemented
531C4×C4⋊C4C22×C1312yescomplemented
532C4×C4⋊C4C22×C1311yescharacteristic, complemented
533C4×C22⋊C4C22×C1312yes—
534C4×C22⋊C4C22×C1312yes—
535C4×C22⋊C4C22×C1312yes—
536C4×C22⋊C4C22×C1312yes—
537C4×C22⋊C4C22×C1312yescomplemented
538C2×#95C22×C1311yescharacteristic
539C2×#95C22×C1311yescharacteristic
540C2×#95C22×C1312yescomplemented
541C22×C13—22no—
542C22×C13—22no—
543C22×C13—22no—
544C22×C13—22no—
545C22×C13—22no—
546C22×C13—22no—
547C22×C13—24no—
548C22×C13—24no—
549C22×C13—24no—
550C22×C13—24no—
551C22×C13—24no—
552C22×C13—24no—
553C22×C13—42no—
554C22×C13—42no—
555C22×C13—42no—
556C22×C13—42no—
557C22×C13—42no—
558C22×C13—42no—
559C22×C13—42no—
560C22×C13—42no—
561C22×C13—88no—
562C22×C13#52014yes—
563C22×C13C24×C411yescharacteristic
564C22×C13C2×H(5,𝔽2)11yescharacteristic
565C22×C13C2×H(5,𝔽2)11yescharacteristic
566C22×C13C2×H(5,𝔽2)11yescharacteristic
567C22×C13C2×2−1+411yescharacteristic
568C22×C13#58511yescharacteristic
569C22×C13#58511yescharacteristic
570C4×C13—24no—
571C4×C13—24no—
572C4×C13—24no—
573C4×C13—22no—
574C4×C13—22no—
575C4×C13—24no—
576C4×C13—22no—
577C4×C13—22no—
578C4×C13—41no—
579C4×C13—42no—
580C4×C13—42no—
581C4×C13—41no—
582C4×C13—42no—
583C4×C13—42no—
584C4×C13—42no—
585C4×C13—42no—
586C25C23×C1311yescharacteristic
587C22×Q8C23×C1311yescharacteristic
588C22×D4C23×C1312yes—
589C22×D4C23×C1312yes—
590C22×D4C23×C1312yes—
591C22×D4C23×C1311yescharacteristic
592C23×C4C23×C1311yescharacteristic
593C23×C4C23×C1311yescharacteristic
594C23×C4C23×C1311yescharacteristic
595C23×C4C23×C1311yescharacteristic
596C23×C4C23×C1312yes—
597C23×C4C23×C1312yes—
598C23×C4C23×C1312yes—
599C23×C4C23×C1312yes—
600C23×C4C23×C1311yescharacteristic
601C23×C4C23×C1311yescharacteristic
602C23×C4C23×C1312yes—
603#126C2×C4×C13116yescomplemented
604#124C2×C4×C13116yescomplemented
605#123C2×C4×C13116yescomplemented
606C22⋊Q8C2×C4×C1318yescomplemented
607#121C2×C4×C13116yescomplemented
608#121C2×C4×C1318yescomplemented
609#120C2×C4×C13116yescomplemented
610C4×Q8—42no—
611C4×D4—44no—
612C4×D4—42no—
613C4×D4—44no—
614C4×D4—44no—
615C4×D4—44no—
616C4×D4C2×C4×C13116yescomplemented
617#117—44no—
618C2×C4⋊C4—42no—
619C2×C4⋊C4C23×C1312yes—
620C2×C4⋊C4C23×C1312yes—
621C2×C4⋊C4C23×C1312yes—
622C2×C4⋊C4C23×C1312yes—
623C2×C4⋊C4C23×C1312yes—
624C2×C4⋊C4C23×C1312yes—
625C2×C4⋊C4C23×C1312yes—
626C2×C4⋊C4C23×C1311yescharacteristic
627C2×C4⋊C4C23×C1311yescharacteristic
628C2×C4⋊C4C23×C1312yes—
629C2×C4⋊C4C23×C1311yescharacteristic
630C2×C4⋊C4C23×C1311yescharacteristic
631C2×C4⋊C4C23×C1312yes—
632C2×C4⋊C4C23×C1312yes—
633C2×C4⋊C4C23×C1312yes—
634C2×C4⋊C4C23×C1312yes—
635C2×C4⋊C4C23×C1311yescharacteristic
636C2×C4⋊C4C23×C1311yescharacteristic
637C2×C22⋊C4—42no—
638C2×C22⋊C4—42no—
639C2×C22⋊C4—44no—
640C2×C22⋊C4C2×C4×C1318yescomplemented
641C2×C22⋊C4C23×C1312yes—
642C2×C22⋊C4C23×C1312yes—
643C2×C22⋊C4C23×C1312yes—
644C2×C22⋊C4C23×C1312yes—
645C2×C22⋊C4C23×C1312yes—
646C2×C22⋊C4C23×C1312yes—
647C2×C22⋊C4C23×C1312yes—
648C2×C22⋊C4C23×C1312yes—
649C2×C22⋊C4C23×C1312yes—
650C2×C22⋊C4C23×C1312yes—
651C2×C22⋊C4C23×C1312yes—
652C2×C22⋊C4C23×C1312yes—
653C2×C22⋊C4C23×C1312yes—
654C2×C22⋊C4C23×C1312yes—
655C2×C22⋊C4C23×C1312yes—
656C2×C22⋊C4C23×C1312yes—
657C2×C22⋊C4C23×C1312yes—
658C2×C22⋊C4C23×C1312yes—
659C2×C22⋊C4C23×C1312yes—
660C2×C22⋊C4C23×C1312yes—
661C2×C22⋊C4C23×C1312yes—
662C2×C42—42no—
663C2×C42C23×C1312yes—
664C2×C42C23×C1311yescharacteristic
665C2×C42C23×C1311yescharacteristic
666C2×C42C23×C1312yes—
667C2×C42C23×C1312yes—
668C2×C42C23×C1312yes—
669C2×C42C23×C1312yes—
670C2×C42C23×C1312yes—
671C2×C42C23×C1311yescharacteristic
672C2×C42C23×C1311yescharacteristic
673C2×C42C23×C1312yes—
674#95C23×C1312yes—
675#95C23×C1312yes—
676#95C23×C1312yes—
677#95C23×C1312yes—
678#95C23×C1312yes—
679#95C23×C1312yes—
680#95C23×C1312yes—
681#95C23×C1312yes—
682#95C23×C1312yes—
683#95C23×C1312yes—
684#95C23×C1312yes—
685#95C23×C1312yes—
686#95C23×C1312yes—
687#95C23×C1312yes—
688#95C23×C1312yes—
689#95C23×C1312yes—
690#95C23×C1312yes—
691#95C23×C1312yes—
692#95C23×C1312yes—
693#95C23×C1312yes—
694C2×C13—24no—
695C2×C13—44no—
696C2×C13—44no—
697C2×C13C2×#52011yescharacteristic
698C2×C13C4×H(5,𝔽2)11yescharacteristic
699C2×C13C4×H(5,𝔽2)11yescharacteristic
700C2×C13#353411yescharacteristic
701C2×C13#353611yescharacteristic
702C2×C13#355811yescharacteristic
703C2×C13#356411yescharacteristic
704C24—22no—
705C24—22no—
706C24—41no—
707C24—41no—
708C24—41no—
709C24—41no—
710C24C22×C4×C1314yes—
711C24C24×C1312yes—
712C24C24×C1312yes—
713C24C24×C1311yescharacteristic
714C2×Q8—41no—
715C2×Q8—41no—
716C2×Q8C22×C4×C1314yes—
717C2×D4—24no—
718C2×D4—24no—
719C2×D4—42no—
720C2×D4—41no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—41no—
724C2×D4—42no—
725C2×D4C22×C4×C1318yes—
726C2×D4C22×C4×C1318yes—
727C2×D4C22×C4×C1318yes—
728C2×D4C22×C4×C1314yes—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—24no—
736C22×C4—41no—
737C22×C4—41no—
738C22×C4—41no—
739C22×C4—42no—
740C22×C4—41no—
741C22×C4—42no—
742C22×C4—41no—
743C22×C4—41no—
744C22×C4—41no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—41no—
748C22×C4—41no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—41no—
758C22×C4—42no—
759C22×C4C22×C4×C1314yes—
760C22×C4C22×C4×C1314yes—
761C22×C4C22×C4×C1318yes—
762C22×C4C24×C1311yescharacteristic
763C22×C4C24×C1312yes—
764C22×C4C24×C1312yes—
765C22×C4C24×C1312yes—
766C22×C4C24×C1312yes—
767C22×C4C24×C1311yescharacteristic
768C22×C4C24×C1312yes—
769C22×C4C24×C1312yes—
770C22×C4C24×C1312yes—
771C22×C4C24×C1312yes—
772C22×C4C24×C1311yescharacteristic
773C22×C4C24×C1311yescharacteristic
774C22×C4C24×C1312yes—
775C22×C4C24×C1312yes—
776C22×C4C24×C1311yescharacteristic
777C22×C4C24×C1311yescharacteristic
778C4⋊C4—24no—
779C4⋊C4—24no—
780C4⋊C4—42no—
781C4⋊C4—42no—
782C4⋊C4—42no—
783C4⋊C4—41no—
784C4⋊C4—42no—
785C4⋊C4—42no—
786C4⋊C4—41no—
787C4⋊C4—42no—
788C4⋊C4—41no—
789C4⋊C4—42no—
790C4⋊C4—41no—
791C4⋊C4—42no—
792C4⋊C4C22×C4×C1318yes—
793C4⋊C4C22×C4×C1318yes—
794C4⋊C4C22×C4×C1314yes—
795C4⋊C4C22×C4×C1314yes—
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—24no—
799C22⋊C4—24no—
800C22⋊C4—24no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—42no—
804C22⋊C4—42no—
805C22⋊C4—42no—
806C22⋊C4—42no—
807C22⋊C4—42no—
808C22⋊C4—42no—
809C22⋊C4—42no—
810C22⋊C4C22×C4×C1318yes—
811C22⋊C4C22×C4×C1318yes—
812C22⋊C4C22×C4×C1318yes—
813C22⋊C4C22×C4×C1318yes—
814C22⋊C4C22×C4×C1318yes—
815C22⋊C4C22×C4×C1318yes—
816C22⋊C4C22×C4×C1318yes—
817C42—22no—
818C42—22no—
819C42—24no—
820C42—41no—
821C42—41no—
822C42—42no—
823C42—42no—
824C42—42no—
825C42—42no—
826C42—42no—
827C42C22×C4×C1318yes—
828C13#3442411yescharacteristic, direct product factor, Sylow
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—28no—
846C23—44no—
847C23—44no—
848C23—82no—
849C23—82no—
850C23—82no—
851C23—82no—
852C23C23×C4×C1314yes—
853C23C23×C4×C1314yes—
854C23C23×C4×C1312yes—
855C23C13×H(5,𝔽2)12yes—
856C23C13×2−1+412yes—
857C23C25×C1311yescharacteristic
858Q8—44no—
859D4—216no—
860D4—48no—
861D4—44no—
862D4—48no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—22no—
871C2×C4—21no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—22no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—22no—
881C2×C4—21no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—22no—
897C2×C4—21no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—44no—
904C2×C4—48no—
905C2×C4—44no—
906C2×C4—44no—
907C2×C4—44no—
908C2×C4—84no—
909C2×C4—82no—
910C2×C4—82no—
911C2×C4—84no—
912C2×C4—84no—
913C2×C4—84no—
914C2×C4C23×C4×C1314yes—
915C2×C4C23×C4×C1314yes—
916C2×C4C23×C4×C1314yes—
917C2×C4C23×C4×C1312yes—
918C2×C4C23×C4×C1312yes—
919C2×C4C23×C4×C1314yes—
920C2×C4C13×H(5,𝔽2)12yes—
921C2×C4C13×H(5,𝔽2)12yes—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—24no—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—24no—
933C22—24no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—88no—
943C22C13×#52014yes—
944C22C24×C4×C1311yescharacteristic
945C22C2×C13×H(5,𝔽2)11yescharacteristic
946C22C2×C13×H(5,𝔽2)11yescharacteristic
947C22C2×C13×H(5,𝔽2)11yescharacteristic
948C22C2×C13×2−1+411yescharacteristic
949C22C13×#58511yescharacteristic
950C22C13×#58511yescharacteristic
951C4—22no—
952C4—22no—
953C4—24no—
954C4—24no—
955C4—24no—
956C4—22no—
957C4—22no—
958C4—24no—
959C4—41no—
960C4—42no—
961C4—42no—
962C4—41no—
963C4—42no—
964C4—42no—
965C4—42no—
966C4—42no—
967C2—24no—
968C2—44no—
969C2—44no—
970C2C2×C13×#52011yescharacteristic
971C2C4×C13×H(5,𝔽2)11yescharacteristic
972C2C4×C13×H(5,𝔽2)11yescharacteristic
973C2C13×#353411yescharacteristic
974C2C13×#353611yescharacteristic
975C2C13×#355811yescharacteristic
976C2C13×#356411yescharacteristic
subgroupG/H
center, socleC23×C13C25
commutatorC22C24×C4×C13
Frattini, cosocleC23C25×C13
prime radicalC2×C13×#538C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2379C2semidirect
3. C13×#2376C2semidirect
4. C13×#2367C2semidirect
5. C13×#2359C2semidirect
6. C13×#2358C2semidirect
7. C13×#2358C2semidirect
8. C13×#2352C2semidirect
9. C13×#2349C2semidirect
10. C13×#2334C2semidirect
11. C13×#2334C2semidirect
12. C13×#2329C2semidirect
13. C13×#2325C2semidirect
14. C13×#2325C2semidirect
15. C13×#2324C2semidirect
16. C13×#2315C2semidirect
17. C4×C13×C22⋊Q8C2semidirect
18. C4×C13×#121C2semidirect
19. C2×C13×#388C2semidirect
20. C13×#538C4semidirect
28. C2×C4×Q8×C13C22semidirect
34. C2×C4×D4×C13C22semidirect
35. C2×C13×#117C22semidirect
42. C13×#391C22semidirect
43. C13×#391C22semidirect
46. C13×#390C22semidirect
47. C13×#389C22semidirect
48. C13×#389C22semidirect
49. C13×#389C22semidirect
50. C13×#389C22semidirect
51. C13×#389C22semidirect
60. C13×#388C22semidirect
61. C13×#388C22semidirect
62. C13×#388C22semidirect
63. C13×#388C22semidirect
64. C13×#387C22semidirect
65. C13×#387C22semidirect
66. C13×#387C22semidirect
67. C13×#387C22semidirect
68. C13×#387C22semidirect
69. C13×#387C22semidirect
76. C13×#386C22semidirect
85. C13×#385C22semidirect
86. C13×#385C22semidirect
87. C13×#385C22semidirect
88. C13×#382C22semidirect
89. C13×#382C22semidirect
93. C13×#380C22semidirect
94. C13×#380C22semidirect
95. C4×C13×C4⋊C4C22semidirect
96. C4×C13×C4⋊C4C22semidirect
97. C4×C13×C4⋊C4C22semidirect
98. C4×C13×C4⋊C4C22semidirect
99. C4×C13×C4⋊C4C22semidirect
104. C4×C13×C22⋊C4C22semidirect
107. C2×C13×#95C22semidirect
125. C13×#126C2×C4semidirect
126. C13×#124C2×C4semidirect
127. C13×#123C2×C4semidirect
128. C13×C22⋊Q8C2×C4semidirect
129. C13×#121C2×C4semidirect
130. C13×#121C2×C4semidirect
131. C13×#120C2×C4semidirect
138. C4×D4×C13C2×C4semidirect
162. C2×C13×C22⋊C4C2×C4semidirect
216. #34424C13direct (N × H)
342. #2379C2×C13semidirect
343. #2376C2×C13semidirect
344. #2367C2×C13semidirect
345. #2359C2×C13semidirect
346. #2358C2×C13semidirect
347. #2358C2×C13semidirect
348. #2352C2×C13semidirect
349. #2349C2×C13semidirect
350. #2334C2×C13semidirect
351. #2334C2×C13semidirect
352. #2329C2×C13semidirect
353. #2325C2×C13semidirect
354. #2325C2×C13semidirect
355. #2324C2×C13semidirect
356. #2315C2×C13semidirect
357. C4×C22⋊Q8C2×C13semidirect
358. C4×#121C2×C13semidirect
359. C2×#388C2×C13semidirect
453. #538C4×C13semidirect
461. C2×C4×Q8C22×C13semidirect
467. C2×C4×D4C22×C13semidirect
468. C2×#117C22×C13semidirect
475. #391C22×C13semidirect
476. #391C22×C13semidirect
479. #390C22×C13semidirect
480. #389C22×C13semidirect
481. #389C22×C13semidirect
482. #389C22×C13semidirect
483. #389C22×C13semidirect
484. #389C22×C13semidirect
493. #388C22×C13semidirect
494. #388C22×C13semidirect
495. #388C22×C13semidirect
496. #388C22×C13semidirect
497. #387C22×C13semidirect
498. #387C22×C13semidirect
499. #387C22×C13semidirect
500. #387C22×C13semidirect
501. #387C22×C13semidirect
502. #387C22×C13semidirect
509. #386C22×C13semidirect
518. #385C22×C13semidirect
519. #385C22×C13semidirect
520. #385C22×C13semidirect
521. #382C22×C13semidirect
522. #382C22×C13semidirect
526. #380C22×C13semidirect
527. #380C22×C13semidirect
528. C4×C4⋊C4C22×C13semidirect
529. C4×C4⋊C4C22×C13semidirect
530. C4×C4⋊C4C22×C13semidirect
531. C4×C4⋊C4C22×C13semidirect
532. C4×C4⋊C4C22×C13semidirect
537. C4×C22⋊C4C22×C13semidirect
540. C2×#95C22×C13semidirect
603. #126C2×C4×C13semidirect
604. #124C2×C4×C13semidirect
605. #123C2×C4×C13semidirect
606. C22⋊Q8C2×C4×C13semidirect
607. #121C2×C4×C13semidirect
608. #121C2×C4×C13semidirect
609. #120C2×C4×C13semidirect
616. C4×D4C2×C4×C13semidirect
640. C2×C22⋊C4C2×C4×C13semidirect
828. C13#34424direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5382
C13×#23792
C13×#23762
C13×#23672
C13×#23592
C13×#23582
C13×#23522
C13×#23492
C13×#23342
C13×#23292
C13×#23252
C13×#23242
C13×#23152
C4×C13×C22⋊Q82
C4×C13×#1212
C2×C13×#3882
#3442413