Finite Group Databasebeta

← C13×#14736 #15701075

Subgroups — C13×#14736 #15701075

Order 3328.

1938 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#398C211yesmaximal, characteristic, complemented
2C2×C13×#385C211yesmaximal, characteristic
3C2×C13×#385C211yesmaximal, characteristic
4C2×C13×#385C211yesmaximal, characteristic
5C2×C13×#380C211yesmaximal, characteristic
6C22×C13×#95C211yesmaximal, characteristic
7C13×#1445C211yesmaximal, characteristic, complemented
8C13×#1444C211yesmaximal, characteristic, complemented
9C13×#1442C211yesmaximal, characteristic, complemented
10C13×#1442C211yesmaximal, characteristic, complemented
11C13×#1441C211yesmaximal, characteristic, complemented
12C13×#1441C211yesmaximal, characteristic, complemented
13C13×#1441C211yesmaximal, characteristic, complemented
14C13×C22⋊#95C211yesmaximal, characteristic
15C13×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C13×C22⋊C4C2211yescharacteristic
31C13×#398—24no—
32C13×#385—24no—
33C13×#385—24no—
34C13×#385—24no—
35C13×#380—24no—
36C2×C13×#95—24no—
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
54C2×C13×#95C2211yescharacteristic
55C2×C13×#95C2211yescharacteristic
56C2×C13×#95C2211yescharacteristic
57C25×C13C2311yescharacteristic
58C23×C4×C13—22no—
59C23×C4×C13—22no—
60C23×C4×C13—22no—
61C23×C4×C13—22no—
62C23×C4×C13—22no—
63C23×C4×C13—22no—
64C23×C4×C13—22no—
65C23×C4×C13—22no—
66C23×C4×C13—22no—
67C23×C4×C13—22no—
68C23×C4×C13—22no—
69C23×C4×C13—22no—
70C23×C4×C13—22no—
71C23×C4×C13—22no—
72C23×C4×C13—41no—
73C23×C4×C13—41no—
74C23×C4×C13—41no—
75C23×C4×C13—41no—
76C23×C4×C13—41no—
77C23×C4×C13—41no—
78C23×C4×C13Q814yes—
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C23×C4×C13C2311yescharacteristic
88C23×C4×C13C2311yescharacteristic
89C23×C4×C13C2311yescharacteristic
90C23×C4×C13C2311yescharacteristic
91C23×C4×C13C2311yescharacteristic
92C23×C4×C13C2311yescharacteristic
93C2×C13×C4⋊C4—22no—
94C2×C13×C4⋊C4—22no—
95C2×C13×C4⋊C4—22no—
96C2×C13×C4⋊C4—22no—
97C2×C13×C4⋊C4—22no—
98C2×C13×C4⋊C4—22no—
99C2×C13×C4⋊C4—22no—
100C2×C13×C4⋊C4—22no—
101C2×C13×C4⋊C4—22no—
102C2×C13×C4⋊C4—22no—
103C2×C13×C4⋊C4—22no—
104C2×C13×C4⋊C4—22no—
105C2×C13×C4⋊C4—22no—
106C2×C13×C4⋊C4—22no—
107C2×C13×C4⋊C4—22no—
108C2×C13×C4⋊C4—22no—
109C2×C13×C4⋊C4—41no—
110C2×C13×C4⋊C4—41no—
111C2×C13×C4⋊C4—41no—
112C2×C13×C4⋊C4—41no—
113C2×C13×C4⋊C4—41no—
114C2×C13×C4⋊C4—41no—
115C2×C13×C4⋊C4—41no—
116C2×C13×C4⋊C4—41no—
117C2×C13×C22⋊C4—22no—
118C2×C13×C22⋊C4—22no—
119C2×C13×C22⋊C4—22no—
120C2×C13×C22⋊C4—22no—
121C2×C13×C22⋊C4—22no—
122C2×C13×C22⋊C4—22no—
123C2×C13×C22⋊C4—22no—
124C2×C13×C22⋊C4—22no—
125C2×C13×C22⋊C4—22no—
126C2×C13×C22⋊C4D414yes—
127C2×C13×C22⋊C4D414yes—
128C2×C13×C22⋊C4Q814yes—
129C13×#95—22no—
130C13×#95—22no—
131C13×#95—22no—
132C13×#95—22no—
133C13×#95—22no—
134C13×#95—22no—
135C13×#95—22no—
136C13×#95—22no—
137C13×#95—22no—
138C13×#95—22no—
139C13×#95—22no—
140C13×#95—22no—
141C13×#95—22no—
142C13×#95—22no—
143C13×#95—22no—
144C13×#95—41no—
145C13×#95—41no—
146C13×#95—41no—
147C13×#95—41no—
148C13×#95D414yes—
149#14736C1311yesmaximal, characteristic, direct product factor, Sylow
150C24×C13—21no—
151C24×C13—21no—
152C24×C13—21no—
153C24×C13—21no—
154C24×C13—21no—
155C24×C13—21no—
156C24×C13—21no—
157C24×C13—21no—
158C24×C13C2×D412yes—
159C24×C13C2×D412yes—
160C24×C13C2×Q812yes—
161C24×C13C2×Q812yes—
162C24×C13#4112yes—
163C24×C13#4112yes—
164C24×C13#4112yes—
165C24×C13C2411yescharacteristic
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—28no—
171C22×C4×C13—28no—
172C22×C4×C13—28no—
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×C13—21no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—21no—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—21no—
224C22×C4×C13—21no—
225C22×C4×C13—21no—
226C22×C4×C13—21no—
227C22×C4×C13—21no—
228C22×C4×C13—21no—
229C22×C4×C13—21no—
230C22×C4×C13—21no—
231C22×C4×C13—21no—
232C22×C4×C13—21no—
233C22×C4×C13—21no—
234C22×C4×C13—21no—
235C22×C4×C13—21no—
236C22×C4×C13—21no—
237C22×C4×C13—21no—
238C22×C4×C13—21no—
239C22×C4×C13—28no—
240C22×C4×C13—21no—
241C22×C4×C13—21no—
242C22×C4×C13—21no—
243C22×C4×C13—21no—
244C22×C4×C13—21no—
245C22×C4×C13—21no—
246C22×C4×C13—21no—
247C22×C4×C13—21no—
248C22×C4×C13—21no—
249C22×C4×C13—21no—
250C22×C4×C13—21no—
251C22×C4×C13—21no—
252C22×C4×C13—21no—
253C22×C4×C13—21no—
254C22×C4×C13—44no—
255C22×C4×C13—44no—
256C22×C4×C13—44no—
257C22×C4×C13—44no—
258C22×C4×C13—44no—
259C22×C4×C13—44no—
260C22×C4×C13—44no—
261C22×C4×C13—44no—
262C22×C4×C13—44no—
263C22×C4×C13—44no—
264C22×C4×C13—44no—
265C22×C4×C13—44no—
266C22×C4×C13—44no—
267C22×C4×C13—44no—
268C22×C4×C13—44no—
269C22×C4×C13—44no—
270C22×C4×C13—44no—
271C22×C4×C13C2×D412yes—
272C22×C4×C13C2×D412yes—
273C22×C4×C13C2×D412yes—
274C22×C4×C13C2×D412yes—
275C22×C4×C13C2×D412yes—
276C22×C4×C13C2×D412yes—
277C22×C4×C13C2×D412yes—
278C22×C4×C13C2×Q812yes—
279C22×C4×C13C2×Q812yes—
280C22×C4×C13C2×Q812yes—
281C22×C4×C13C2×Q812yes—
282C22×C4×C13#4112yes—
283C22×C4×C13#4112yes—
284C22×C4×C13#4112yes—
285C13×C4⋊C4—44no—
286C13×C4⋊C4—44no—
287C13×C4⋊C4—44no—
288C13×C4⋊C4—44no—
289C13×C4⋊C4—44no—
290C13×C4⋊C4—44no—
291C13×C4⋊C4—44no—
292C13×C4⋊C4—44no—
293C13×C22⋊C4—28no—
294C13×C22⋊C4—28no—
295C13×C22⋊C4—28no—
296C13×C22⋊C4—44no—
297C2×#398C2×C1311yescharacteristic, complemented
298C2×#385C2×C1311yescharacteristic
299C2×#385C2×C1311yescharacteristic
300C2×#385C2×C1311yescharacteristic
301C2×#380C2×C1311yescharacteristic
302C22×#95C2×C1311yescharacteristic
303#1445C2×C1311yescharacteristic, complemented
304#1444C2×C1311yescharacteristic, complemented
305#1442C2×C1311yescharacteristic, complemented
306#1442C2×C1311yescharacteristic, complemented
307#1441C2×C1311yescharacteristic, complemented
308#1441C2×C1311yescharacteristic, complemented
309#1441C2×C1311yescharacteristic, complemented
310C22⋊#95C2×C1311yescharacteristic
311C22⋊#95C2×C1311yescharacteristic
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—22no—
326C23×C13—22no—
327C23×C13—22no—
328C23×C13—22no—
329C23×C13—22no—
330C23×C13—22no—
331C23×C13—22no—
332C23×C13—22no—
333C23×C13—22no—
334C23×C13—22no—
335C23×C13—22no—
336C23×C13—22no—
337C23×C13—22no—
338C23×C13—22no—
339C23×C13—22no—
340C23×C13#12114yes—
341C23×C13C22⋊Q814yes—
342C23×C13C22⋊Q814yes—
343C23×C13#12314yes—
344C23×C13#12514yes—
345C23×C13#12514yes—
346C23×C13C4⋊Q814yes—
347C23×C13C22×D411yescharacteristic
348C23×C13C22×D411yescharacteristic
349C23×C13C22×D411yescharacteristic
350C23×C13C22×Q811yescharacteristic
351C23×C13C22×Q811yescharacteristic
352C23×C13C2×#4111yescharacteristic
353C23×C13C2×#4111yescharacteristic
354C23×C13C2×#4111yescharacteristic
355C23×C13C2×#4111yescharacteristic
356C23×C13C2×#4111yescharacteristic
357C23×C13C2×#4111yescharacteristic
358C23×C13H(5,𝔽2)11yescharacteristic
359C23×C13H(5,𝔽2)11yescharacteristic
360C23×C13H(5,𝔽2)11yescharacteristic
361C23×C132−1+411yescharacteristic
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—22no—
375C2×C4×C13—22no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—22no—
382C2×C4×C13—22no—
383C2×C4×C13—22no—
384C2×C4×C13—22no—
385C2×C4×C13—22no—
386C2×C4×C13—22no—
387C2×C4×C13—22no—
388C2×C4×C13—22no—
389C2×C4×C13—22no—
390C2×C4×C13—22no—
391C2×C4×C13—22no—
392C2×C4×C13—22no—
393C2×C4×C13—22no—
394C2×C4×C13—22no—
395C2×C4×C13—22no—
396C2×C4×C13—22no—
397C2×C4×C13—22no—
398C2×C4×C13—22no—
399C2×C4×C13—22no—
400C2×C4×C13—22no—
401C2×C4×C13—416no—
402C2×C4×C13—416no—
403C2×C4×C13—416no—
404C2×C4×C13—41no—
405C2×C4×C13—41no—
406C2×C4×C13—41no—
407C2×C4×C13—41no—
408C2×C4×C13—41no—
409C2×C4×C13—41no—
410C2×C4×C13—41no—
411C2×C4×C13—41no—
412C2×C4×C13—41no—
413C2×C4×C13—41no—
414C2×C4×C13—41no—
415C2×C4×C13—41no—
416C2×C4×C13—41no—
417C2×C4×C13—41no—
418C2×C4×C13—41no—
419C2×C4×C13—41no—
420C2×C4×C13—41no—
421C2×C4×C13—41no—
422C2×C4×C13—41no—
423C2×C4×C13—41no—
424C2×C4×C13—41no—
425C2×C4×C13—41no—
426C2×C4×C13—41no—
427C2×C4×C13—41no—
428C2×C4×C13—41no—
429C2×C4×C13—41no—
430C2×C4×C13—41no—
431C2×C4×C13—41no—
432C2×C4×C13—41no—
433C2×C4×C13—41no—
434C2×C4×C13—41no—
435C2×C4×C13—41no—
436C2×C4×C13—41no—
437C2×C4×C13—41no—
438C2×C4×C13—41no—
439C2×C4×C13—41no—
440C2×C4×C13—41no—
441C2×C4×C13—41no—
442C2×C4×C13—41no—
443C2×C4×C13—41no—
444C2×C4×C13—41no—
445C2×C4×C13—41no—
446C2×C4×C13—41no—
447C2×C4×C13—41no—
448C2×C4×C13—41no—
449C2×C4×C13—41no—
450C2×C4×C13—41no—
451C2×C4×C13—41no—
452C2×C4×C13—41no—
453C2×C4×C13—41no—
454C2×C4×C13—41no—
455C2×C4×C13—41no—
456C2×C4×C13—41no—
457C2×C4×C13—41no—
458C2×C4×C13—41no—
459C2×C4×C13—41no—
460C2×C4×C13—41no—
461C2×C4×C13—41no—
462C2×C4×C13C22⋊Q814yes—
463C24×C4C22×C1311yescharacteristic
464C24×C4C22×C1311yescharacteristic
465C24×C4C22×C1311yescharacteristic
466C22×C4⋊C4C22×C1311yescharacteristic
467C22×C4⋊C4C22×C1311yescharacteristic
468C22×C4⋊C4C22×C1311yescharacteristic
469C22×C4⋊C4C22×C1311yescharacteristic
470C22×C4⋊C4C22×C1311yescharacteristic
471C22×C4⋊C4C22×C1311yescharacteristic
472C22×C4⋊C4C22×C1311yescharacteristic
473C22×C4⋊C4C22×C1311yescharacteristic
474C22×C22⋊C4C22×C1311yescharacteristic
475C22×C22⋊C4C22×C1311yescharacteristic
476C22×C22⋊C4C22×C1311yescharacteristic
477C22×C22⋊C4C22×C1311yescharacteristic
478#398—24no—
479#385—24no—
480#385—24no—
481#385—24no—
482#380—24no—
483C2×#95—24no—
484C2×#95C22×C1311yescharacteristic
485C2×#95C22×C1311yescharacteristic
486C2×#95C22×C1311yescharacteristic
487C2×#95C22×C1311yescharacteristic
488C2×#95C22×C1311yescharacteristic
489C2×#95C22×C1311yescharacteristic
490C2×#95C22×C1311yescharacteristic
491C2×#95C22×C1311yescharacteristic
492C2×#95C22×C1311yescharacteristic
493C2×#95C22×C1311yescharacteristic
494C2×#95C22×C1311yescharacteristic
495C2×#95C22×C1311yescharacteristic
496C2×#95C22×C1311yescharacteristic
497C2×#95C22×C1311yescharacteristic
498C2×#95C22×C1311yescharacteristic
499C2×#95C22×C1311yescharacteristic
500C2×#95C22×C1311yescharacteristic
501C2×#95C22×C1311yescharacteristic
502C2×#95C22×C1311yescharacteristic
503C2×#95C22×C1311yescharacteristic
504C22×C13—24no—
505C22×C13—24no—
506C22×C13—24no—
507C22×C13—24no—
508C22×C13—24no—
509C22×C13—24no—
510C22×C13—24no—
511C22×C13—24no—
512C22×C13—24no—
513C22×C13—24no—
514C22×C13—24no—
515C22×C13—24no—
516C22×C13—24no—
517C22×C13—24no—
518C22×C13#39818yescomplemented
519C22×C13C2×#12111yescharacteristic
520C22×C13C2×C22⋊Q811yescharacteristic
521C22×C13C2×C22⋊Q811yescharacteristic
522C22×C13C2×C22⋊Q811yescharacteristic
523C22×C13C2×#12311yescharacteristic
524C22×C13#52511yescharacteristic
525C22×C13#52511yescharacteristic
526C22×C13C2×#12511yescharacteristic
527C22×C13C2×#12511yescharacteristic
528C22×C13#52911yescharacteristic
529C22×C13#52911yescharacteristic
530C22×C13C2×C4⋊Q811yescharacteristic
531C22×C13#53311yescharacteristic
532C22×C13#53811yescharacteristic
533C22×C13#53811yescharacteristic
534C22×C13#53911yescharacteristic
535C22×C13#53911yescharacteristic
536C22×C13#54311yescharacteristic
537C22×C13#54411yescharacteristic
538C22×C13D4211yescharacteristic
539C22×C13D4211yescharacteristic
540C22×C13#54611yescharacteristic
541C22×C13#54611yescharacteristic
542C22×C13#54611yescharacteristic
543C22×C13#54611yescharacteristic
544C22×C13#54611yescharacteristic
545C22×C13#54711yescharacteristic
546C22×C13#54711yescharacteristic
547C22×C13D4×Q811yescharacteristic
548C22×C13#55111yescharacteristic
549C22×C13#55111yescharacteristic
550C22×C13#55211yescharacteristic
551C22×C13#55411yescharacteristic
552C22×C13#55411yescharacteristic
553C22×C13#55411yescharacteristic
554C4×C13—24no—
555C4×C13—42no—
556C4×C13—42no—
557C4×C13—42no—
558C4×C13—42no—
559C4×C13—42no—
560C4×C13—42no—
561C4×C13—42no—
562C4×C13—42no—
563C4×C13—42no—
564C4×C13—42no—
565C4×C13—42no—
566C4×C13—81no—
567C4×C13—81no—
568C25C23×C1311yescharacteristic
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—22no—
573C23×C4—22no—
574C23×C4—22no—
575C23×C4—22no—
576C23×C4—22no—
577C23×C4—22no—
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—22no—
582C23×C4—22no—
583C23×C4—41no—
584C23×C4—41no—
585C23×C4—41no—
586C23×C4—41no—
587C23×C4—41no—
588C23×C4—41no—
589C23×C4Q8×C1314yes—
590C23×C4C23×C1311yescharacteristic
591C23×C4C23×C1311yescharacteristic
592C23×C4C23×C1311yescharacteristic
593C23×C4C23×C1311yescharacteristic
594C23×C4C23×C1311yescharacteristic
595C23×C4C23×C1311yescharacteristic
596C23×C4C23×C1311yescharacteristic
597C23×C4C23×C1311yescharacteristic
598C23×C4C23×C1311yescharacteristic
599C23×C4C23×C1311yescharacteristic
600C23×C4C23×C1311yescharacteristic
601C23×C4C23×C1311yescharacteristic
602C23×C4C23×C1311yescharacteristic
603C23×C4C23×C1311yescharacteristic
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—22no—
617C2×C4⋊C4—22no—
618C2×C4⋊C4—22no—
619C2×C4⋊C4—22no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4—41no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4D4×C1314yes—
638C2×C22⋊C4D4×C1314yes—
639C2×C22⋊C4Q8×C1314yes—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—22no—
650#95—22no—
651#95—22no—
652#95—22no—
653#95—22no—
654#95—22no—
655#95—41no—
656#95—41no—
657#95—41no—
658#95—41no—
659#95D4×C1314yes—
660C2×C13—28no—
661C2×C13C2×#39811yescharacteristic
662C2×C13#241811yescharacteristic
663C2×C13#241911yescharacteristic
664C2×C13#242411yescharacteristic
665C2×C13#242511yescharacteristic
666C2×C13#243711yescharacteristic
667C2×C13#243811yescharacteristic
668C2×C13#244011yescharacteristic
669C2×C13#244911yescharacteristic
670C2×C13#245011yescharacteristic
671C2×C13#247311yescharacteristic
672C2×C13#250511yescharacteristic
673C2×C13#254911yescharacteristic
674C2×C13#264611yescharacteristic
675C2×C13#285111yescharacteristic
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24C2×D4×C1312yes—
685C24C2×D4×C1312yes—
686C24C2×Q8×C1312yes—
687C24C2×Q8×C1312yes—
688C24C13×#4112yes—
689C24C13×#4112yes—
690C24C13×#4112yes—
691C24C24×C1311yescharacteristic
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—28no—
697C22×C4—28no—
698C22×C4—28no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—28no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4C2×D4×C1312yes—
798C22×C4C2×D4×C1312yes—
799C22×C4C2×D4×C1312yes—
800C22×C4C2×D4×C1312yes—
801C22×C4C2×D4×C1312yes—
802C22×C4C2×D4×C1312yes—
803C22×C4C2×D4×C1312yes—
804C22×C4C2×Q8×C1312yes—
805C22×C4C2×Q8×C1312yes—
806C22×C4C2×Q8×C1312yes—
807C22×C4C2×Q8×C1312yes—
808C22×C4C13×#4112yes—
809C22×C4C13×#4112yes—
810C22×C4C13×#4112yes—
811C4⋊C4—44no—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4—44no—
815C4⋊C4—44no—
816C4⋊C4—44no—
817C4⋊C4—44no—
818C4⋊C4—44no—
819C22⋊C4—28no—
820C22⋊C4—28no—
821C22⋊C4—28no—
822C22⋊C4—44no—
823C13#1473611yescharacteristic, direct product factor, Sylow
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
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—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23C13×#12114yes—
853C23C13×C22⋊Q814yes—
854C23C13×C22⋊Q814yes—
855C23C13×#12314yes—
856C23C13×#12514yes—
857C23C13×#12514yes—
858C23C13×C4⋊Q814yes—
859C23C22×D4×C1311yescharacteristic
860C23C22×D4×C1311yescharacteristic
861C23C22×D4×C1311yescharacteristic
862C23C22×Q8×C1311yescharacteristic
863C23C22×Q8×C1311yescharacteristic
864C23C2×C13×#4111yescharacteristic
865C23C2×C13×#4111yescharacteristic
866C23C2×C13×#4111yescharacteristic
867C23C2×C13×#4111yescharacteristic
868C23C2×C13×#4111yescharacteristic
869C23C2×C13×#4111yescharacteristic
870C23C13×H(5,𝔽2)11yescharacteristic
871C23C13×H(5,𝔽2)11yescharacteristic
872C23C13×H(5,𝔽2)11yescharacteristic
873C23C13×2−1+411yescharacteristic
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
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—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—416no—
914C2×C4—416no—
915C2×C4—416no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4C13×C22⋊Q814yes—
975C22—24no—
976C22—24no—
977C22—24no—
978C22—24no—
979C22—24no—
980C22—24no—
981C22—24no—
982C22—24no—
983C22—24no—
984C22—24no—
985C22—24no—
986C22—24no—
987C22—24no—
988C22—24no—
989C22C13×#39818yescomplemented
990C22C2×C13×#12111yescharacteristic
991C22C2×C13×C22⋊Q811yescharacteristic
992C22C2×C13×C22⋊Q811yescharacteristic
993C22C2×C13×C22⋊Q811yescharacteristic
994C22C2×C13×#12311yescharacteristic
995C22C13×#52511yescharacteristic
996C22C13×#52511yescharacteristic
997C22C2×C13×#12511yescharacteristic
998C22C2×C13×#12511yescharacteristic
999C22C13×#52911yescharacteristic
1000C22C13×#52911yescharacteristic
1001C22C2×C13×C4⋊Q811yescharacteristic
1002C22C13×#53311yescharacteristic
1003C22C13×#53811yescharacteristic
1004C22C13×#53811yescharacteristic
1005C22C13×#53911yescharacteristic
1006C22C13×#53911yescharacteristic
1007C22C13×#54311yescharacteristic
1008C22C13×#54411yescharacteristic
1009C22D42×C1311yescharacteristic
1010C22D42×C1311yescharacteristic
1011C22C13×#54611yescharacteristic
1012C22C13×#54611yescharacteristic
1013C22C13×#54611yescharacteristic
1014C22C13×#54611yescharacteristic
1015C22C13×#54611yescharacteristic
1016C22C13×#54711yescharacteristic
1017C22C13×#54711yescharacteristic
1018C22D4×Q8×C1311yescharacteristic
1019C22C13×#55111yescharacteristic
1020C22C13×#55111yescharacteristic
1021C22C13×#55211yescharacteristic
1022C22C13×#55411yescharacteristic
1023C22C13×#55411yescharacteristic
1024C22C13×#55411yescharacteristic
1025C4—24no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—42no—
1030C4—42no—
1031C4—42no—
1032C4—42no—
1033C4—42no—
1034C4—42no—
1035C4—42no—
1036C4—42no—
1037C4—81no—
1038C4—81no—
1039C2—28no—
1040C2C2×C13×#39811yescharacteristic
1041C2C13×#241811yescharacteristic
1042C2C13×#241911yescharacteristic
1043C2C13×#242411yescharacteristic
1044C2C13×#242511yescharacteristic
1045C2C13×#243711yescharacteristic
1046C2C13×#243811yescharacteristic
1047C2C13×#244011yescharacteristic
1048C2C13×#244911yescharacteristic
1049C2C13×#245011yescharacteristic
1050C2C13×#247311yescharacteristic
1051C2C13×#250511yescharacteristic
1052C2C13×#254911yescharacteristic
1053C2C13×#264611yescharacteristic
1054C2C13×#285111yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC25×C13C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#398C2semidirect
7. C13×#1445C2semidirect
8. C13×#1444C2semidirect
9. C13×#1442C2semidirect
10. C13×#1442C2semidirect
11. C13×#1441C2semidirect
12. C13×#1441C2semidirect
13. C13×#1441C2semidirect
149. #14736C13direct (N × H)
297. C2×#398C2×C13semidirect
303. #1445C2×C13semidirect
304. #1444C2×C13semidirect
305. #1442C2×C13semidirect
306. #1442C2×C13semidirect
307. #1441C2×C13semidirect
308. #1441C2×C13semidirect
309. #1441C2×C13semidirect
518. C22×C13#398semidirect
823. C13#14736direct (N × H)
989. C22C13×#398semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#3982
C2×C13×#3852
C2×C13×#3802
C22×C13×#952
C13×#14452
C13×#14442
C13×#14422
C13×#14412
C13×C22⋊#952
#1473613